CE6451 - FLUID MECHANICS AND MACHINERY

R.M.K COLLEGE OF ENGINEERING
AND TECHNOLOGY
RSM NAGAR, PUDUVOYAL-601206
DEPARTMENT OF MECHANICAL ENGINEERING
CE6451 – FLUID MECHANICS & MACHINERY
III SEM MECHANICAL ENGINEERING
Regulation 2013
QUESTION BANK
PREPARED BY
C.BIBIN / R.ASHOK KUMAR / N.SADASIVAN

R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2017 – NOV 2017
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK
Prepared By BIBIN.C / ASHOK KUMAR.R / SADASIVAN . N (AP / Mech) 2
CE6451 FLUID MECHANICS AND MACHINERY L T P C
3 0 0 3
OBJECTIVES:
 The applications of the conservation laws to flow through pipes and hydraulic machines are
studied
 To understand the importance of dimensional analysis.
 To understand the importance of various types of flow in pumps and turbines.
UNIT – I FLUID PROPERTIES AND FLOW CHARACTERISTICS 8
Units and dimensions- Properties of fluids- mass density, specific weight, specific volume, specific
gravity, viscosity, compressibility, vapor pressure, surface tension and capillarity. Flow
characteristics – concept of control volume - application of continuity equation, energy equation and
momentum equation.
UNIT – II FLOW THROUGH CIRCULAR CONDUITS 8
Hydraulic and energy gradient - Laminar flow through circular conduits and circular annuli-Boundary
layer concepts – types of boundary layer thickness – Darcy Weisbach equation –friction factor-
Moody diagram- commercial pipes- minor losses – Flow through pipes in series and parallel.
UNIT – III DIMENSIONAL ANALYSIS 9
Need for dimensional analysis – methods of dimensional analysis – Similitude –types of similitude -
Dimensionless parameters- application of dimensionless parameters – Model analysis.
UNIT – IV PUMPS 10
Impact of jets – Euler’s equation - Theory of roto-dynamic machines – various efficiencies– velocity
components at entry and exit of the rotor- velocity triangles - Centrifugal pumps– working principle
- work done by the impeller - performance curves - Reciprocating pump- working principle – Rotary
pumps –classification.
UNIT – V TURBINES 10
Classification of turbines – heads and efficiencies – velocity triangles. Axial, radial and mixed flow
turbines. Pelton wheel, Francis turbine and Kaplan turbines- working principles - work done by water
on the runner – draft tube. Specific speed - unit quantities – performance curves for turbines –
governing of turbines. TOTAL: 45 PERIODS
OUTCOMES:
 Upon completion of this course, the students can able to apply mathematical knowledge to
predict the properties and characteristics of a fluid.
 Can critically analyse the performance of pumps and turbines.
TEXT BOOK:
 Modi P.N. and Seth, S.M. "Hydraulics and Fluid Mechanics", Standard Book House, New
Delhi 2004.
REFERENCES:
 Streeter, V. L. and Wylie E. B., "Fluid Mechanics", McGraw Hill Publishing Co. 2010
 Kumar K. L., "Engineering Fluid Mechanics", Eurasia Publishing House (p) Ltd., New Delhi
2004
 Robert W.Fox, Alan T. McDonald, Philip J.Pritchard, “Fluid Mechanics and Machinery”,
2011.
 Graebel. W.P, "Engineering Fluid Mechanics", Taylor & Francis, Indian Reprint, 2011

UNIT - I - FLUID PROPERTIES AND FLOW CHARACTERISTICS
Part - A
1.1) What is a fluid? How are fluids classified?
1.2) Define fluid. Give examples. [AU, Nov / Dec - 2010]
1.3) How fluids are classified? [AU, Nov / Dec - 2008, May / June - 2012]
1.4) Distinguish between solid and fluid. [AU, May / June - 2006]
1.5) Differentiate between solids and liquids. [AU, May / June - 2007]
1.6) Discuss the importance of ideal fluid. [AU, April / May - 2011]
1.7) Write the properties of ideal fluid [AU, Nov / Dec - 2016]
1.8) What is a real fluid? [AU, April / May - 2003]
1.9) Define Newtonian and Non – Newtonian fluids. [AU, Nov / Dec - 2008]
1.10) What are Non – Newtonian fluids? Give example. [AU, Nov / Dec - 2009]
1.11) Differentiate between Newtonian and Non – Newtonian fluids.
[AU, Nov / Dec - 2007]
1.12) What is the difference between an ideal and a real fluid?
1.13) Differentiate between liquids and gases.
1.14) Define Pascal’s law. [AU, Nov / Dec – 2005, 2008]
1.15) Define the term density.
1.16) Define mass density and weight density. [AU, Nov / Dec - 2007]
1.17) Distinguish between the mass density and weight density.
[AU, May / June - 2009]
1.18) Define the term specific volume and express its units. [AU, April / May - 2011]
1.19) Define specific weight.
1.20) Define specific weight and density. [AU, May / June - 2012]
1.21) Define density and specific gravity of a fluid. [AU, Nov / Dec - 2012]
1.22) Define specific gravity of fluid. [AU, Nov / Dec - 2016]
1.23) What is specific weight and specific gravity of a fluid? [AU, April / May - 2010]
1.24) What is specific gravity? How is it related to density? [AU, April / May - 2008]
1.25) What do you mean by the term viscosity?
1.26) What is viscosity? What is the cause of it in liquids and in gases?
[AU, Nov / Dec - 2005]
1.27) Define Viscosity and give its unit. [AU, Nov / Dec - 2003]

1.28) Define viscosity and what is the effect due to temperature on liquid and gases.
[AU, April / May - 2017]
1.29) Define Newton’s law of viscosity. [AU, Nov / Dec - 2012]
1.30) State the Newton's law of viscosity.
[AU, April / May, Nov / Dec - 2005, May / June - 2007]
1.31) Define Newton’s law of viscosity and write the relationship between shear stress
and velocity gradient? [AU, Nov / Dec - 2006]
1.32) What is viscosity and give its units? [AU, April / May - 2011]
1.33) Define coefficient of viscosity. [AU, April / May - 2005]
1.34) Define coefficient of volume of expansion. [AU, Nov / Dec - 2012]
1.35) Define relative or specific viscosity. [AU, May / June - 2013]
1.36) Define kinematic viscosity. [AU, Nov / Dec - 2009]
1.37) Define kinematic and dynamic viscosity. [AU, May / June - 2006]
1.38) What is the importance of kinematic viscosity? [AU, Nov / Dec - 2014]
1.39) Mention the significance of kinematic viscosity. [AU, Nov / Dec - 2011]
1.40) What is dynamic viscosity? What are its units?
1.41) Define dynamic viscosity. [AU, Nov / Dec - 2008, May / June - 2012]
1.42) Define the terms kinematic viscosity and give its dimensions.
[AU, May / June - 2009]
1.43) What is kinematic viscosity? State its units? [AU, May / June - 2014]
1.44) Differentiate between kinematic viscosity of liquids and gases with respect to
pressure. [AU, Nov / Dec - 2013]
1.45) Write the units and dimensions for kinematic and dynamic viscosity.
[AU, Nov / Dec - 2005]
1.46) What are the units and dimensions for kinematic and dynamic viscosity of a fluid?
[AU, Nov / Dec - 2006, 2012]
1.47) Differentiate between kinematic and dynamic viscosity.
[AU, May / June - 2007, Nov / Dec – 2008, 2011]
1.48) How does the dynamic viscosity of liquids and gases vary with temperature?
[AU, Nov / Dec - 2007, April / May - 2008]
1.49) What are the variations of viscosity with temperature for fluids?
[AU, Nov / Dec - 2009]

1.50) Explain the variation of viscosity with temperature. [AU, Nov / Dec - 2015]
1.51) What is the effect of temperature on viscosity of water and that of air?
1.52) Write down the effect of temperature of viscosity of liquids and gases.
[AU, Nov / Dec - 2016]
1.53) Brief on the effect of temperature on viscosity in gases. [AU, May / June - 2016]
1.54) Why is it necessary in winter to use lighter oil for automobiles than in summer?
To what property does the term lighter refer? [AU, Nov / Dec - 2010]
1.55) How does Redwood viscometer work? [AU, May / June - 2016]
1.56) Define the term pressure. What are its units? [AU, Nov / Dec - 2005]
1.57) Give the dimensions of the following physical quantities
a) Pressure b) surface tension
c) Dynamic viscosity d) kinematic viscosity
1.58) Define eddy viscosity. How it differs from molecular viscosity?
[AU, Nov / Dec - 2010]
1.59) Define surface tension. [AU, May / June - 2006]
1.60) Define surface tension and expression its unit. [AU, April / May - 2011]
1.61) Define capillarity. [AU, Nov / Dec - 2005, May / June - 2006]
1.62) What is the difference between cohesion and adhesion?
1.63) Define the term vapour pressure.
1.64) What is meant by vapour pressure of a fluid? [AU, April / May - 2010]
1.65) Brief on the significance of vapour pressure. [AU, Nov / Dec - 2014]
1.66) What are the types of pressure measuring devices?
1.67) What do you understand by terms:
i) Isothermal process ii) adiabatic process
1.68) What do you mean by capillarity? [AU, Nov / Dec - 2009]
1.69) Explain the phenomenon of capillarity.
1.70) Define capillarity and surface tension. [AU, Nov / Dec - 2015]
1.71) Define surface tension.
1.72) What is compressibility of fluid?

1.73) Define compressibility of the fluid.
[AU, Nov / Dec – 2008, May / June - 2009]
1.74) Define compressibility and viscosity of a fluid. [AU, April / May - 2005]
1.75) Define coefficient of compressibility. What is its value for ideal gases?
[AU, Nov / Dec - 2010]
1.76) List the components of total head in a steady, in compressible irrotational flow.
[AU, Nov / Dec - 2009]
1.77) Define the bulk modulus of fluid. [AU, Nov / Dec - 2008]
1.78) Define - compressibility and bulk modulus. [AU, Nov / Dec – 2011]
1.79) Write short notes on thyxotropic fluid.
1.80) What is Thyxotrphic fluid? [AU, Nov / Dec - 2003]
1.81) One poise’s equal to __________Pa.s.
1.82) State the empirical pressure density relation for a liquid.
[AU, Nov / Dec - 2014]
1.83) Give the types of fluid flow.
1.84) Define steady flow and give an example.
1.85) Define unsteady flow and give an example.
1.86) Differentiate between the steady and unsteady flow. [AU, May / June - 2006]
1.87) When is the flow regarded as unsteady? Give an example for unsteady flow.
1.88) Define uniform flow and give an example.
1.89) Define non uniform flow and give an example.
1.90) State the conditions under which uniform and non-uniform flows are produced.
[AU, May / June - 2016]
1.91) Differentiate between steady flow and uniform flow. [AU, Nov / Dec - 2007]
1.92) Define laminar and turbulent flow and give an example.
1.93) Differentiate between laminar and turbulent flow.
[AU, Nov / Dec – 2005, 2008, April / May - 2015]
1.94) Distinguish between Laminar and Turbulent flow. [AU, April / May - 2010]
1.95) State the criteria for laminar flow. [AU, Nov / Dec - 2008]
1.96) State the characteristics of laminar flow. [AU, April / May - 2010]
1.97) What are the characteristics of laminar flow? [AU, May / June - 2014]

1.98) Mention the general characteristics of laminar flow.
[AU, May / June - 2013 Nov / Dec - 2016]
1.99) Define - Incompressible fluid. [AU, Nov / Dec - 2014]
1.100) Define compressible and incompressible flow and give an example.
1.101) Define rotational and irrotational flow and give an example.
1.102) Distinguish between rotation and circularity in fluid flow.
1.103) Define stream line. What do stream lines indicate? [AU, Nov / Dec - 2007]
1.104) Define streamline and path line in fluid flow. [AU, Nov / Dec - 2005]
1.105) What is stream line and path line in fluid flow? [AU, April / May - 2010]
1.106) What is a streamline? [AU, Nov / Dec - 2010]
1.107) Define streak line. [AU, April / May - 2008]
1.108) Define stream function. [AU, April / May – 2010, May / June - 2012]
1.109) Define control volume. [AU, April / May - 2015]
1.110) What is the use of control volume? [AU, April / May - 2015]
1.111) What is meant by continuum? [AU, Nov / Dec - 2008, April / May - 2017]
1.112) Define continuity equation.
1.113) Write down the equation of continuity. [AU, Nov / Dec –2008, 2009, 2012]
1.114) State the continuity equation in one dimensional form?
[AU, May / June - 2012]
1.115) State the general continuity equation for a 3 - D incompressible fluid flow.
[AU, May / June - 2007, Nov / Dec - 2012]
1.116) State the continuity equation for the case of a general 3-D flow.
[AU, Nov / Dec - 2007]
1.117) State the equation of continuity in 3 dimensional incompressible flow.
[AU, Nov / Dec - 2005]
1.118) State the assumptions made in deriving continuity equation.
[AU, Nov / Dec - 2011]
1.119) Define Euler's equation of motion.
1.120) Write the Euler's equation. [AU, April / May - 2011]
1.121) What is Euler’s equation of motion? [AU, Nov / Dec - 2008]
1.122) Define Bernoulli's equation.

1.123) Write the Bernoulli’s equation in terms of head. Explain each term.
[AU, Nov / Dec - 2007]
1.124) What are the basic assumptions made is deriving Bernoulli’s theorem?
[AU, Nov / Dec – 2005, 2012]
1.125) List the assumptions which are made while deriving Bernoulli’s equation.
[AU, May / June - 2012]
1.126) State at least two assumptions of Bernoulli’s equation.
[AU, May / June - 2009]
1.127) What are the three major assumptions made in the derivation of the Bernoulli’s
equation? [AU, April / May - 2008]
1.128) State the assumptions used in the derivation of the Bernoulli's equation.
[AU, Nov / Dec - 2014]
1.129) State Bernoulli’s theorem as applicable to fluid flow. [AU, Nov / Dec - 2003]
1.130) Give the assumptions made in deriving Bernoulli’s equation.
[AU, Nov / Dec - 2012]
1.131) What are the applications of Bernoulli’s theorem? [AU, April / May - 2010]
1.132) Give the application of Bernoulli’s equation.
1.133) List the types of flow measuring devices fitted in a pipe flow, which uses the
principle of Bernoulli’s equation. [AU, May / June - 2012]
1.134) Mention the uses of manometer. [AU, Nov / Dec - 2009]
1.135) State the use of venturimeter. [AU, May / June - 2006]
1.136) Define momentum principle.
1.137) Define impulse momentum equation.
1.138) Write the impulse momentum equation. [AU, May / June - 2007]
1.139) What is an impulse – momentum equation? [AU, May / June - 2016]
1.140) What do you understand by impulse momentum equation?
[AU, May / June - 2013]
1.141) State the momentum equation. When can it applied. [AU, May / June - 2009]
1.142) State the usefulness of momentum equation as applicable to fluid flow
phenomenon. [AU, May / June – 2007, Nov / Dec - 2012]
1.143) Define discharge (or) rate of flow.
1.144) Discuss the momentum flux. [AU, April / May - 2011]

1.145) Find the continuity equation, when the fluid is incompressible and densities are
equal.
1.146) What is the moment of momentum equation? [AU, May / June - 2014]
1.147) Give the dimensions of the following: (a) Torque (b) Momentum.
[AU, Nov / Dec - 2015]
1.148) Explain classification of fluids based on viscosity.
1.149) State and prove Euler's equation of motion. Obtain Bernoulli's equation from
Euler's equation.
1.150) State and prove Bernoulli's equation. What are the limitations of the Bernoulli's
equation?
1.151) State the momentum equation. How will you apply momentum equation for
determining the force exerted by a flowing liquid on a pipe bend?
1.152) Give the equation of continuity. Obtain an expression for continuity equation for
a three - dimensional flow.
1.153) Calculate the density of one litre petrol of specific gravity 0.7?
1.154) If a liquid has a viscosity of 0.051 poise and kinematic viscosity of 0.14 stokes,
calculate its specific gravity. [AU, April / May - 2015]
1.155) Calculate the mass density and specific volume of one litre of a liquid which
weighs 7 N. [AU, April / May - 2015]
1.156) Calculate the specific weight and specific gravity of 1 litre of a liquid with a
density of 713.5 kg/m3
and which weighs 7N. [AU, Nov / Dec - 2015]
1.157) A soap bubble is formed when the inside pressure is 5 N/m2
above the
atmospheric pressure. If surface tension in the soap bubble is 0.0125 N/m, find the
diameter of the bubble formed. [AU, April / May - 2010]
1.158) Determine the gauge pressure inside a soap bubble of diameter 0.25 cm and 6
cm at 22°C. [AU, Nov / Dec - 2014]
1.159) The converging pipe with inlet and outlet diameters of 200 mm and 150 mm
carries the oil whose specific gravity is 0.8. The velocity of oil at the entry is 2.5
m/s, find the velocity at the exit of the pipe and oil flow rate in kg/sec.

1.160) Find the height through which the water rises by the capillary action in a 2mm
bore if the surface tension at the prevailing temperature is0.075 g/cm.
1.161) Find the height of a mountain where the atmospheric pressure is 730mm of Hg
at normal conditions. [AU, Nov / Dec - 2009]
1.162) Suppose the small air bubbles in a glass of tap water may be on the order of50 μ
m in diameter. What is the pressure inside these bubbles? [AU, Nov / Dec - 2010]
1.163) An open tank contains water up to depth of 2.85m and above it an oil of specific
gravity 0.92 for the depth of 2.1m. Calculate the pressures at the interface of two
liquids and at the bottom of the tank. [AU, April / May - 2011]
1.164) A quantity of helium (molecular weight = 4) when confined to a volume of 100
litres at -20°C weight 25N. Find the pressure exerted by the gas.
1.165) Two horizontal plates are placed 12.5mm apart, the space between them is being
filled with oil of viscosity 14 poise. Calculate the shear stress in the oil if the upper
plate is moved with the velocity of 2.5m/s. Define specific weight.
[AU, May / June - 2012]
1.166) Calculate the height of capillary rise for water in a glass tube of diameter 1mm.
[AU, May / June - 2012, April / May - 2017]
1.167) Calculate the capillarity rise in glass tube of 2.5mm diameter when immersed
vertically in (a) water and (b) mercury. Take the surface tension σ = 0.0725 N/m for
water and σ = 0.52 N/m for mercury in contact with air. The specific gravity for
mercury is given as 13.6 and angle of contact = 130° [AU, Nov / Dec - 2016]
PART - B
1.168) What are the various classification of fluids? Discuss [AU, Nov / Dec - 2012]
1.169) State and prove Pascal's law. [AU, May / June, Nov / Dec - 2007]
1.170) What is Hydrostatic law? Derive an expression to show the same.
[AU, Nov / Dec - 2009]
1.171) Explain the properties of hydraulic fluid. [AU, Nov / Dec - 2009]
1.172) Discuss the equation of continuity. Obtain an expression for continuity equation
in three dimensional forms. [AU, April / May - 2011]

1.173) Explain in detail the Newton's law of viscosity. Briefly classify the fluids based
on the density and viscosity. Give the limitations of applicability of Newton's law of
viscosity. [AU, April / May - 2011]
1.174) Classify the fluids according to the nature of variation of viscosity. Give
examples [AU, April / May - 2015]
1.175) State the effect of temperature and pressure on viscosity.
[AU, May / June - 2009]
1.176) Explain the term specific gravity, density, compressibility and vapour pressure.
[AU, May / June - 2009]
1.177) Explain the terms Specific weight, Density, Absolute pressure and Gauge
pressure. [AU, April / May - 2011]
1.178) Define Surface tension and also compressibility of a fluid?
[AU, Nov / Dec - 2006]
1.179) Explain the practical significance of the following liquid properties: surface
tension, capillarity and vapour pressure. [AU, April / May - 2015]
1.180) Explain the phenomenon surface tension and capillarity.
1.181) Derive an expression for the capillary rise of a liquid having surface tension σ
and contact angle θ between two vertical parallel plates at a distance W apart. If the
plates are of glass, what will be the capillary rise of water? Assume σ = 0.773N / m,
θ= 0° Take W=l mm. [AU, May / June - 2014]
1.182) What is compressibility of fluids? Give the relationship between compressibility
and bulk modulus [AU, Nov / Dec - 2009]
1.183) Prove that the relationship between surface tension and pressure inside the
droplet of liquid in excess of outside pressure is given by P = 4σ/d.
[AU, April / May –2010, 2011, Nov / Dec - 2008]
1.184) Explain the following
 Capillarity
 Surface tension
 Compressibility
 Kinematic viscosity [AU, May / June - 2012]

1.185) Derive the energy equation and state the assumptions made while deriving the
equation. [AU, Nov / Dec - 2010]
1.186) Derive Euler's equation of motion. [AU, May / June - 2014]
1.187) Derive from the first principles, the Euler’s equation of motion for a steady flow
along a stream line. Hence derive Bernoulli’ equation. State the various assumptions
involved in the above derivation. [AU, May / June - 2009]
1.188) Derive from basic principle the Euler’s equation of motion in 2D flow in X-Y
coordinate system and reduce the equation to get Bernoulli’s equation for
unidirectional stream lined flow. [AU, April / May - 2005]
1.189) State Euler’s equation of motion, in the differential form. Derive Bernoulli’s
equation from the above for the cases of an ideal fluid flow.
1.190) With basic assumptions-derive the Bernoulli's Equation from the Euler's
Equation. [AU, Nov / Dec - 2015]
1.191) State the law of conservation of man and derive the equation of continuity in
Cartesian coordinates for an incompressible fluid. Would it alter if the flow were
unsteady, highly viscous and compressible? [AU, April / May - 2011]
1.192) Derive the equation of continuity for one dimensional flow.
1.193) Derive the continuity equation for 3 dimensional flow in Cartesian coordinates.
[AU, May / June - 2006]
1.194) Derive the general form of continuity equation in Cartesian coordinates.
[AU, Nov / Dec - 2012]
1.195) Derive the continuity equation of differential form. Discuss weathers equation is
valid for a steady flow or unsteady flow, viscous or in viscid flow, compressible or
incompressible flow. [AU, April / May - 2003]
1.196) Derive continuity equation from basic principles. [AU, Nov / Dec - 2009]
1.197) Derive Bernoulli’s equation with the assumptions.
1.198) State Bernoulli’s theorem for steady flow of an in compressible fluid.
[AU, Nov / Dec – 2004, 2005, April / May – 2010, May / June - 2013]

1.199) State Bernoulli’s theorem for steady flow of an in compressible fluid. Derive an
expression for Bernoulli equation and state the assumptions made.
[AU, May / June - 2009]
1.200) State the assumptions in the derivation of Bernoulli’s equation.
[AU, May / June, Nov / Dec - 2007]
1.201) Derive an expression for Bernoulli’s equation for a fluid flow.
1.202) Derive Bernoulli’s equation from the first principles? State the assumptions
made while deriving Bernoulli’s equation. [AU, May / June - 2012]
1.203) Derive from basic principle the Euler’s equation of motion in Cartesian co –
ordinates system and deduce the equation to Bernoulli’s theorem steady irrotational
flow. [AU, April / May - 2004]
1.204) Derive the expression of Bernoulli’s equation from the Euler’s equation and state
the assumptions made for such a derivation? [AU, April / May - 2017]
1.205) Derive the Euler’s equation of motion and deduce the expression to Bernoulli’s
equation. [AU, Nov / Dec - 2012]
1.206) Develop the Euler equation of motion and then derive the one dimensional form
of Bernoulli’s equation. [AU, Nov / Dec - 2011]
1.207) Derive the Reynold’s Transport theorem [AU, Nov / Dec - 2016]
1.208) Show that for a perfect gas the bulk modulus of elasticity equals its pressure for
 An isothermal process
 γ times the pressure for an isentropic process
1.209) State and derive impulse momentum equation. [AU, April / May - 2005]
1.210) Derive momentum equation for a steady flow. [AU, May / June - 2012]
1.211) Derive the linear momentum equation using the control volume approach and
determine the force exerted by the fluid flowing through a pipe bend.
[AU, Nov / Dec - 2011]
1.212) With a neat sketch, explain briefly an orifice meter and obtain an expression for
the discharge through it. [AU, Nov / Dec - 2012]
1.213) Draw the sectional view of Pitot’s tube and write its concept to measure velocity
of fluid flow? [AU, April / May - 2005]

PROBLEMS
1.214) A soap bubble is 60mm in diameter. If the surface tension of the soap film is
0.012 N/m. Find the excess pressure inside the bubble and also derive the expression
used in this problem. [AU, Nov / Dec - 2009]
1.215) A spherical water droplet of 5 mm in diameter splits up in the air into 16 smaller
droplets of equal size. Find the work involved in splitting up the droplet. The surface
tension of water may be assumed as 0.072 N/m [AU, Nov / Dec - 2012]
1.216) A liquid weighs 7.25N per litre. Calculate the specific weight, density and
specific gravity of the liquid.
1.217) One litre of crude oil weighs 9.6N. Calculate its specific weight, density and
specific gravity. [AU, Nov / Dec - 2008]
1.218) Determine the viscosity of a liquid having a kinematic viscosity 6 stokes and
specific gravity 1.9. [AU, Nov / Dec - 2008, April / May - 2010]
1.219) Determine the mass density; specific volume and specific weight of liquid whose
specific gravity 0.85. [AU, April / May - 2010]
1.220) If the volume of a balloon is to reach a sphere of 8m diameter at an altitude where
the pressure is 0.2 bar and temperature -40°C. Determine the mass hydrogen to be
charged into the balloon and volume and diameter at ground level. Where the
pressure is 1bar and temperature is 25°C. [AU, Nov / Dec - 2009]
1.221) A liquid has a specific gravity of 0.72. Find its density and specific weight. Find
also the weight per litre of the liquid.
1.222) A liquid has a specific gravity of 0.72. Find its density and specific weight. Find
also the weight per litre of the liquid. If the above liquid is used as lubrication
between the shaft and the sleeve of length 100mm. Determine the power lost in the
bearing, where the diameter of the shaft is 0.5m and the thickness of the liquid film
between the shaft and the sleeve is 1mm. Take the viscosity of the fluid as 0.5N-s/m2
and the speed of the shaft rotates at 200 rpm. [AU, April / May - 2017]
1.223) A 1.9mm diameter tube is inserted into an unknown liquid whose density is
960kg/m3
, and it is observed that the liquid raise 5mm in the tube, making a contact
angle of 15°. Determine the surface tension of the liquid. [AU, April / May - 2008]

1.224) A hollow cylinder of 150 mm OD with its weight equal to the buoyant forces is
to be kept floating vertically in a liquid with a surface tension of 0.45 N/m2
. The
contact angle is 60º. Determine the additional force required due to surface tension.
[AU, Nov / Dec - 2014]
1.225) A 0.3m diameter pipe carrying oil at 1.5m/s velocity suddenly expands to 0.6m
diameter pipe. Determine the discharge and velocity in 0.6m diameter pipe.
[AU, May / June - 2012]
1.226) Explain surface tension. Water at 20°C (σ = 0.0.73N/m, γ = 9.8kN/m3
and angle
of contact = 0°) rises through a tube due to capillary action. Find the tube diameter
requires, if the capillary rise is less than 1mm. [AU, Nov / Dec - 2010]
1.227) A Newtonian fluid is filled in the clearance between a shaft and a concentric
sleeve. The sleeve attains a speed of 50cm/s, when a force of 40N is applied to the
sleeve parallel to the shaft. Determine the speed of the shaft, if a force of 200N is
applied. [AU, Nov / Dec - 2006]
1.228) An oil film thickness 10mm is used for lubrication between the square parallel
plate of size 0.9 m * 0.9 m, in which the upper plate moves at 2m/s requires a force
of 100 N to maintain this speed. Determine the
 Dynamic viscosity of the oil in poise and
 Kinematic viscosity of the oil in stokes.
The specific gravity of the oil is 0.95. [AU, Nov / Dec – 2003]
1.229) The space between two square flat parallel plates is filled with oil. Each side of
the plate is 60cm. The thickness of the oil film is 12.5mm. The upper plate, which
moves at 2.5 meter per sec, requires a force of 98.1N to maintain the speed.
Determine the
 Dynamic viscosity of the oil in poise and
 Kinematic viscosity of the oil in stokes.
The specific gravity of the oil is 0.95. [AU, Nov / Dec - 2012]
1.230) What is the bulk modulus of elasticity of a liquid which is compressed in a
cylinder from a volume of 0.0125m3
at 80N/cm2
pressure to a volume of 0.0124m3
at pressure 150N/cm2
[AU, Nov / Dec - 2004]

1.231) Determine the bulk modulus of elasticity of elasticity of a liquid, if the pressure
of the liquid is increased from 7MN/m2
to 13MN/m2
, the volume of liquid decreases
by 0.15%. [AU, May / June - 2009]
1.232) The measuring instruments fitted inside an airplane indicate the pressure 1.032
*105
Pa, temperature T0 = 288 K and density ρ0 = 1.285 kg/m3
at takeoff. If a standard
temperature lapse rate of 0.0065° K/m is assumed, at what elevation is the plane
when a pressure of 0.53*105
recorded? Neglect the variations of acceleration due
gravity with the altitude and take airport elevation as 600m.
1.233) A person must breathe a constant mass rate of air to maintain his metabolic
process. If he inhales 20 times per minute at the airport level of 600m, what would
you except his breathing rate at the calculated altitude of the plane?
[AU, May / June - 2009]
1.234) Two points (1) and (2) which are at the same level in the body of water in a
whirlpool are at radial distances of 1.2m and 0.6m respectively from the axis of
rotation. The pressure and then velocity of water at point (1) and 15KPa (gauge) and
2 m/s respectively. What are the pressure and velocity at point (2)? What is the
difference in water surface elevations above points (1) and (2)? What are the radial
distances of a point on the water surface which is at same level (1) and (2)?
1.235) The space between two square parallel plates is filled with oil. Each side of the
plate is 75 cm. The thickness of oil film is 10 mm. The upper plate which moves at
3 m/s requires a force of 100 N to maintain the speed. Determine the
 Dynamic viscosity of the oil
 Kinematic viscosity of the oil, if the specific gravity of the oil is 0.9.
1.236) A rectangular plate of size 25cm* 50cm and weighing at 245.3 N slides down at
30° inclined surface with uniform velocity of 2m/s. If the uniform 2mm gap between
the plates is inclined surface filled with oil. Determine the viscosity of the oil.
[AU, April / May – 2004, Nov / Dec - 2012]
1.237) Calculate the dynamic viscosity of oil which is used for lubrication between a
square plate of size 0.8m x 0.8m and an inclined plane with angle of inclination 30°.
The weight of the square plate is 330 N and it slide down the inclined plane with a

uniform velocity of 0.3 m/s. The thickness of the oil film is 1.5 mm.
1.238) A space between two parallel plates 5mm apart, is filled with crude oil of specific
gravity 0.9. A force of 2N is require to drag the upper plate at a constant velocity of
0.8m/s. the lower plate is stationary. The area of upper plate is 0.09m2
. Determine
the dynamic viscosity in poise and kinematic viscosity of oil in strokes.
[AU, May / June - 2009]
1.239) The space between two large flat and parallel walls 25mm apart is filled with
liquid of absolute viscosity 0.7 Pa.sec. Within this space a thin flat plate 250mm *
250mm is towed at a velocity of 150mm/s at a distance of 6mm from one wall, the
plate and its movement being parallel to the walls. Assuming linear variations of
velocity between the plates and the walls, determine the force exerted by the liquid
on the plate. [AU, May / June - 2012]
1.240) A jet issuing at a velocity of 25 m/s is directed at 35° to the horizontal. Calculate
the height cleared by the jet at 28 m from the discharge location? Also determine the
maximum height the jet will clear and the corresponding horizontal location.
[AU, Nov / Dec - 2011]
1.241) Determine the velocity of a jet directed at 35º to the horizontal to clear 8 m height
at a distance of 22 m. Also determine the maximum height this jet will clear and the
total horizontal travel. What will be the horizontal distance at which the jet will be
again at 8 m height? [AU, Nov / Dec - 2014]
1.242) A flat plate of area 0.125m2
is pulled at 0.25 m/sec with respect to another
parallel plate 1mm distant from it, the space between the plates containing water of
viscosity 0.001Ns/ m2
. Find the force necessary to maintain this velocity. Find also
the power required.
1.243) The velocity distribution for flow over a plate is given by u = 2y – y2
where u is
the velocity in m/sec at a distance y meters above the plate. Determine the velocity
gradient and shear stress at the boundary and 0.15m from it. Dynamic viscosity of
the fluid is 0.9Ns/m2
1.244) The velocity distribution over a plate is given by u = (3/4) * y – y2
where u is
velocity in m/s and at depth y in m above the plate. Determine the shear stress at a

distance of 0.3m from the top of plate. Assume dynamic viscosity of the fluid is taken
as 0.95 Ns/m2
1.245) The velocity distribution over a plate is given by a relation,
𝑢 = 𝑦 (
2
3
− 𝑦 )
Where y is the vertical distance above the plate in meters. Assuming a viscosity of
0.9Pa.s, find the shear stress at y = 0 and y = 0.15m. [AU, Nov / Dec - 2012]
1.246) The velocity distribution for flow over a plate is given by 𝑢 =
2
3
𝑦 − 𝑦2
where
u is the point velocity in m/sec at a distance y meters above the plate. Determine
shear stress at y = 0 and y = 15cm from it. Assume dynamic viscosity of the fluid is
8.63 poise. [AU, Nov / Dec - 2016]
1.247) If the velocity distribution of a fluid over a plate is given by 𝑢 = 𝑎𝑦2
+ 𝑏𝑦 + 𝑐
with the vertex 0.2m from the plate, where the velocity is 1.2 m/s. calculate the
velocity gradients and shear stresses at a distance of 0m, 0.1m and 0.2m from the
plate, if the viscosity of the fluid is 0.85Ns/m2
. [AU, April / May - 2015]
1.248) Lateral stability of a long shaft 150 mm in diameter is obtained by means of a
250 mm stationary bearing having an internal diameter of 150.25 mm. If the space
between bearing and shaft is filled with a lubricant having a viscosity 0.245 N s/m2
,
what power will be required to overcome the viscous resistance when the shaft is
rotated at a constant rate of 180 rpm? [AU, Nov / Dec - 2010]
1.249) A hydraulic lift consist of a ram having diameter of 35cm, which slides in a
35.015cm diameter cylinder. The annular space between the ram and the cylinder is
filled with an oil of kinematic viscosity of 280 centistokes and a specific gravity of
0.9. Find the viscous resistance experienced by the ram travelling at a rate of 15m
per minute with 3m of the ram engaged in the cylinder. [AU, April / May - 2017]
1.250) Find the kinematic viscosity of water whose specific gravity is 0.95 and viscosity
is0.0011Ns/m2
.
1.251) The dynamic viscosity of oil, used for lubrication between a shaft and sleeve
is6poise. The shaft is of diameter 0.4m and rotates at 190 rpm. Calculate the power
lost in the bearing for a sleeve length of 90mm. The thickness of the oil film is
1.5mm. [AU, Nov / Dec - 2007, 2016, May / June - 2012]

1.252) A 200 mm diameter shaft slides through a sleeve, 200.5 mm in diameter and 400
mm long, at a velocity of 30 cm/s. The viscosity of the oil filling the annular space
is m = 0.1125 NS/ m2
. Find resistance to the motion. [A.U. Nov / Dec - 2008]
1.253) A 0.5m shaft rotates in a sleeve under lubrication with viscosity 5 Poise at
200rpm. Calculate the power lost for a length of 100mm if the thickness of the oil is
1mm. [AU, Nov / Dec - 2009]
1.254) A 15 cm diameter vertical cylinder rotates concentrically inside another cylinder
of diameter 15.10 cm. Both cylinders are 25 cm high. The space between the
cylinders is filled with a liquid whose viscosity is unknown. If a torque of 12.0 Nm
is required to rotate the inner cylinder at 100 rpm, determine the viscosity of the
fluid. [AU, May / June - 2013]
1.255) A conical bearing of outer radius 0.5 m and inner radius 0.3 m and height 0.3 m
runs on a conical support with a uniform clearance between surfaces. Oil with
viscosity 33 centi. Poise is used. The support is rotated at 450 rpm. Determine the
clearance if the power required was 1400 W. [AU, May / June - 2016]
1.256) Oil flows through a pipe 150mm in diameter and 650mm in length with a
velocity of 0.5m/s. If the kinematic viscosity of oil is 18.7 * 10-4
m2
/s, find the power
lost in overcoming friction. Take the specific gravity of oil as 0.9.
1.257) A horizontal shaft of diameter 5cm rotates at a speed of 1200rpm, inside a sleeve
of length l0cm. The clearance between the shaft and the sleeve is 1mm. If it is
lubricated with an oil of dynamic viscosity 3.5 poise, find the HP lost in the bearing.
[AU, Nov / Dec - 2015]
1.258) A400 mm diameter shaft is rotating at 200 r.p.m. in a bearing of length 120 mm.
If the thickness of film is 1.5 mm and the dynamic viscosity of the oil is 0.7 N.s/m2
,
determine (i) Torque required to overcome friction in bearing (ii) Power utilized to
overcoming viscous friction. Assume linear velocity profile.
[AU, May / June - 2014]
1.259) The viscosity of a fluid is to be measured by a viscometer constructed of two
80cm long concentric cylinders. The outer diameter of the inner cylinder is 16 cm,
and the gap between the two cylinders is 0.12 cm. The inner cylinder is rotated at

210 rpm, and the torque is measured to be 0.8 N m. Determine the viscosity of the
fluid. [AU, Nov / Dec - 2014]
1.260) Calculate the gauge pressure and absolute pressure within (i) a droplet of water
0.4cm in diameter (ii) a jet of water 0.4cm in diameter. Assume the surface tension
of water as 0.03N/m and the atmospheric pressure as 101.3kN/m2
.
1.261) What do you mean by surface tension? If the pressure difference between the
inside and outside of air bubble of diameter, 0.01 mm is 29.2kPa, what will be the
surface tension at air water interface? Derive an expression for the surface tension in
the air bubble and from it, deduce the result for the given conditions.
[AU, Nov / Dec - 2005]
1.262) Determine the viscous drag torque and power absorbed on one surface of a
collar bearing of 0.2 m ID and 0.3 m OD with an oil film thickness of 1 mm and a
viscosity of 30 centi poise if it rotates at 500 rpm. [AU, Nov / Dec - 2014]
1.263) A 1.9-mm - diameter tube is inserted into an unknown liquid whose density is
960 kg/ m3
, and it is observed that the liquid rises 5 mm in the tube, making a contact
angle of 15°. Determine the surface tension of the liquid.
1.264) At the depth of 2km in ocean the pressure is 82401kN/m2
. Assume the specific
weigth at the surface as 10055 N/m3
and the average bulk modulus of elasticity is
2.354 * 109
N/m2
for the pressure range. Determine the change in specific volume
between the surface and 2km depth and also determine the specific weight at the
depth? [AU, April / May – 2004, Nov / Dec - 2012]
1.265) At the depth of 8km from the surface of the ocean, the pressure is stated to be
82MN/m2
. Determine the mass density, weight density and specific volume of water
at this depth. Take density at the surface ρ = 1025kg/m3
and bulk modulus K =
2350MPa for indicated pressure range. [AU, May / June - 2009]
1.266) Eight kilometers below the surface of ocean pressure is 81.75MPa. Determine
the density of sea water at this depth if the density at the surface is 1025 kg/m3
and
the average bulk modulus of elasticity is 2.34GPa. [AU, May / June - 2012]

1.267) A cylinder of radius 0.65 m filled partially with a fluid and axially rotated at 18
rad/s is empty up to 0.3 m radius. The pressure at the extreme edge at the bottom was
0.3 bar gauge. Determine the density of the fluid. [AU, Nov / Dec - 2014]
1.268) A liquid is compressed in a cylinder having a volume of 0.012 m3
at a pressure
of 690 N/cm2
. What should be the new pressure in order to make its volume 0.0119
m3? Assume bulk modulus of elasticity (K) for the liquid = 6.9 x 104
N/cm2
.
[AU, May / June - 2013]
1.269) Calculate the capillary rise in glass tube of 3 mm diameter when immersed in
mercury; take the surface tension and the angle of contact of mercury as 0.52 N/m
and 130° respectively. Also determine the minimum size of the glass tube, if it is
immersed in water, given that the surface tension of water is 0.0725 N/m and
capillary rise in the tube is not to exceed 0.5mm. [AU, Nov / Dec – 2003, 2016]
1.270) The capillary rise in a glass tube is not to exceed 0.2mm of water. Determine its
minimum size, given that the surface tension for water in contact with air =
0.0725N/m. [AU, Nov / Dec - 2007, May / June - 2012]
1.271) Calculate the capillary effect in millimeters in a glass tube of 4mm diameter
when immersed in(i) water and (ii) mercury. The temperature of the liquid is 20°C
and the values of surface tension of water and mercury at 20°C in contact with air
are 0.0735 N/m and 0.51 N/m respectively. The contact angle for water θ = 0° and
for mercury θ = 130°. Take specific weight of water at 20°C as equal to 9780 N/m3
.
[AU, Nov / Dec - 2007]
1.272) Derive an expression for the capillary rise at a liquid in a capillary tube of radius
r having surface tension σ and contact angle θ . If the plates are of glass, what will
be the capillary rise of water having σ = 0.073 N/m, θ = 0°? Take r = 1mm.
[AU, Nov / Dec - 2011]
1.273) A pipe containing water at 180kN/m2
pressure is connected to differential gauge
to another pipe 1.6m lower than the first pipe and containing water at high pressure.
If the difference in height of 2 mercury columns of the gauge is equal to 90mm, what
is the pressure in the lower pipe? [AU, Nov / Dec - 2008]

1.274) Determine the minimum size of glass tubing that can be used to measure water
level. If the capillary rise in the tube is not exceed 2.5mm. Assume surface tension
of water in contact with air as 0.0746 N/m. [AU, Nov / Dec – 2004, 2012]
1.275) Calculate the capillary effect in millimeters in a glass tube of 4 mm diameter,
when immersed in (i) water and (ii) mercury. The temperature of the liquid is 20°C
and the values of surface tension of water and mercury at 20°C in contact with air
are 0.0735 N/m and 0.51 N/m respectively. The contact angle for water θ = 0 and
for mercury θ = 130°. Take specific weight of water at 20°C as equal to 9790N/ m3
.
[AU, Nov / Dec – 2005, 2007]
1.276) A Capillary tube having inside diameter 6 mm is dipped in CCl4at 20o C. Find
the rise of CCl4 in the tube if surface tension is 2.67 N/m and Specific gravity is
1.594 and contact angle u is 60° and specific weight of water at 20° C is 9981 N/m3
.
[AU, Nov / Dec - 2008]
1.277) Two pipes A & B are connected to a U – tube manometer containing mercury of
density 13,600kg/m3
. Pipe A carries a liquid of density 1250kg/m3
and a liquid of
density 800kg/m3
flows through a pipe B, The center of pipe A is 80mm above the
pipe B. The difference of mercury level manometer is 200mm and the mercury
surface on pipe A side is 100mm below the center. Find the difference of pressure
between the two connected points of the pipes. [AU, Nov / Dec - 2010]
1.278) A crude oil of viscosity 0.9 poise and relative density 0.9 is flowing through a
horizontal circular pipe of diameter 120 mm and length 12 m. Calculate the
difference of pressure at the two ends of the pipe, if 785 N of the oils collected in a
tank in 25 seconds. [AU, May / June - 2014]
1.279) A simple U tube manometer containing mercury is connected to a pipe in which
a fluid of specific gravity 0.8 and having vacuum pressure is flowing. The other end
of the manometer is open to atmosphere. Find the vacuum pressure in the pipe, if the
difference of mercury level in the two limbs is 40cm and the height of the fluid in
the left from the center pipe is 15cm below. Draw the sketch for the above problem.
[AU, April / May - 2011, May / June - 2012]
1.280) A U-tube is made of two capillaries of diameter 1.0 mm and 1.5 mm respectively.
The tube is kept vertically and partially filled with water of surface tension 0.0736

N/m and zero contact angles. Calculate the difference in the levels of the mercury
caused by the capillary. [AU, Nov / Dec - 2010]
1.281) Define the terms gauge pressure and absolute pressure. A U tube containing
mercury has its right limb open to atmosphere. The left limb is full of water and is
connected to a pipe containing water under pressure, the centre of which is in the
level with the free surface of mercury. If the difference in the levels of mercury in
the limbs id 5.1cm, calculate the water pressure in the pipe. [AU, Nov / Dec - 2012]
1.282) The barometric pressure at sea level is 760 mm of mercury while that on a
mountain top is 735 mm. If the density of air is assumed constant at 1.2 kg/m3
,
what is the elevation of the mountain top? [AU, Nov / Dec - 2007]
1.283) The barometric pressure at the top and bottom of a mountain are 734mm and
760mm of mercury respectively. Assuming that the average density of air =
1.15kg/m3, calculate the height of the mountain. [AU, Nov / Dec - 2009]
1.284) The maximum blood pressure in the upper arm of a healthy person is about 120
mmHg. If a vertical tube open to the atmosphere is connected to the vein in the arm
of the person, determine how high the blood will rise in the tube. Take the density
of the blood to be 1050 kg/ m3
. [AU, April / May - 2008]
1.285) When a pressure of 20.7 MN/m2
is applied to 100 litres of a liquid, its volume
decreases by one litre. Find the bulk modulus of the liquid and identify this liquid.
[AU, Nov / Dec - 2007]
1.286) The water level in a tank is 20 m above the ground. A hose is connected to the
bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The
tank is at sea level, and the water surface is open to the atmosphere. In the line leading
from the tank to the nozzle is a pump, which increases the pressure of water. If the
water jet rises to a height of 27 m from the ground, determine the minimum pressure
rise supplied by the pump to the water line. [AU, Nov / Dec - 2014]
1.287) Determine the minimum size of the glass tubing that can be used to measure
water level. If the capillary rise in the tube is not to exceed 2.5mm. Assume surface
tension of water in contact with air as 0.0746 N/m [AU, April / May - 2004]
1.288) A cylinder of 0.6m3
in volume contains air at 50°C and 0.3N/mm2
absolute
pressure. The air is compressed to 0.3m3
. Find the (i) pressure inside the cylinder

assuming isothermal process and (ii) pressure and temperature assuming adiabatic
process. Take k = 1.4.
1.289) A 30cm diameter pipe, conveying water, branches into two pipes of diameters
20cm and 15cm respectively. If the average velocity in the 30cm diameter pipe is
2.5m/sec, find the discharge in this pipe. Also determine the velocity in the 15cm
diameter pipe if the average velocity in the 20cm diameter pipe is 2m/sec.
[AU, Nov / Dec - 2008, 2015, April / May - 2010]
1.290) Water flows through a pipe AB 1.2m diameter at 3m/second then passes through
a pipe BC 1.5m diameter. At C, the pipe branches. Branch CD is 0.8m in diameter
and carries one - third of the flow in AB. The flow velocity in branch CE is 2.5m/sec.
Find the volume rate of flow in AB, the velocity in BC, the velocity in CD and the
diameter of CE.
1.291) Water is flowing through a pipe having diameters 20cm and 10cm at sections 1
and 2 respectively. The rate of flow, through the pipe is 35litre/sec. The section 1 is
6m above datum and section 2 is 4m above datum. If the pressure at section 1 is
39.24N/cm2
, find the intensity of pressure at section 2. [AU, Nov / Dec - 2008]
1.292) Water is flowing through a pipe having diameters 30cm and 20cm at sections 1
and 2 respectively. The rate of flow, through the pipe is 35litre/sec. The section 1 is
8m above datum and section 2 is 6m above datum. If the pressure at section 1 is
44.5N/cm2
, find the intensity of pressure at section 2. [AU, Nov / Dec - 2015]
1.293) A pipe 200m long slopes down at 1 in 100 and tapers from 600mm diameter at
the higher end to 300mm diameter at the lower end and carries 100 litres/sec of oil
having specific gravity 0.8. If the pressure gauge at the higher end reads 60kN/m2
,
determine the velocities at the two ends and also the pressure at the lower end.
Neglect all losses [AU, April / May - 2015]
1.294) Water is flowing through a taper pipe of length 100m having diameters 600mm
at the upper end and 300mm at the lower end, at the rate of 50 litres/ sec. The pipe
has a slope of 1 in 30. Find the pressure at the lower end if the pressure at the higher
level is 19.62 N/cm2
.
1.295) Water flows at the rate of 200 litres per second upwards through a tapered
vertical pipe. The diameter at the bottom is 240 mm and at the top 200 mm and the
length is 5 m. The pressure at the bottom is 8 bar, and the pressure at the topside is

7.3 bar. Determine the head loss through the pipe. Express it as a function of exit
velocity head. [AU, Nov / Dec - 2014]
1.296) Water flows through a certain cross section of a 20cm diameter pipe at a pressure
of 130KPa absolute. The elevation of the cross section is 3.0m above the datum and
the rate of flow is 300 liters/s. Find (i) the flow work (ii) potential energy (iii) kinetic
energy, per unit mass at the cross section. [AU, April / May - 2017]
1.297) A pipe of diameter 400mm carries water at a velocity of 25m/sec. The pressures
at the points A and B are given as 29.43N/cm2
and 22.563 N/cm2
respectively, while
the datum head at A and B are 28m and 30m. Find the loss of head between A and
B.
1.298) A drainage pipe is tapered in a section running with full of water. The pipe
diameters at the inlet and exit are 1000 mm and 50 mm respectively. The water
surface is 2 m above the center of the inlet and exit is 3 m above the free surface of
the water. The pressure at the exit is250 mm of Hg vacuum. The friction loss
between the inlet and exit of the pipe is 1/10 of the velocity head at the exit.
Determine the discharge through the pipe. [AU, April / May - 2010]
1.299) A pipeline 60 cm in diameter bifurcates at a Y-junction into two branches 40 cm
and 30 cm in diameter. If the rate of flow in the main pipe is 1.5 m3
/s, and the mean
velocity of flow in the 30 cm pipe is 7.5 m/s, determine the rate of flow in the 40 cm
pipe. [AU, Nov / Dec - 2010]
1.300) A pipeline of 175 mm diameter branches into two pipes which delivers the water
at atmospheric pressure. The diameter of the branch 1 which is at 35° counter-
clockwise to the pipe axis is 75mm. and the velocity at outlet is 15 m/s. The branch
2 is at 15° with the pipe center line in the clockwise direction has a diameter of 100
mm. The outlet velocity is 15 m/s. The pipes lie in a horizontal plane. Determine the
magnitude and direction of the forces on the pipes. [AU, Nov / Dec - 2011]
1.301) The water is flowing through a taper pipe of length 100 m having diameters 600
mm at the upper end and 300 mm at the lower end, at the rate of 50 litres/s. The pipe
has a slope of 1 in 30. Find the pressure at the lower end if the pressure at the higher
level is 19.62 N/cm2
. [AU, May / June - 2013]

1.302) A 45° reducing bend is connected in a pipe line, the diameters at the inlet and
outlet of the bend being 600mm and 300mm respectively. Find the force exerted by
water on the bend if the intensity of pressure at the inlet to the bend is 8.829N/cm2
and rate of flow of water is600 litre / sec.
1.303) 250 litres/sec., of water is flowing in a pipe having diameter of 300mm. If the
pipe is bent by 135°, find the magnitude and direction of the resultant force on the
bend. The pressure of the water flowing is 400kN/m2
. Take specific weight of water
as 9.81kN/m3
. [AU, May / June - 2016]
1.304) A 45° reducing bend is connected to a pipe line. The inlet and outlet diameters
of the bend being 600mm and 300mm respectively. Find the force exerted by water
on the bend, if the intensity of pressure at inlet to bend is 8.829N/cm2
and the rate of
flow of water is 600 liters/s. [AU, Nov / Dec - 2007]
1.305) A pipe of 30 cm diameter carrying 0.25 m3
/s water. The pipe is bent by 135°
from the horizontal anti-clockwise. The pressure of water flowing through the pipe
is 400 kN. Find the magnitude and direction of the resultant force on the bend.
[AU, Nov / Dec - 2011]
1.306) Gasoline (specific gravity = 0.8) is flowing upwards through a vertical pipe line
which tapers from300mm to 150mm diameter. A gasoline mercury differential
manometer is connected between 300 mm and 150 mm pipe sections to measure the
rate of flow. The distance between the manometer tappings is 1meter and the gauge
heading is 500 mm of mercury. Find the (i) differential gauge reading in terms of
gasoline head (ii) rate of flow. Assume frictional and other losses are negligible.
[AU, May / June – 2007, 2014, Nov / Dec - 2012]
1.307) Water enters a reducing pipe horizontally and comes out vertically in the
downward direction. If the inlet velocity is 5 m/s and pressure is 80 kPa (gauge) and
the diameters at the entrance and exit sections are 30 cm and 20 cm respectively,
calculate the components of the reaction acting on the pipe.
[AU, May / June – 2007, Nov / Dec - 2012]
1.308) A horizontal pipe has an abrupt expansion from 10 cm to 16 cm. The water
velocity in the smaller section is 12 m/s, and the flow is turbulent. The pressure in
the smaller section is 300 kPa. Determine the downstream pressure, and estimate the

error that would have occurred if Bernoulli’s equation had been used.
[AU, Nov / Dec - 2011]
1.309) Air flows through a pipe at a rate of 20 L/s. The pipe consists of two sections of
diameters20 cm and 10 cm with a smooth reducing section that connects them. The
pressure difference between the two pipe sections is measured by a water
manometer. Neglecting frictional effects, determine the differential height of water
between the two pipe sections. Take the air density to be 1.20 kg/m3
.
1.310) A horizontal venturimeter with inlet diameter 200 mm and throat diameter 100
mm is employed to measure the flow of water. The reading of the differential
manometer connected to the inlet is 180 mm of mercury. If Cd = 0.98, determine
the rate of flow. [AU, April / May - 2010]
1.311) An oil of specific gravity 0.8 is flowing through the venturimeter having inlet
diameter 20cm and the throat diameter is 10cm. The oil – mercury differential
manometer shows the reading of 25cm. Calculate the discharge of oil through the
horizontal venturimeter. Take Cd = 0.98. [AU, April / May - 2017]
1.312) A horizontal venturimeter of specification 200mm * 100mm is used to measure
the discharge of an oil of specific gravity 0.8. A mercury manometer is used for the
purpose. If the discharge is 100 litres per second and the coefficient of discharge of
meter is 0.98, find the manometer deflection. [AU, May / June - 2007]
1.313) Determine the pressure difference between inlet and throat of a vertical
venturimeter of size 150 mm x 75 mm carrying oil of S = 0.8 at flow rate of 40 lps.
The throat is 150 mm above the inlet.
1.314) A pipe of 300 mm diameter inclined at 30° to the horizontal is carrying gasoline
(specific gravity = 0.82). A venturimeter is fitted in the pipe to find out the flow rate
whose throat diameter is 150 mm. The throat is 1.2 m from the entrance along its
20 cm
air
200 L/s
h

length. The pressure gauges fitted to the venturimeter read 140 kN/m2
and
80kN/m2
respectively. Find out the co-efficient of discharge of venturimeter if the
flow is 0.20 m3
/s. [AU, April / May - 2010]
1.315) A venturimeter of throat diameter 0.085m is fitted in a 0.17m diameter vertical
pipe in which liquid a relative density 0.85 flows downwards. Pressure gauges ate
fitted at the inlet and to the throat sections. The throat being 0.9m below the inlet.
Taking the coefficient of the meter as 0.95 find the discharge when the pressure
gauges read the same and also when the inlet gauge reads 15000N/m2
higher than
the throat gauge. [AU, April / May - 2011]
1.316) A Venturimeter having inlet and throat diameters 30 cm and 15 cm is fitted in a
horizontal diesel pipe line (Sp. Gr. = 0.92) to measure the discharge through the pipe.
The venturimeter is connected to a mercury manometer. It was found that the
discharge is 8 litres /sec. Find the reading of mercury manometer head in cm. Take
Cd =0.96. [AU, Nov / Dec - 2011]
1.317) A venturimeter is inclined at 60° to the vertical and its 150 mm diameter throat
is 1.2 m from the entrance along its length. It is fitted to a pipe of diameter 300 mm.
The pipe conveys gasoline of S = 0.82 and flowing at 0.215 m3
/s upwards. Pressure
gauges inserted at entrance and throat show the pressures of 0.141 N/mm2
and 0.077
N/mm2
respectively. Determine the co-efficient of discharge of the venturimeter.
Also determine the reading in mm of differential mercury column, if instead of
pressure gauges the entrance and the throat of the venturimeter are connected to the
limbs of a U tube mercury manometer. [AU, April / May - 2004]
1.318) A horizontal venturimeter with inlet and throat diameter 300mm and 100mm
respectively is used to measure the flow of water. The pressure intensity at inlet is
130 kN/m2
while the vacuum pressure head at throat is 350 mm of mercury.
Assuming 3% head lost between the inlet and throat. Find the value of coefficient of
discharge for venturimeter and also determine the rate of flow.
1.319) A vertical venturimeter carries a liquid of relative density 0.8 and has inlet throat
diameters of 150mm and 75mm. The pressure connection at the throat is 150mm

above the inlet. If the actual rate of flow is 40litres/sec and Cd = 0.96, find the
pressure difference between inlet and throat in N/m2
. [AU, May / June - 2006]
1.320) A 300 mm x 150 mm venturimeter is provided in a vertical pipeline carrying oil
of relative density 0.9, the flow being upwards. The differential U tube mercury
manometer shows a gauge deflection of 250 mm. Calculate the discharge of oil, if
the co-efficient of meter is 0.98. [AU, Nov / Dec - 2007]
1.321) In a vertical pipe conveying oil of specific gravity 0.8, two pressure gauges have
been installed at A and B, where the diameters are 160mm a 80mm respectively. A
is 2m above B. The pressure gauge readings have shown that the pressure at B is
greater than at A by 0.981 N/cm2
. Neglecting all losses, calculate the flow rate. If the
gauges at A and B are replaced by tubes filled with the same liquid and connected to
a U – tube containing mercury, calculate the difference in the level of mercury in the
two limbs of the U – tube. [AU, May / June - 2012]
1.322) Determine the flow rate of oil of S = 0.9 through an orifice meter of size 15 cm
diameter fitted in a pipe of 30 cm diameter. The mercury deflection of U tube
differential manometer connected on the two sides of the orifice is 50 cm. Assume
Cd of orifice meter as 0.64.
1.323) At a certain location, wind at a temperature of 30 °C is blowing steadily at 15
m/s. Determine the mechanical energy of air per unit mass and the power generation
potential of a wind turbine with 40-m diameter blades at that location. Also
determine the actual electric power generation assuming an overall efficiency of
35%. [AU, May / June - 2016]
1.324) A submarine moves horizontally in sea and has its axis 15 m below the surface
of water. A pitot static tube properly placed just in front of the submarine along its
axis and is connected to the two limbs of a U - tube containing mercury. The
difference of mercury level is found to be170 mm. Find the speed of submarine
knowing that the sp. gr of sea water is 1.026.
1.325) A submarine fitted with a Pitot tube move horizontally in sea. Its axis is 20m
below surface of water. The Pitot tube placed in front of the submarine along its axis
is connected to a differential mercury manometer showing the deflection of 20cm.
Determine the speed of the submarine. [AU, April / May - 2005]

1.326) A pitot-static probe is used to measure the velocity of an aircraft flying at 3000
m. If the differential pressure reading is 3 kPa, determine the velocity of the aircraft.
1.327) A 15 cm diameter vertical pipe is connected to 10 cm diameter vertical pipe
with a reducing socket. The pipe carries a flow of 1001/s. At point 1 in 15 cm pipe
gauge pressure is 250 kPa. At point 2 in the 10 cm pipe located 1.0 m below point 1
the gauge pressure is 175 kPa.
 Find whether the flow is upwards / downwards.
 Head loss between the two points.
1.328) Water enters a reducing pipe horizontally and comes out vertically in the
downward direction. If the inlet velocity is 5 m/sec and pressure is 80 kPa (gauge)
and the diameters at the entrance and exit sections are 300 mm and 200 mm
respectively. Calculate the components of the reaction acting on the pipe.
1.329) In cold climates, the water pipes may freeze and burst if proper precautions are
not taken. In such an occurrence, the exposed part of a pipe on the ground ruptures,
and water shoots up to 34 m. Estimate the gage pressure of water in the pipe. State
your assumptions and discuss if the actual pressure is more or less than the value you
predicted. [AU, May / June - 2016]

UNIT - II - FLOW THROUGH CIRCULAR CONDUCTS
PART - A
2.1) How are fluid flows classified? [AU, May / June - 2012]
2.2) Distinguish between Laminar and Turbulent flow. [AU, Nov / Dec - 2006]
2.3) Write down Hagen Poiseuille’s equation for viscous flow through a pipe.
2.4) Write down Hagen Poiseuille’s equation for laminar flow.
[AU, April / May - 2005, Nov / Dec - 2012]
2.5) Write the Hagen – Poiseuille’s Equation and enumerate its importance.
2.6) State Hagen – Poiseuille’s formula for flow through circular tubes.
[AU, May / June - 2012]
2.7) Write down the Darcy - Weisbach’s equation for friction loss through a pipe
2.8) What is the relationship between Darcy Friction factor, Fanning Friction Factor
and Friction coefficient? [AU, May / June - 2012]
2.9) Brief on Darcy-Weisbach equation. [AU, May / June - 2016]
2.10) Mention the types of minor losses. [AU, April / May - 2010]
2.11) List the minor losses in flow through pipe.
[AU, April / May - 2005, May / June - 2007]
2.12) What are minor losses? Under what circumstances will they be negligible?
[AU, May / June - 2012]
2.13) What are the minor losses in pipes? [AU, Nov / Dec - 2015]
2.14) Distinguish between the major loss and minor losses with reference to flow
through pipes. [AU, May / June - 2009]
2.15) List the causes of minor energy losses in flow through pipes.
[AU, Nov / Dec - 2009]
2.16) What are the losses experienced by a fluid when it is passing through a pipe?
2.17) What is a minor loss in pipe flows? Under what conditions does a minor loss
become a major loss?
2.18) What do you understand by minor energy losses in pipes?
[AU, Nov / Dec - 2008]

2.19) List out the various minor losses in a pipeline
2.20) What are ‘major’ and ‘minor losses’ of flow through pipes?
[AU, May / June 2007, Nov / Dec - 2007, 2012, April / May - 2010]
2.21) List the minor and major losses during the flow of liquid through a pipe.
2.22) Enlist the various minor losses involved in a pipe flow system.
[AU, Nov / Dec - 2008]
2.23) Write the expression for calculating the loss due to sudden expansion of the pipe.
2.24) What are the factors influencing the frictional loss in pipe flow?
[AU, Nov / Dec - 2016]
2.25) What factors account in energy loss in laminar flow. [AU, May / June - 2012]
2.26) Differentiate between pipes in series and pipes in parallel.
[AU, Nov / Dec - 2006]
2.27) What is Darcy's equation? Identify various terms in the equation.
2.28) What is the relation between Darcy friction factor, Fanning friction factor and
friction coefficient? [AU, Nov / Dec - 2010]
2.29) When is the pipe termed to be hydraulically rough? [AU, Nov / Dec - 2009]
2.30) How does the roughness of channel affect the Chezy's constant?
[AU, May / June - 2016]
2.31) What is the physical significance of Reynold's number?
[AU, May / June, Nov / Dec - 2007]
2.32) Define Reynolds Number. [AU, Nov / Dec - 2012]
2.33) Write the Navier's Stoke equations for unsteady 3 - dimensional, viscous,
incompressible and irrotational flow. [AU, April / May - 2008]
2.34) State the equation of discharge of water through an open channel.
[AU, May / June - 2016]
2.35) Define Moody’s diagram
2.36) What are the uses of Moody’s diagram?
2.37) Mention the use of Moody diagram. [AU, April / May - 2015]

2.38) State the importance of Moody's chart. [AU, Nov / Dec - 2014]
2.39) Write down the formulae for loss of head due to
(i) sudden enlargement in pipe diameter
(ii) sudden contraction in pipe diameter and
(iii) Pipe fittings.
2.40) Define (i) relative roughness and (ii) absolute roughness of a pipe inner surface.
2.41) Explain what is meant by a smooth pipe? [AU, Nov / Dec - 2015]
2.42) How does surface roughness affect the pressure drop in a pipe if the flow is
turbulent? [AU, Nov / Dec - 2013]
2.43) A piping system involves two pipes of different diameters (but of identical length,
material, and roughness) connected in parallel. How would you compare the flow
rates and pressure drops in these two pipes? [AU, Nov / Dec - 2013]
2.44) What do you mean by flow through parallel pipes? [AU, May / June - 2013]
2.45) What is equivalent pipe? Mention the equation used for it.
2.46) What is the use of Dupuit’s equations?
2.47) What is the condition for maximum power transmission through a pipe line?
2.48) Give the expression for power transmission through pipes?
[AU, Nov / Dec - 2008]
2.49) Write down the formula for friction factor of pipe having viscous flow.
2.50) Define boundary layer. [AU, April / May - 2017]
2.51) Define boundary layer and boundary layer thickness.
[AU, Nov / Dec – 2007, 2012]
2.52) Define boundary layer thickness.
2.53) What is boundary layer? Give its sketch of a boundary layer region over a flat
plate. [AU, April / May - 2003]
2.54) State boundary layer thickness with a neat sketch. [AU, April / May - 2017]
2.55) What is boundary layer? Why is it significant? [AU, Nov / Dec - 2009]
2.56) Define boundary layer and give its significance. [AU, April / May - 2010]
2.57) What is boundary layer and write its types of thickness?
[AU, Nov / Dec – 2005, 2006]

2.58) What do you understand by the term boundary layer? [AU, Nov / Dec - 2008]
2.59) Define the following (i) laminar boundary layer (ii) turbulent boundary layer
(iii) laminar sub layer.
2.60) What is a laminar sub layer? [AU, Nov / Dec - 2010]
2.61) Define momentum thickness and energy thickness.
[AU, May / June – 2007, 2012]
2.62) Define the term boundary layer. [AU, May / June - 2009]
2.63) Define the terms boundary layer, boundary thickness. [AU, Nov / Dec - 2008]
2.64) What is boundary layer separation? [AU, Nov / Dec - 2012]
2.65) Give the classification of boundary layer flow based on the Reynolds number.
2.66) Define the following:
(i) Displacement thickness (ii) Momentum thickness
(iii)Energy thickness.
2.67) What do you mean by displacement thickness and momentum thickness?
[AU, Nov / Dec - 2008]
2.68) What is the condition for maximum power transmission w.r.t. head available?
[AU, May / June - 2016]
2.69) What do you understand by hydraulic diameter? [AU, Nov / Dec - 2011]
2.70) What is hydraulic gradient line? [AU, May / June - 2009]
2.71) Define hydraulic gradient line and energy gradient line.
2.72) Brief on HGL. [AU, April / May - 2011]
2.73) Differentiate between Hydraulic gradient line and total energy line.
[AU, Nov / Dec - 2003, 2015, April / May - 2005, 2010, May / June–2007, 2009]
2.74) What is T.E.L? [AU, Nov / Dec - 2009]
2.75) Distinguish between hydraulic and energy gradients. [AU, Nov / Dec - 2011]
2.76) Differentiate hydraulic gradient line and energy gradient line.
[AU, May / June - 2014]
2.77) Differentiate between hydraulic grade line and energy grade line.
[AU, Nov / Dec - 2014]

2.78) What are stream lines, streak lines and path lines in fluid flow?
[AU, Nov / Dec –2006, 2009]
2.79) What do you mean by Prandtl’s mixing length?
2.80) Draw the typical boundary layer profile over a flat plate.
2.81) Define flow net. [AU, Nov / Dec - 2008]
2.82) What is flow net and state its use? [AU, April / May - 2011]
2.83) Define lift. [AU, Nov / Dec - 2005]
2.84) Define the terms: drag and lift. [AU, Nov / Dec – 2007, May / June - 2009]
2.85) Define drag and lift co-efficient.
2.86) Give the expression for Drag coefficient and Lift coefficient.
2.87) What is meant by laminar flow instability? [AU, Nov / Dec - 2014]
2.88) Considering laminar flow through a circular pipe, draw the shear stress and
velocity distribution across the pipe section. [AU, Nov / Dec - 2010]
2.89) Considering laminar flow through a circular pipe, obtain an expression for the
velocity distribution. [AU, Nov / Dec - 2012]
2.90) Draw the velocity distribution and the shear stress distribution for the flow of
circular pipes. [AU, Nov / Dec - 2016]
2.91) A circular and a square pipe are of equal sectional area. For the same flow rate,
determine which section will lead to a higher value of Reynolds number.
[AU, Nov / Dec - 2011]
2.92) A 20cm diameter pipe 30km long transport oil from a tanker to the shore at
0.01m3
/s. Find the Reynolds number to classify the flow. Take the viscosity μ = 0.1
Nm/s2
and density ρ = 900 kg/m3
for oil. [AU, April / May - 2003]
2.93) Find the loss of head when a pipe of diameter 200 mm is suddenly enlarged to a
diameter 0f 400 mm. Rate of flow of water through the pipe is 250 litres/s.
2.94) Find the displacement thickness for the velocity distribution in the boundary layer
given by
𝑢
𝑈
= 2
𝑦
𝛿
− (
𝑦
𝛿
)
2
[AU, Nov / Dec - 2016]
PART - B
2.95) What are the various types of fluid flows? Discuss [AU, Nov / Dec - 2010]

2.96) Define minor losses. How they are different from major losses?
[AU, May / June - 2009]
2.97) Discuss on various minor losses in pipe flow. [AU, Nov / Dec - 2013]
2.98) Discuss on minor losses in pipe flow. [AU, Nov / Dec - 2014]
2.99) Which has a greater minor loss co-efficient during pipe flow: gradual expansion
or gradual contraction? Why? [AU, April / May - 2008]
2.100) Derive Chezy’s formula for loss of head due to friction in pipes.
[AU, Nov / Dec - 2012]
2.101) What is the hydraulic gradient line? How does it differ from the total energy
line? Under what conditions do both lines coincide with the free surface of a liquid?
2.102) Write notes on the following:
 Concept of boundary layer.
 Hydraulic gradient
 Moody diagram.
2.103) Briefly explain Moody’s diagram regarding pipe friction
[AU, May / June - 2014]
2.104) Describe the Moody's chart. [AU, Nov / Dec - 2014]
2.105) For a flow of viscous fluid flowing through a circular pipe under laminar flow
conditions, show that the velocity distribution is a parabola. And also show that the
average velocity is half of the maximum velocity. [AU, May / June - 2013]
2.106) For flow of viscous fluids through an annulus derive the following expressions:
 Discharge through the annulus.
 Shear stress distribution. [AU, May / June – 2007, 2012]
2.107) For a laminar flow through a pipe line, show that the average velocity is half of
the maximum velocity.
2.108) Prove that the Hagen-Poiseuille’s equation for the pressure difference between
two sections 1 and 2 in a pipe is given by with usual notations.
2.109) Derive Hagen – Poiseuille’s equation and state its assumptions made.
[AU, Nov / Dec - 2005]
2.110) Derive Hagen – Poiseuille’s equation [AU, Nov / Dec - 2008]

2.111) Obtain the expression for Hagen – Poiseuille’s flow. Deduce the condition of
maximum velocity. [AU, Nov / Dec - 2007]
2.112) Derive the expression for shear stress and velocity distribution for the flow
through circular pipe and using that derive the Hagen Poiseuille formula.
[AU, Nov / Dec - 2015]
2.113) Derive Hagen – Poiseuille’s equation formula for the flow through the circular
pipes. [AU, Nov / Dec - 2016]
2.114) Give a proof a Hagen – Poiseuille’s equation for a fully – developed laminar
flow in a pipe and hence show that Darcy friction coefficient is equal to 16/Re, where
Re is Reynold’s number. [AU, May / June - 2012]
2.115) For a flow of viscous fluid flowing through a circular pipe under laminar flow
conditions show that the velocity distribution is a parabola. And also show that the
average velocity is half of the maximum velocity. [AU, April / May - 2017]
2.116) An incompressible fluid flows downward through a vertical cylindrical pipe
under the action of gravity. The flow is fully developed and laminar. Use the Navier-
Strokes equations to derive an expression for the flow rate for the case of zero
pressure gradients along the pipe. [AU, May / June - 2016]
2.117) A thin layer of liquid of constant thickness flow down an inclined plate such that
the only velocity component is parallel to the plate. Use the Navier-Strokes equations
to determine the relationship between the thickness of the layer and the flow rate per
unit width. Assume a steady, laminar, and uniform flow. Also assume that air
resistance is negligible. [AU, May / June - 2016]
2.118) Distinguish between Laminar and Turbulent flow in pipes.
2.119) Derive an expression for head loss through pipes due to friction.
2.120) Explain Reynold’s experiment to demonstrate the difference between laminar
flow and turbulent flow through a pipe line.
2.121) Explain Reynold’s Experiment. [AU, Nov / Dec - 2016]
2.122) Derive Darcy - Weisbach formula for calculating loss of head due to friction in
a pipe. [AU, Nov / Dec - 2011]

2.123) Derive Darcy - Weisbach formula for head loss due to friction in flow through
2.124) Derive the Darcy – Weisbach equation for the loss of head due to friction in
2.125) Obtain expression for Darcy – Weisbach friction factor f for flow in pipe.
[AU, May / June - 2012]
2.126) Explain the losses of energy in flow through pipes. [AU, Nov / Dec - 2009]
2.127) Derive an expression for Darcy – Weisbach formula to determine the head loss
due to friction. Give an expression for relation between friction factor ‘f’ and
Reynolds’s number ‘Re’ for laminar and turbulent flow. [AU, April / May - 2003]
2.128) Derive an expression for the depth of paraboloid formed by the surface of a
liquid contained in a cylindrical tank which is rotated at a constant angular velocity
w about its vertical axis. [AU, May / June - 2016]
2.129) Prove that the head lost due to friction is equal to one third of the total head at
inlet for maximum power transmission through pipes. [AU, Nov / Dec - 2008]
2.130) Show that for laminar flow, the frictional loss of head is given by
hf= 8 fLQ2
/gπ2
D5
[AU, Nov / Dec - 2009]
2.131) Derive Euler’s equation of motion for flow along a stream line. What are the
assumptions involved. [AU, Nov / Dec - 2009]
2.132) A uniform circular tube of bore radius R1 has a fixed co axial cylindrical solid
core of radius R2. An incompressible viscous fluid flows through the annular passage
under a pressure gradient (-∂p/∂x). Determine the radius at which shear stress in the
stream is zero, given that the flow is laminar and under steady state condition.
[AU, May / June - 2009]
2.133) If the diameter of the pipe is doubled, what effect does this have on the flow rate
for a given head loss for laminar flow and turbulent flow. [AU, April / May - 2011]
2.134) Derive an expression for the variation of jet radius r with distance y downwards
for a jet directed downwards. The initial radius is R and the head of fluid is H.
[AU, Nov / Dec - 2011]
2.135) Distinguish between pipes connected in series and parallel.
[AU, Nov / Dec - 2005]
2.136) Discuss on hydraulic and energy gradient. [AU, Nov / Dec - 2014]

2.137) Determine the equivalent pipe corresponding to 3 pipes in series with lengths
and diameters l1, l2, l3, d1, d2, d3 respectively. [AU, Nov / Dec - 2009]
2.138) For sudden expansion in a pipe flow, work out the optimum ratio between the
diameter of before expansion and the diameter of the pipe after expansion so that the
pressure rise is maximum. [AU, May / June - 2012]
2.139) Obtain the condition for maximum power transmission through a pipe line.
2.140) Explain stream lines, path lines and flow net. [AU, Nov / Dec - 2012]
2.141) What are the uses and limitations of flow net? [AU, May / June - 2009]
2.142) Briefly explain about boundary layer separation. [AU, Nov / Dec - 2008]
2.143) Explain on boundary layer separation and its control.
2.144) Considering a flow over a flat plate, explain briefly the development of
hydrodynamic boundary layer. [AU, Nov / Dec - 2010]
2.145) Discuss in detail about boundary layer thickness and separation of boundary
layer. [AU, April / May - 2011]
2.146) What is boundary layer and write its types of thickness?
2.147) Explain in detail
 Drag and lift coefficients
 Boundary layer thickness
 Boundary layer separation
 Navier’s – strokes equation. [AU, May / June - 2012]
2.148) In a water reservoir flow is through a circular hole of diameter D at the side wall
at a vertical distance H from the free surface. The flow rate through an actual hole
with a sharp-edged entrance (kL
= 0.5) will be considerably less than the flow rate
calculated assuming frictionless flow. Obtain a relation for the equivalent diameter
of the sharp-edged hole for use in frictionless flow relations.
[AU, Nov / Dec - 2011]
2.149) Define: Boundary layer thickness (δ); Displacement thickness (δ*
); Momentum
thickness (θ) and energy thickness (δ**
). [AU, April / May - 2010]
2.150) Briefly explain the following terms
 Displacement thickness

 Momentum thickness
 Energy thickness [AU, May / June - 2014]
2.151) Find the displacement thickness momentum thickness and energy thickness for
the velocity distribution in the boundary layer given by (u/v) = (y/δ), where ‘u’is the
velocity at a distance ‘y’ from the plate and u=U at y=δ, where δ = boundary layer
thickness. Also calculate (δ*
/θ). [AU, Nov / Dec - 2007, April / May - 2010]
2.152) Explain the concept of boundary layer in pipes for both laminar and turbulent
flows with neat sketches. [AU, Nov / Dec - 2013]
2.153) What is hydraulic gradient line? How does it differ from the total energy line?
Under what conditions do both lines coincide with surface of the liquid?
2.154) Derive an expression for the velocity distribution for viscous flow through a
circular pipe. [AU, May / June - 2007]
2.155) Write a brief note on velocity potential function and stream function.
[AU, May / June - 2009]
2.156) Derive an expression for the velocity distribution for viscous flow through a
circular pipe. Also sketch the distribution of velocity cross a section of the pipe.
[AU, Nov / Dec - 2011]
PROBLEMS
2.157) A 20 cm diameter pipe 30 km long transports oil from a tanker to the shore at
0.01m3
/s. Find the Reynold’s number to classify the flow. Take viscosity and
density for oil.
2.158) A pipe line 20cm in diameter, 70m long, conveys oil of specific gravity 0.95 and
viscosity 0.23 N.s/m2
. If the velocity of oil is 1.38m/s, find the difference in pressure
between the two ends of the pipe. [AU, May / June - 2012]
2.159) Oil of absolute viscosity 1.5 poise and density 848.3kg/m3
flows through a
300mm pipe. If the head loss in 3000 m, the length of pipe is 200m, assuming
laminar flow, find
(i) the average velocity,
(ii) Reynolds’s number and
(iii) Friction factor. [AU, May / June - 2012]

2.160) A fluid of viscosity 0.7 Pa.s and specific gravity 1.3 is flowing through a pipe
diameter of 120mm. The maximum shear stress at the pipe value is 205.2N/m2
.
Determine the pressure gradient, Reynolds number and average velocity.
2.161) An oil of specific gravity 0.7 is flowing through the pipe diameter 30cm at the
rate of 500litres/sec. Find the head lost due to friction and power required to maintain
the flow for a length of 1000m. Take γ = 0.29 stokes.
2.162) A pipe line 10km, long delivers a power of 50kW at its outlet ends. The pressure
at inlet is 5000kN/m2
and pressure drop per km of pipeline is 50kN/m2
. Find the size
of the pipe and efficiency of transmission. Take 4f = 0.02.
[AU, Nov / Dec - 2005]
2.163) A lubricating oil flows in a 10 cm diameter pipe at 1 m/s. Determine whether the
flow is laminar or turbulent.
2.164) An oil of specific gravity 0.80 and kinematic viscosity 15 x 106
m2
/s flows in a
smooth pipe of 12 cm diameter at a rate of 150 lit/min. Determine whether the flow
is laminar or turbulent. Also, calculate the velocity at the centre line and the velocity
at a radius of 4 cm. What is head loss for a length of 10 m? What will be the entry
length? Also determine the wall shear. [AU, Nov / Dec - 2014]
2.165) For the lubricating oil 2 μ = 0.1Ns /m and ρ = 930 kg/m3
. Calculate also transition
and turbulent velocities. [AU, April / May - 2011]
2.166) Oil of ,mass density 800kg/m3
and dynamic viscosity 0.02 poise flows through
50mm diameter pipe of length 500m at the rate of 0.19 liters/ sec. Determine
 Reynolds number of flow
 Center line of velocity
 Pressure gradient
 Loss of pressure in 500m length
 Wall shear stress
 Power required to maintain the flow. [AU, May / June - 2012]
2.167) In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway
between the wall surface and the center line) is measured to be 6m/s. Determine the
velocity at the center of the pipe. [AU, April / May - 2008]

2.168) A lubricating oil, having S = 0.89 and μ = 82.5*10-3
Ns/m3
flows through a
250mm diameter horizontal cast iron pipe 2000m long at the rate of 0.035 m3
/s. Show
that (i) the flow is laminar. Hence (ii) find the pressure difference between the two
ends of the pipe. Also find (iii) the power needed by a pump (η=0.9) in KW, to
maintain the flow. [AU, April / May - 2017]
2.169) A pipe 85m long conveys a discharge of 25litres per second. If the loss of head
is 10.5m. Find the diameter of the pipe take friction factor as 0.0075.
[AU, Nov / Dec - 2009]
2.170) A smooth pipe carries 0.30m3
/s of water discharge with a head loss of 3m per
100m length of pipe. If the water temperature is 20°C, determine diameter of the
pipe. [AU, May / June - 2012]
2.171) A smooth pipe carries 6.5 litres/sec of water at 20°C (Kinematic viscosity = l0-6
m2
/s) with a head loss of 7.5cm per 10m length. Determine the diameter of the pipe.
[AU, Nov / Dec - 2015]
2.172) Water is flowing through a pipe of 250 mm diameter and 60 m long at a rate of
0.3 m3
/sec. Find the head loss due to friction. Assume kinematic viscosity of water
0.012 stokes.
2.173) A crude oil of kinematic viscosity 0.4 strokes is flowing through a pipe of
diameter 300mm at the rate of 300 litres per sec. Find the head lost due to friction
for a length of 50m of the pipe. Take the coefficient of frictions as 0.006.
2.174) Consider turbulent flow (f = 0.184 Re-0.2
) of a fluid through a square channel
with smooth surfaces. Now the mean velocity of the fluid is doubled. Determine the
change in the head loss of the fluid. Assume the flow regime remains unchanged.
What will be the head loss for fully turbulent flow in a rough pipe?
[AU, Nov / Dec - 2013]
2.175) A pipe of 12cm diameter is carrying an oil (μ = 2.2 Pa.s and ρ = 1250 kg/m3
)
with a velocity of 4.5 m/s. Determine the shear stress at the wall surface of the pipe,
head loss if the length of the pipe is 25 m and the power lost.
[AU, Nov / Dec - 2011]

2.176) Find the head loss due to friction in a pipe of diameter 30cm and length 50cm,
through which water is flowing at a velocity of 3m/s using Darcy’s formula.
[AU, Nov / Dec - 2008]
2.177) For a turbulent flow in a pipe of diameter 300 mm, find the discharge when the
center-line velocity is 2.0 m/s and the velocity at a point 100 mm from the center as
measured by pitot-tube is 1.6 m/s. [AU, April / May - 2010]
2.178) A laminar flow is taking place in a pipe of diameter 20cm. The maximum
velocity is 1.5m/s. Find the mean velocity and radius at which this occurs. Also
calculate the velocity at 4cm from the wall pipe. [AU, May / June - 2009]
2.179) Water is flowing through a rough pipe of diameter 60 cm at the rate of
600litres/second. The wall roughness is 3 mm. Find the power loss for 1 km length
of pipe.
2.180) Water having a coefficient of kinematic viscosity of 1.12 x 10-6
m2
/s and a mass
density of 1 mg/m3
flows at a mean speed of 1.75m/s through a 75mm diameter pipe
line. What corresponding volumetric rate (measured at atmospheric pressure) of air
flow through this pipeline would give rise to essentially similar dynamical flow
conditions and why would this be so? Air may be assured to have a coefficient of
kinematic viscosity of 14.7 x 10-6
m2
/sand a mass density of 1.23 kg/m3
Determine
for each fluid, the pressure drop which would occur in 10m length of this pipeline.
Take f= 0.010 (Darcy's friction factor) for both fluids. [AU, May / June - 2016]
2.181) Water flows in a 150 mm diameter pipe and at a sudden enlargement, the loss of
head is found to be one-half of the velocity head in 150 mm diameter pipe. Determine
the diameter of the enlarged portion.
2.182) A 150mm diameter pipe reduces in diameter abruptly to 100mm diameter. If the
pipe carries water at 30 liters per second, calculate the pressure loss across the
contraction. The coefficient of contraction as 0.6. [AU, Nov / Dec - 2012]
2.183) A pipe line carrying oil of specific gravity 0.85, changes in diameter from
350mm at position 1 to 550mm diameter to a position 2, which is at 6m at a higher
level. If the pressure at position 1 and 2 are taken as 20N/cm2
and 15N/cm2
respectively and discharge through the pipe is 0.2m3
/s. Determine the loss of head.
[AU, May / June - 2007]

2.184) A pipe line carrying oil of specific gravity 0.87, changes in diameter from
200mm at position A to 500mm diameter to a position B, which is at 4m at a higher
level. If the pressure at position A and B are taken as 9.81N/cm2
and 5.886N/cm2
respectively and discharge through the pipe is 200 litres/s. Determine the loss of head
and direction of flow. [AU, Nov / Dec - 2008]
2.185) A 30cm diameter pipe of length 30cm is connected in series to a 20 cm diameter
pipe of length 20cm to convey discharge. Determine the equivalent length of pipe
diameter 25cm, assuming that the friction factor remains the same and the minor
losses are negligible. [AU, April / May - 2003]
2.186) A pipe of 0.6m diameter is 1.5 km long. In order of augment the discharge,
another line of the same diameter is introduced parallel to the first in the second half
of the length. Neglecting minor losses. Find the increase in discharge, if friction
factor f= 0.04. The head at inlet is 40m. [AU, Nov / Dec – 2004, 2005, 2012]
2.187) A pipe of 10 cm in diameter and 1000 m long is used to pump oil of viscosity
8.5 poise and specific gravity 0.92 at the rate of1200 lit./min. The first 30 m of the
pipe is laid along the ground sloping upwards at 10° to the horizontal and remaining
pipe is laid on the ground sloping upwards 15° to the horizontal. State whether the
flow is laminar or turbulent? Determine the pressure required to be developed by the
pump and the power required for the driving motor if the pump efficiency is 60%.
Assume suitable data for friction factor, if required. [AU, Nov / Dec - 2010]
2.188) Oil with a density of 900 kg/m3
and kinematic viscosity of 6.2 × 10-4
m2
/s is being
discharged by a 6 mm diameter, 40 m long horizontal pipe from a storage tank open
to the atmosphere. The height of the liquid level above the center of the pipe is 3 m.
Neglecting the minor losses, determine the flow rate of oil through the pipe.
[AU, Nov / Dec - 2011]
2.189) Oil at 27°C (ρ = 900 kg/m3
and µ = 40 centi poise) is flowing steadily in a
1.25cm diameter 40m long During the flow, the pressure at the pipe inlet and exit is
measured to be 8.25 bar and 0.95 bar, respectively. Determine the flow rate of oil
through the pipe assuming the pipe is [AU, Nov / Dec - 2014]
 Horizontal,
 Inclined 20º upward, and
 Inclined 20º downward.

2.190) A discharge of 30 liters / sec of oil (SG = 0.81) occurs downwards through a
conveying pipe line held inclined at 60° to the horizontal. The inlet diameter is 2cm
and the outlet diameter is 15cm and the length of the Pipe is 2m.If the pressure at the
top of the inlet is 0.8 kgf/cm2
, find the pressure at the outlet. Neglect the energy loss.
[AU, Nov / Dec - 2015]
2.191) The velocity of water in a pipe 200mm diameter is 5m/s. The length of the pipe
is 500m. Find the loss of head due to friction, if f = 0.008. [AU, Nov / Dec - 2005]
2.192) A 200mm diameter (f = 0.032) 175m long discharges a 65mm diameter water jet
into the atmosphere at a point which is 75m below the water surface at intake. The
entrance to the pipe is reentrant with ke = 0.92 and the nozzle loss coefficient is 0.06.
Find the flow rate and the pressure head at the base of the nozzle.
2.193) A pipe line 2000m long is used for power transmission 110kW is to be
transmitted through a pipe in which water is having a pressure of 5000kN/m2
at inlet
is flowing. If the pressure drop over a length of a pipe is 1000kN/m2
and coefficient
of friction is 0.0065, find the diameter of the pipe and efficiency of transmission.
[AU, May / June - 2012]
2.194) A horizontal pipe of 400 mm diameter is suddenly contracted to a diameter of
200 mm. The pressure intensities in the large and small pipe are given as 15 N/cm2
and 10 N/cm2
respectively. Find the loss of head due to contraction, if Cc = 0.62,
determine also the rate of flow of water.
2.195) A horizontal pipe line 40 m long is connected to a water tank at one end and
discharges freely into the atmosphere at the other end. For the first 25 m of its length
from the tank, the pipe is 150 mm diameter and its diameter is suddenly enlarged to
300 mm. The height of water level in the tank is 8 m above the centre of the pipe.
Considering all losses of head which occur, determine the rate of flow. Take f = 0.01
for both sections of the pipe. [AU, May / June - 2013]
2.196) A 15cm diameter vertical pipe is connected to 10cm diameter vertical pipe with
a reducing socket. The pipe carries a flow of 100 l/s. At a point 1 in 15cm pipe gauge
pressure is 250kPa. At point 2 in the 10cm pipe located 1m below point 1 the gauge
pressure is 175kPa.

 Find weather the flow is upwards /downwards
 Head loss between the two points [AU, Nov / Dec - 2008]
2.197) The rate of flow of water through a horizontal pipe is 0.25 m3
/sec. The diameter
of the pipe, which is 20 cm, is suddenly enlarged to 40 cm. The pressure intensity
in the smaller pipe is 11.7 N/cm2
. Determine the loss of head due to sudden
enlargement and pressure intensity in the larger pipe, power loss due to enlargement.
[AU, May / June - 2009]
2.198) In a city water supply systems, water is flowing through a pipe line 30cm in
diameter. The pipe diameter is suddenly reduced to 20cm. estimate the discharge
through the pipe if the difference across the sudden contraction is 5kPa.
2.199) Horizontal pipe carrying water is gradually tapering. At one section the diameter
is 150mm and the flow velocity is 1.5m/s. If the drop pressure is 1.104bar is reduced
section, determine the diameter of that section. If the drop is 5kN/m2
, what will be
the diameter – Neglect the losses? [AU, Nov / Dec - 2009]
2.200) The rate of flow of water through a horizontal pipe is 0.3m3
/sec. The diameter
of the pipe, which is 25cm, is suddenly enlarged to 50 cm. The pressure intensity in
the smaller pipe is 14N/cm2
. Determine the loss of head due to sudden enlargement,
pressure intensity in the larger pipe power lost due to enlargement.
[AU, Nov / Dec – 2003, 2016]
2.201) Water at 15°C ( ρ =999.1 kg/m3
andμ = 1.138 x 10-3
kg/m. s) is flowing steadily
in a30-m-long and 4 cm diameter horizontal pipe made of stainless steel at a rate of
8 L/s. Determine (i) the pressure drop, (ii) the head loss, and (iii) the pumping power
requirement to overcome this pressure drop. Assume friction factor for the pipe as
0.015. [AU, April / May - 2008]
2.202) The discharge of water through a horizontal pipe is 0.25m3/s. The diameter of
above pipe which is 200mm suddenly enlarges to 400mm at a point. If the pressure
of water in the smaller diameter of pipe is 120kN/m2
, determine loss of head due to
sudden enlargement; pressure of water in the larger pipe and the power lost due to
sudden enlargement. [AU, May / June - 2009]
2.203) A pipe of varying sections has a sectional area of 3000, 6000 and 1250 mm2
at
point A, B and C situated 16 m, 10 m and 2 m above the datum. If the beginning of

the pipe is connected to a tank which is filled with water to a height of 26 m above
the datum, find the discharge, velocity and pressure head at A, B and C. Neglect all
losses. Take atmospheric pressure as 10 m of water.
2.204) An existing 300mm diameter pipeline of 3200m length connects two reservoirs
having 13m difference in their water levels. Calculate the discharge Q1. If a parallel
pipe 300mm in diameter is attached to the last 1600m length of the above existing
pipe line, find the new discharge Q2. What is the change in discharge? Express it as
a % of Q1. Assume friction factor f = 0.14 in Darcy – Weisbach formula.
[AU, May / June - 2009]
2.205) Two reservoirs with a difference in water surface elevation of 15 m are
connected by a pipe line ABCD that consists of three pipes AB, BC and CD joined
in series. Pipe AB is 10 cm in diameter, 20 m long and has f = 0.02. Pipe BC is of
16 cm diameter, 25 m long and has f = 0.018. Pipe CD is of 12 cm diameter, 15 m
long and has f = 0.02. The junctions with the reservoirs and between the pipes are
abrupt. (a) Calculate the discharge (b) What difference in reservoir elevation is
necessary to have a discharge of 20 litres/sec? Include all minor losses.
2.206) Two reservoirs are connected by a pipe line consisting of a 400m long pipe of
20cm diameter in series with a 600m long pipe of 30cm diameter. The difference in
water level between the reservoirs is 8m. If friction factor for the bigger pipe is 0.01
and for the smaller pipe is 0.016, find the discharge. Account for all the losses.
Sketch the hydraulic grade line. [AU, Nov / Dec - 2015]
2.207) Two tanks of fluid ( ρ = 998 kg/m3
and µ = 0.001 kg/ms.) at 20°C are connected
by a capillary tube 4 mm in diameter and 3.5 m long. The surface of tank 1 is 30 cm
higher than the surface of tank 2. Estimate the flow rate in m3
/h. Is the flow laminar?
For what tube diameter will Reynolds number be 500?
[AU, Nov / Dec - 2013]
2.208) Three pipes of 400mm, 350mm and 300mm diameter connected in series
between two reservoirs. With difference in level of 12m. Friction factor is 0.024,
0.021 and 0.019 respectively. The lengths are 200m, 300m and 250m. Determine
flow rate neglecting the minor losses. [AU, Nov / Dec - 2009]
2.209) Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths450 m, 255
m and 315 m respectively are connected in series. The difference in water surface

levels in two tanks is 18 m. Determine the rate of flow of water if coefficients of
friction are 0.0075, 0.0078and 0.0072 respectively considering: the minor losses and
by neglecting minor losses. [AU, Nov / Dec - 2011]
2.210) Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths 300 m, 170
m and 210 m respectively are connected in series. The difference in water surface
levels in two tanks is 12 m. Determine the rate of flow of water if coefficients of
friction are 0.005, 0.0052 and 0.0048 respectively considering: the minor losses and
by neglecting minor losses [AU, May / June– 2012]
2.211) Three pipes connected in series to make a compound pipe. The diameters and
lengths of pipes are respectively, 0.4m, 0.2m, 0.3m and 400m, 200m, 300m. The
ends of the compound pipe are connected to 2 reservoirs whose difference in water
levels is 16m. The friction factor for all the pipes is same and equal to 0.02. The
coefficient of contraction is 0.6. Find the discharge through the compound pipe if,
minor losses are negligible. Also find the discharge if minor losses are included.
[AU, Nov / Dec - 2010]
2.212) Three pipes of 400 mm, 200 mm and 300 mm diameters have lengths of 400 m,
200 m and 300 m respectively. They are connected in series to make a compound
pipe. The ends of the compound pipe are connected with two tanks whose difference
of water levels is 16 m. If the coefficient of friction for these pipes is same and equal
to 0.005, determine the discharge through the compound pipe neglecting first the
minor losses and then including them. [AU, Nov / Dec – 2015, 2016]
2.213) A compound piping system consists of 1800 m of 0.5 m, 1200 m of 0.4 m and
600 m of 0.3 m new cast-iron pipes connected in series. Convert the system to (i) an
equivalent length of0.4 m diameter pipe and (ii) an equivalent size of pipe of 3600
m length. [AU, April / May - 2003]
2.214) A 100m long pipe line of 300mm in diameter contains two 90º elbows and two
gate valves (wide open). Calculate the equivalent pipe length and total loss of head
when the flow rate is 0.5m3
/s, f = 0.005, and the pipe has a sharp entry and exit.
2.215) A pipe line of 600 mm diameter is 1.5 km long. To increase the discharge,
another line of the same diameter is introduced parallel to the first in the second half
of the length. If f = 0.01 and head at inlet is 30 m, calculate the increase in discharge.

2.216) A pipe line of 0.6m diameter is 1.5Km long. To increase the discharge, another
line of same diameter is introduced in parallel to the first in second half of the length.
Neglecting the minor losses, find the increase in discharge if 4f = 0.04. The head at
inlet is 30cm. [AU, April / May - 2011]
2.217) A pipe line of 0.6m diameter is 1.5Km long. To increase the discharge, another
line of same diameter is introduced in parallel to the first in second half of the length.
Neglecting the minor losses, find the increase in discharge if Darcy’s friction factor
0.04. The head at inlet is 300mm. [AU, April / May - 2015]
2.218) Two pipes of 15cm and 30cm diameters are laid in parallel to pass a total
discharge of 100 litres per second. Each pipe is 250m long. Determine discharge
through each pipe. Now these pipes are connected in series to connect two tanks
500m apart, to carry same total discharge. Determine water level difference between
the tanks. Neglect the minor losses in both cases, f=0.02 fn both pipes.
[AU, May / June - 2007]
2.219) Two pipes of diameter 40 cm and 20 cm are each 300 m long. When the pipes
are connected in series and discharge through the pipe line is0.10 m3
/sec, find the
loss of head incurred. What would be the loss of head in the system to pass the same
total discharge when the pipes are connected in parallel? Take f = 0.0075 for each
pipe. [AU, May / June – 2007, 2012, Nov / Dec - 2010]
2.220) Two pipes each 200m long are available for connections to reservoir from which
a flow of 0.090 m3
/s is required. If the diameters of the pipes are 0.30m and 0.15m
respectively, determine the ratio of head lost when the pipes are connected in series
to the head lost when they are connected in parallel. Neglect minor losses.
2.221) A main pipe divides into two parallel pipes, which again forms one pipe. The
length and diameter for the first parallel pipe are 2000m and 1m respectively, while
the length and diameter of second parallel pipe are 200m and 0.8m respectively. Find
the rate of flow in each parallel pipe, if total flow in the main is 3m3
/s. The coefficient
of friction for each parallel pipe is same and equal to 0.005.
2.222) The main pipe is divided into two parallel pipes which again forms one pipe, the
first parallel pipe has length of 1000 m and diameter of 0.8 m. The second parallel

pipe has length of 1000 m and diameter of 0.6 m. The coefficient friction for each
parallel pipe is 0.005. If the total rate of flow in the main pipe is 2 m3
/sec, find the
rate of flow in each parallel pipe. [AU, May / June - 2014]
2.223) For a town water supply, a main pipe line of diameter 0.4 m is required. As pipes
more than 0.35m diameter are not readily available, two parallel pipes of same
diameter are used for water supply. If the total discharge in the parallel pipes is same
as in the single main pipe, find the diameter of parallel pipe. Assume co-efficient of
discharge to be the same for all the pipes. [AU, April / May - 2010]
2.224) A pipeline conveys 10 lit/s of water from an overhead tank to a building. The
pipe is 2km long and 15cm diameter, the friction factor is 0.03. It is planned to
increase the discharge by 30% by installing another pipeline in parallel with this over
half the length. Find the suitable diameter of pipe to be installed. Is there any upper
limit on discharge augmentation by this arrangement? [AU, Nov / Dec - 2012]
2.225) Two pipes of identical length and material are connected in parallel. The
diameter of pipe A is twice the diameter of pipe B. Assuming the friction factor to
be the same in both cases and disregarding minor losses, determine the ratio of the
flow rates in the two pipes. [AU, April / May - 2008]
2.226) A pipe line 30cm in diameter and 3.2m long is used to pump up 50Kg per second
of oil whose density is 950 Kg/m3
and whose kinematic viscosity is 2.1 strokes, the
center of the pipe line at the upper end is 40m above than the lower end. The
discharge at the upper end is atmospheric. Find the pressure at the lower end and
draw the hydraulic gradient and total energy line. [AU, April / May - 2011]
2.227) Two water reservoirs A and B are connected to each other through a 50 m long,
2.5 cm diameter cast iron pipe with a sharp-edged entrance. The pipe also involves
a swing check valve and a fully open gate valve. The water level in both reservoirs
is the same, but reservoir A is pressurized by compressed air while reservoir B is
open to the atmosphere. If the initial flow rate through the pipe is 1.5 l/s, determine
the absolute air pressure on top of reservoir A. Take the water temperature to be
25°C. [AU, Nov / Dec - 2011]
2.228) Water at 15 °C is to be discharged from a reservoir at a rate of 20 L/s using two
horizontal cast iron pipes connected in series and a pump between them. The first
pipe is 22m long and has a 6 cm diameter, while the second pipe is 33 m long and

has a 4 cm diameter. The water level in the reservoir is 30 m above the center line of
the pipe. The pipe entrance is sharp-edged, and losses associated with the connection
of the pump are negligible. Determine the required pumping head and the minimum
pumping power to maintain the indicated flow rate. The density and dynamic
viscosity of water at 15 °C are ρ = 999.1 kg/m3
and μ= 1.138 x 10-3
kg/ms. The
roughness of cast iron pipes is 0.00026 m. [AU, May / June - 2016]
2.229) When water is being pumped is a pumping plant through a 600mm diameter
main, the friction head was observed as 27m. In order to reduce the power
consumption, it is proposed to lay another main of appropriate diameter along the
side of existing one, so that the two pipes will work in parallel for the entire length
and reduce the friction head to 9.6m only. Find the diameter of the new main if with
the exception of diameter; it is similar to the existing one in all aspects.
[AU, Nov / Dec - 2007]
2.230) Kerosene (SG = 0.810) at a temperature of 22ºC flows in a 75-mm diameter
smooth brass pipeline at a rate of 0.90 lit/s. Find the friction head loss per meter, For
the same head loss, what would be the flow rate if the temperature of the kerosene
were raised to 40°C? [AU, Nov / Dec - 2014]
2.231) Determine the
 Pressure gradient
 The shear stress at the two horizontal parallel plates and
 Discharge per meter width for the laminar flow of oil with maximum
velocity 2m/s between two horizontal parallel fixed plates which are
10cm apart. Given μ = 2.4525 Ns/m2
2.232) In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway
between the wall surface and the centerline) is measured to be 6 m/s. Determine the
velocity at the center of the pipe. [AU, April / May - 2008]
2.233) A smooth two –dimensional flat plate is exposed to a wind velocity of 100 km/h.
If laminar boundary layer exists up to a value of Rexequal to 3 x 105
, find the
maximum distance up to which laminar boundary layer exists and find its maximum
thickness. Assume kinematic viscosity of air as 1.49 x 10-5
m2
/sec.

2.234) Air is flowing over a flat plate with a velocity of 5 m/s. The length of the plate
is 2.5 m and width 1 m. The kinematic viscosity of air is given as 0.15 x 10-4
m2
/s.
Find the
(i) boundary layer thickness at the end of plate
(ii) shear stress at 20 cm from the leading edge
(iii) shear stress at 175 cm from the leading edge
(iv) Drag force on one side of the plate.
(v) Take the velocity profile
𝑢
𝑈
=
3
2
(
𝑦
𝛿
) −
1
2
(
𝑦
𝛿
)
3
over a plate as and the
density of air1.24 kg/m3
.
2.235) A plate of 600mm length and 400mm wide is immersed in a fluid of specific
gravity 0.9 and kinematic viscosity of = 10-4
m2
/s. The fluid is moving with velocity
of 6m/s. Determine
 Boundary layer thickness
 Shear stress at the end of the plate
 Drag force on one side of the plate. [AU, Nov / Dec - 2012]
2.236) Water at 20° C enters a pipe with a uniform velocity (U) of 3m/s. What is the
distance at which the transition (x) occurs from a laminar to a turbulent boundary
layer? If the thickness of this initial laminar boundary layer is given by 4.91√(vx/U)
what is its thickness at the point of transition?(v – kinematic viscosity).
2.237) A hydraulic lift shaft of 450 mm diameter moves in a cylinder of 451 mm
diameter with the length of engagement of 3 m. The interface is filled with oil of
kinematic viscosity of 2.5 x 10-4
m2
/s and density of 900 kg/m3
Determine the
uniform velocity of movement of the shaft if the drag resistance was 320 N.
[AU, May / June - 2016]
2.238) A flat plate 1.5 m x 1.5 m moves at 50 km/h in stationary air of density 1.15
kg/m3
. If the co-efficient of drag and lift are 0.15 and 0.75 respectively, determine
the
(i) Lift force
(ii) Drag force
(iii) The resultant force and

(iv) The power required to set the plate in motion. [AU, Nov / Dec - 2007]
2.239) A jet plane which weighs 29430 N and has the wing area of 20m2
flies at the
velocity of 250km/hr. When the engine delivers 7357.5kW. 65% of power is used to
overcome the drag resistance of the wing. Calculate the coefficient of lift and
coefficient of drag for the wing. Take density of air = 1.21 kg/m3
[AU, May / June - 2009]
2.240) For the velocity profile in laminar boundary layer as u/U = 3/2 (y/δ)-1/2(y/δ)3
.
Find the thickness of the boundary layer and shear stress, 1.8m from the leading edge
of a plate. The plate is 2.5 m long and 1.5 m wide is placed in water, which is moving
with a velocity of 15 cm/sec. Find the drag on one side of the plate if the viscosity
of water is 0.01 poise. [AU, Nov / Dec - 2003]
2.241) Consider flow of oil through a pipe of 0.3m diameter. The velocity distribution
is parabolic with maximum velocity of 3 m/s at the pipe centre. Estimate the shear
stress at the pipe wall and within the fluid 50mm from the pipe wall. The viscosity
of the oil is 1.7Pa.s. [AU, Nov / Dec - 2012]
2.242) The velocity distribution in the boundary layer is given by u/U = y/δ, where u is
the velocity at the distance y from the plate u = U at y = δ, δ being boundary layer
thickness. Find the displacement thickness, momentum thickness and energy
thickness. [AU, April / May - 2010]
2.243) Find the displacement thickness, the momentum thickness, and energy thickness
for the velocity distribution in the boundary layer given by
𝑢
𝑈
= 2
𝑦
𝛿
− (
𝑦
𝛿
)
2
[AU, Nov / Dec - 2016]
2.244) If the velocity distribution in a laminar boundary layer over a flat plate is given
by 𝑢/𝑈∞ = sin(𝜋/2 𝑦 /𝛿), calculate the value of 𝛿, 𝛿∗
, 𝜃 and shear stress.
2.245) Water at 20°C flow through a 160mm diameter pipe with roughness of 0.016
mm. If the mean velocity is 6 m/s, what is the nominal thickness of the viscous sub-
layer? What will be the viscous sub -layer if the velocity is increased to 7.2 m/s?
[AU, Nov / Dec - 2014]

2.246) The flow rate in a 260mm diameter pipe is 220 litres/sec. The flow is turbulent,
and the centerline velocity is 4.85m/s. Plot the velocity profile, and determine the
head loss per meter of pipe. [AU, April / May - 2011]
2.247) An oil of viscosity 0.9Pa.s and density 900kg/m3
flows through a pipe of 100mm
diameter. The rate of pressure drop for every meter length of pipe is 25kPa. Find the
oil flow arte, drag force per meter length, pumping power required to maintain the
flow over a distance of 1km, velocity and shear stress at 15, from the pipe wall.
[AU, Nov / Dec - 2010]
2.248) Shell-and-tube heat exchangers with hundreds· of tubes housed in a shell are
commonly used in practice for heat transfer between two fluids. Such a heat
exchanger used in· an active solar hot-water system transfers heat from a water
antifreeze solution flowing through the shell and the solar collector to fresh water
flowing through the tubes at an average temperature of 60 °C at a rate of 15 L/s. The
heat exchanger contains 80 brass tubes 1 cm in inner diameter and 1.5 m in length.
Disregarding inlet, exit and header losses, determine the pressure drop across a single
tube and the pumping power required by the tube-side fluid of the heat exchanger.
The density and dynamic viscosity of water at 60°C are ρ = 983.3 kg/m3
and μ =
0.467 x 10-3
kg/m s, respectively. The roughness of brass tubing is 1.5 x 10-6
m.
[AU, May / June - 2016]
2.249) Consider the flow of a fluid with viscosity m through a circular pipe. The
velocity profile in the pipe is given as where is the maximum flow velocity, which
occurs at the centerline; r is the radial distance from the centerline; is the flow
velocity at any position r; and R is the Reynold's number. Develop a relation for the
drag force exerted on the pipe wall by the fluid in the flow direction per unit length
of the pipe. [AU, April / May - 2008]
umax
u(r) = umax(1-r / R )n n
R
r
o

2.250) Velocity components in flow are given by U = 4x, V = -4y. Determine the stream
and potential functions. Plot these functions for φ 60, 120, 180, and 240 and Ф 0, 60,
120, 180, +60, +120, +180. Check for continuity. [AU, Nov / Dec - 2009]
2.251) A fluid of specific gravity 0.9 flows along a surface with a velocity profile given
by v = 4y - 8y3m/s, where y is in m. What is the velocity gradient at the boundary?
If the kinematic viscosity is 0.36S, what is the shear stress at the boundary?
[A.U. Nov / Dec - 2008]
2.252) In a two dimensional incompressible flow the fluid velocities are given by u = x
– ay and v = - y – 4x. Show that the velocity potential exists and determine its form.
Find also the stream function. [AU, May / June - 2009]
2.253) A smooth flat plate with a sharp leading edge is placed along a free stream of
water flowing at 3m/s. Calculate the distance from the leading edge and the boundary
thickness where the transition from laminar to turbulent- flow may commence.
Assume the density of water as 1000 kg/m3
and viscosity as 1centipoise.
2.254) A smooth two dimensional flat plate is exposed to a wind velocity of 100 km/hr.
If laminar boundary layer exists up to a value of RN
= 3 x105
, find the maximum
distance up to which laminar boundary layer persists and find its maximum
thickness. Assume kinematic viscosity of air as 1.49x10-5
m2
/s.
[AU, Nov / Dec - 2008]
2.255) A power transmission pipe 10 cm diameter and 500 m long is fitted with a nozzle
at the exit, the inlet is from a river with water level 60 m above the discharge nozzle.
Assume f = 0.02, calculate the maximum power which can be transmitted and the
diameter of nozzle required. [AU, Nov / Dec - 2008]

UNIT - III - DIMENSIONAL ANALYSIS
PART - A
3.1) What do you understand by fundamental units and derived units?
3.2) Differentiate between fundamental units and derived units. Give examples.
[AU, Nov / Dec - 2011]
3.3) State the application of dimensional numbers and mention its significance.
[AU, May / June - 2016]
3.4) Define dimensional analysis.
3.5) What do you mean by dimensional analysis? [AU, Nov / Dec - 2009]
3.6) Brief on dimensional variables with examples. [AU, Nov / Dec - 2014]
3.7) Brief on Intuitive method. Give some examples. [AU, Nov / Dec - 2014]
3.8) Define dimensional homogeneity. [AU, Nov / Dec - 2015]
3.9) What is dimensional homogeneity and write any one sample equation?
[AU, Nov / Dec - 2006]
3.10) Explain the term dimensional homogeneity. [AU, Nov / Dec - 2011]
3.11) Give the methods of dimensional analysis.
3.12) State the methods of dimensional analysis. [AU, Nov / Dec - 2016]
3.13) State a few applications, usefulness of dimensional analysis.
[AU, May / June - 2007]
3.14) Give the applications of dimensional analysis. [AU, Nov / Dec - 2015]
3.15) What are the limitations of dimensional analysis? [AU, Nov / Dec - 2016]
3.16) What is a dimensionally homogenous equation? Give example.
[AU, Nov / Dec - 2003]
3.17) Cite examples for dimensionally homogeneous and non-homogeneous equations.
[AU, Nov / Dec - 2010]
3.18) Check whether the following equation is dimensionally homogeneous.
Q =Cd .a √(2 gh) . [AU, April / May - 2011]
3.19) Define Rayleigh's method.
3.20) Give the Rayleigh method to determine dimensionless groups.
[AU, Nov / Dec - 2011]

3.21) State any two choices of selecting repeating variables in Buckingham π theorem.
3.22) State Buckingham’s π theorem.
[AU, Nov / Dec – 2008, 2012, April / May – 2015, 2017]
3.23) State Buckingham’s π theorem. Why this method is considered superior to
Rayleigh’s method? [AU, Nov / Dec - 2016]
3.24) What is Buckingham's π theorem?
3.25) The excess pressure Δp inside a bubble is known to be a function of the surface
tension and the radius. By dimensional reasoning determine how the excess pressure.
Will vary if we double the surface tension and the radius.
[AU, Nov / Dec - 2013]
3.26) Distinguish between Rayleigh's method and Buckingham's π- theorem.
3.27) Under what circumstances, will Buckingham’s π theorem yield incorrect number
of dimensionless group?
3.28) State a few applications / usefulness of dimensional analysis.
3.29) Define Euler's number. [AU, May / June - 2009]
3.30) List out any four rules to select repeating variable.
3.31) Define similitude. [AU, April / May - 2017]
3.32) Give the three types of similarities.
3.33) What are the types of similarities? [AU, Nov / Dec - 2012]
3.34) Explain the types of similarities. [AU, April / May - 2017]
3.35) Define geometric similarity.
3.36) Define kinematic similarity.
3.37) What is meant by kinematic similarity?
3.38) Define dynamic similarity.
3.39) What is meant by dynamic similarity? [AU, Nov / Dec - 2008]
3.40) What is dynamic similarity? [AU, Nov / Dec - 2009]
3.41) What is similarity in model study? [AU, April / May - 2005]
3.42) What is scale effect in physical model study?
[AU, Nov / Dec – 2005, 2006, May / June– 2012]

3.43) If two systems (model and prototype) are dynamically similar, is it implied that
they are also kinematically and geometrically similar? [AU, May / June - 2012]
3.44) Distinguish between a control and differential control volume.
3.45) Mention the circumstances which necessitate the use of distorted models.
[AU, Nov / Dec - 2010]
3.46) What is the effect of scale effect and distorted model in dimensional analysis?
[AU, May / June - 2016]
3.47) Give the types of forces in a moving fluid.
3.48) Give the dimensions of power and specific weight. [AU, Nov / Dec - 2009]
3.49) Define inertia force.
3.50) Define viscous force.
3.51) Define gravity and pressure force.
3.52) Define surface tension force.
3.53) Define dimensionless numbers.
3.54) Give the types of dimensionless numbers.
3.55) Give the dimensions of the following physical quantities: surface tension and
dynamic viscosity. [AU, May / June - 2013]
3.56) Write the dimensions of surface tension and vapour pressure in MLT system.
3.57) Define Reynold’s number. What its significance? [AU, Nov / Dec - 2010]
3.58) Define Reynold’s number and state its significance? [AU, April / May - 2015]
3.59) Define Reynold’s number and Froude’s numbers. [AU, Nov / Dec – 2007, 2011]
3.60) Derive the expression for Reynolds's Number. [AU, Nov / Dec - 2015]
3.61) Define the Froude's dimensionless number. [AU, May / June - 2014]
3.62) Define Froude's number.
[AU, Nov / Dec – 2005, 2009, 2008, April / May – 2010, May / June - 2012]
3.63) State Froude's model law. [AU, May / June - 2013]
3.64) Brief on Euler number. [AU, May / June - 2016]
3.65) Define Euler number and Mach number. [AU, May / June - 2007]
3.66) Define Reynold’s number and Mach number. [AU, Nov / Dec - 2012]
3.67) Define Mach number. [AU, May / June - 2009]

3.68) What is Mach number? Mention its field of use. [AU, April / May - 2003]
3.69) Define Mach's number and mention its field of use.
3.70) Define -Mach number and state its application. [AU, Nov / Dec - 2014]
3.71) Write the expression for Mach number and state its applications.
3.72) Write down the dimensionless number for pressure. [AU, Nov / Dec - 2011]
3.73) What are the similitudes that should exist between the model and its prototype?
3.74) Derive the scale ratio for velocity and pressure intensity using Froude model law.
[AU, Nov / Dec - 2016]
3.75) What is Thoma’s Cavitation factor? [AU, April / May - 2017]
PART - B
3.76) Discuss on Buckingham's π theorem. [AU, Nov / Dec - 2014]
3.77) What is repeating variables? How are these selected? [AU, May / June - 2007]
3.78) Discuss on the applications of dimensionless parameters. [AU, Nov / Dec - 2014]
3.79) Define similitude and explain its types. [AU, Nov / Dec - 2016]
3.80) State the similarity laws used in model analysis. [AU, April / May - 2010]
3.81) Explain similitude with types of similarities [AU, Nov / Dec - 2015]
3.82) State and explain the various laws of similarities between model and its prototype.
3.83) What is meant by geometric, kinematic and dynamic similarities?
[AU, May / June – 2007, 2014]
3.84) What is meant by geometric, kinematic and dynamic similarities? Are these
similarities truly attainable? If not, why? [AU, May / June - 2009]
3.85) Enumerate the different laws on which models are designed for dynamic
similarity. Where are they used? [AU, May / June - 2016]
3.86) Explain the different types of similarities exist between a proto type and its model.
[AU, Nov / Dec - 2003]
3.87) What is distorted model and also give suitable example?
3.88) What are distorted models? State merits and demerits. [AU, May / June - 2014]

3.89) What are distorted models? What are their advantages and disadvantages?
[AU, Nov / Dec - 2015]
3.90) Write briefly about (i) distorted models (ii) undistorted models and (iii) scale
effect in model. [AU, April / May - 2017]
3.91) Define dimensional homogeneity and also give example for homogenous
equation. [AU, April / May - 2005]
3.92) Classify Models with scale ratios. [AU, Nov / Dec - 2009]
3.93) Derive on the basis of dimensional analysis suitable parameters to present the
thrust developed by a propeller. Assume that the thrust P depends upon the angular
velocity ω , speed of advance V, diameter D, dynamic viscosity μ, mass density ρ ,
elasticity of the fluid medium which can be denoted by the speed of sound in the
medium C. [AU, Nov / Dec – 2011, 2012]
3.94) Check the following equations are dimensionally homogenous
 Drag force = ½ ( Cd ρU2
A) where Cd is coefficient of drag which is
constant
 F = γQ ( U1 – U2) / g – ( P1A1 – P2A2)
 Total energy per unit mass = v2
/2 + gz + P/ρ
 Q = δ / 15Cd tan(θ/2) √(2g) * (H)5/2
where Cd is coefficient of discharge
constant [AU, April / May - 2004, 2010, Nov / Dec - 2005]
3.95) Derive five different types of dimensionless numbers. [AU, Nov / Dec - 2016]
3.96) Define and explain Reynold’s number, Froude’s number, Euler’s number and
Mach’s number. [AU, Nov / Dec - 2003]
3.97) What are the significance and the role of the following parameters?
 Reynolds number
 Froude number
 Mach number
 Weber number. [AU, April / May - 2011]
3.98) Define the following dimensionless numbers and state their significance for fluid
flow problems. [AU, May / June - 2014]
 Reynolds number
 Mach number
3.99) Explain the Reynolds model law and state its applications.

3.100) Use dimensionless analysis to arrange the following groups into dimensionless
parameters; ∆p, V, γ, g and f, ρ, L, V use MLT system. [AU, April / May - 2011]
3.101) Use dimensional analysis and the MLT system to arrange the following into a
dimensionless number: L, ρ , µ and a. [AU, Nov / Dec - 2013]
3.102) Consider force F acting on the propeller of an aircraft, which depends upon the
variable U, ρ, μ, D and N. Derive the non – dimensional functional form F/(ρU2
D2
)
= f ((UDρ/μ),(ND/U)) [AU, Nov / Dec - 2003]
3.103) The frictional torque T of a disc diameter D rotating at a speed N in a fluid of
viscosity μ and density ρ in a turbulent flow is given by
T = D5
N2
ρ Ф[μ/D2
Nρ]. Prove this by Buckingham’s π theorem.
[AU, Nov / Dec - 2003]
3.104) Resistance R, to the motion of a completely submerged body is given by R =
ρv2
l2
φ(VL/γ), where ρ and γ are the mass density and kinematic viscosity of the fluid;
v– velocity of flow; l – length of the body. If the resistance of a one – eighth scale
air - ship model when tested in water at 12m/s is 22N, what will be the resistance of
the air –ship at the corresponding aped, in air? Assume kinematic viscosity of air is
13times that of water and density of water is 810 times of air.
3.105) The resisting force R to a supersonic plane during flight can be considered as
dependent upon the length of the aircraft l, velocity V, air viscosity m, air density
and bulk modulus of air K. Express the functional relationship between these
variables and the resisting force.
3.106) The resisting force F of a plane during flight can be considered as dependent
upon the length of aircraft (l), velocity (v), air viscosity (μ), air density (ρ) and bulk
modulus of air (K). Express the functional relationship between these variables using
dimensional analysis. Explain the physical significance of the dimensionless groups
arrived. [AU, Nov / Dec - 2010]
3.107) Derive an expression for the shear stress at the pipe wall when an incompressible
fluid flows through a pipe under pressure. Use dimensional analysis with the
following significant parameters: pipe diameter D, flow velocity V, and viscosity µ
and density ρ of the fluid. [AU, Nov / Dec - 2013]

3.108) The resistance R, to the motion of a completely submerged body depends upon
the length of the body (L), velocity of flow (V), mass density of fluid (ρ), kinematic
viscosity (γ). Prove by dimensional analysis that
R = ρV2
L2
φ(VL/γ) [AU, May / June - 2009]
3.109) Obtain a relation using dimensional analysis, for the resistance to uniform
motion of a partially submerged body in a viscous compressible fluid.
[AU, Nov / Dec - 2014]
3.110) Using Buckingham π method of dimensional analysis obtain an expression for
the drag force R on a partially submerged body moving with a relative velocity V in
a fluid; the other variables being the linear dimension L, height of surface roughness
K, Fluid density ρ and the gravitational acceleration g. [AU, April / May - 2015]
3.111) The drag resistance R to motion of a high velocity projectile may be expressed
by a homogenous equation of the form F(R, μ, C, P, V, D) = 0. Where C = velocity
of sound in the fluid medium D = diameter of the projectile. By dimensional analysis,
find an expression for R as a function of standard non dimensional numbers
connected with the problem. [AU, April / May - 2017]
3.112) The power developed by hydraulic machines is found to depend on the head h,
flow rate Q, density ρ, speed N, runner diameter D, and acceleration due to gravity
g. Obtain suitable dimensionless parameters to correlate experimental results.
[AU, Nov / Dec – 2011, 2014]
3.113) Show that the power P developed in a water turbine can be expressed as:
Where, ρ = Mass density of the liquid,
N = Speed in rpm,
D = Diameter of the runner,
B = Width of the runner and
µ = Dynamic viscosity [AU, Nov / Dec - 2011]
3.114) The capillary rise h is found to be influenced by the tube diameter D, density ρ,
gravitational acceleration g and surface tension σ. Determine the dimensionless
parameters for the correlation of experimental results. [AU, Nov / Dec - 2011]

3.115) Using dimensional analysis, obtain a correlation for the frictional torque due to
rotation of a disc in a viscous fluid. The parameters influencing the torque can be
identified as the diameter, rotational speed, viscosity and density of the fluid.
[AU, Nov / Dec - 2011]
3.116) The drag force on a smooth sphere is found to be affected by the velocity of flow,
u, the diameter D of the sphere and the fluid properties density ρ and viscosity μ.
Find the dimensionless groups to correlate the parameters. [AU, Nov / Dec - 2011]
3.117) The discharge Q through a pump depends on the brake horse power P, the
diameter d , speed in rpm N, the energy to be imparted per unit mass gH, the dynamic
viscosity μ and specific mass ρ. Find the dimensionless parameters affecting the
phenomenon. [AU, Nov / Dec - 2015]
3.118) State Buckingham's π - theorem. What do you mean by repeating variables? How
are the repeating variables selected in dimensional analysis?
3.119) State Buckingham's π - theorem. What are the considerations in the choice of
repeating variables? [AU, April / May - 2010]
3.120) Express efficiency in terms of dimensionless parameters using density,
viscosity, angular velocity, diameter of rotor and discharge using Buckingham π
theorem. [AU, Nov / Dec - 2009]
3.121) State the Buckingham π theorem. What are the criteria for selecting repeating
variable in this dimensional analysis? [AU, Nov / Dec - 2009]
3.122) State Buckingham – π theorem. Mention the important principle for selecting
the repeating variables. [AU, May / June - 2009]
3.123) State and prove Buckingham π theorem.
[AU, Nov / Dec – 2009, April / May - 2010]
3.124) Using Buckingham’s π- theorem show that the velocity through a circular orifice
is given by 𝑉 = √(2𝑔𝐻) 𝜑 [
𝐷
𝐻
,
𝜇
𝜌𝑉𝐻
]
Where H is the head causing the flow
D is the diameter of the orifice
μ is the coefficient of viscosity
ρ is the mass density

g is the acceleration due to gravity
[AU, Nov / Dec - 2008, 2015, April / May - 2010, 2017]
3.125) The pressure difference ∆P in a pipe of diameter D and length l due to turbulent
flow depends on the velocity V, viscosity µ, density ρ and roughness k. Using
Buckingham's π theorem, obtain an expression for Δp. [AU, Nov / Dec - 2016]
3.126) The efficiency (η) of a fan depends on ρ (density), μ (viscosity) of the fluid, ω
(angular velocity), d (diameter of rotor) and Q (discharge). Express η in terms of
non-dimensional parameters. Use Buckingham's theorem.
[AU, April / May - 2010, 2011, Nov / Dec - 2016]
3.127) The efficiency (η) of a fan depends on ρ (density), μ (viscosity) of the fluid, ω
(angular velocity), d(diameter of rotor) and Q(discharge). Express η in terms of non-
dimensional parameters. Use Rayleigh’s method. [AU, April / May - 2015]
3.128) The pressure difference Δp in a pipe of diameter D and length L due to viscos
flow depends on the velocity V, viscosity µ and density ρ. Using Buckingham's π
theorem, obtain an expression for Δp. [AU, May / June – 2014, April / May - 2015]
3.129) The power required by the pump is a function of discharge Q, head H,
acceleration due to gravity g, viscosity μ, mass density of the fluid ρ, speed of
rotation N and impeller diameter D. Obtain the relevant dimensionless parameters.
[AU, May / June - 2012]
3.130) State Buckingham's π -theorem. The discharge of a centrifugal pump (Q) is
dependent on N (speed of pump), d (diameter of impeller), g (acceleration due to
gravity), H (manometric head developed by pump) and ρ and µ (density and dynamic
viscosity of the fluid). Using the dimensional analysis and Buckingham's π -theorem,
prove that it is given by [AU, May / June - 2013]
𝑄 = 𝑁𝑑3
𝑓 (
𝑔𝐻
𝑁2 𝑑2
,
𝜇
𝑁𝑑2 𝜌
)
3.131) Consider viscous flow over a very small object. Analysis of the equations of
motion shows that the inertial terms are much smaller than viscous and pressure
terms. Fluid density drops out, and these are called creeping flows. The only
important parameters are velocity U, viscosity µ, and body length scale d. For three-
dimensional bodies,. Like spheres, creeping flow analysis yields very good results.
It is uncertain, however, if creeping flow applies to two-dimensional bodies, such as

cylinders, since even though the diameter may be very small, the length of the
cylinder is infinite. Let us see if dimensional analysis can help. (1) Apply the Pi
theorem to two-dimensional drag force F2-D, as a function of the other parameters.
Be careful: two-dimensional drag has dimensions of fake per unit length, not simply
force. (2) Is your analysis in part (1) physically plausible? If not, explain why not.
(3) It turns out that fluid density ρ cannot be neglected in analysis of creeping flow
over two dimensional bodies. Repeat the dimensional analysis, this time including ρ
as a variable, and find the resulting non dimensional relation between the parameters
in this problem. [AU, Nov / Dec - 2013]
3.132) Oil is moved up in a lubricating system by a rope dipping in the sump containing
oil and moving up. The quantity of oil pumped Q, depends on the speed u of the
rope, the layer thickness 6, the density and viscosity of the oil and acceleration due
to gravity. Obtain the dimensionless parameters to correlate the flow.
[AU, Nov / Dec - 2014]
3.133) When fluid in a pipe is accelerated linearly from rest, it begins as laminar flow
and then undergoes transition to turbulence at a time t, which depends upon the pipe
diameter D, fluid acceleration a, density ρ and viscosity µ. Arrange this into a
dimensionless relation between t and D. [AU, Nov / Dec - 2013]
3.134) The temperature difference θ at a location x at time τ in a slab of thickness L
originally at a temperature difference θ0 with outside is found to depend on the
thermal diffusivity α. thermal conductivity k and convection coefficient h. Using
dimensional analysis determine the dimensionless parameters to correlate the
situation. [AU, May / June - 2016]
3.135) Convective heat transfer coefficient in free convection over a surface is found to
be influenced by the density, viscosity, thermal conductivity, coefficient of cubical
expansion, temperature difference, gravitational acceleration, Specific heat, the
height of surface and the flow velocity. Using dimensional analysis, determine the
dimensionless parameters that will correlate the phenomenon.
[AU, May / June - 2016]
3.136) What are the similarities between model and prototype? Mention the
applications of model testing. [AU, May / June - 2013]

PROBLEMS
3.137) Find the discharge through a weir model by knowing the discharge over the
actual (proto type) weir is measured as 1.5m3
/s. The horizontal dimension of the
model = 1/50 of the horizontal dimensions of the proto type and the vertical
dimension of the model = 1/10 of the vertical dimension of the proto type. (Hint:
Apply Froude model law) [AU, April / May - 2004]
3.138) Model of an air duct operating with water produces a pressure drop of 10 kN/m2
over 10 m length. If the scale ratio is 1/50. Density of water is 1000 kg/m3
and density
of air is 1.2 kg/m3
. Viscosity of water is 01.001 Ns/m2
and viscosity of air 0.00002
Ns/m2
. Estimate corresponding drop in a 20m long air duct.
3.139) A model of a hydroelectric power station tail race is proposed to build by
selecting vertical scale 1 in 50 and horizontal scale 1 in 100. If the design pipe has
flow rate of 600m3
/s and allow the discharge of 800m3
/s. Calculate the corresponding
flow rates for the model testing. [AU, April / May - 2005]
3.140) Model studies are done on a 1/5 scale model at 1200 rpm. The head developed
and power input were found to be 10m and 4.5 kW respectively. The discharge was
found to be 35 litres/sec. Find the efficiency. If the prototype runs at 360rpm, find
the head developed, discharge and power required for the prototype.
[AU, Nov / Dec - 2015]
3.141) A pipe of diameter 1.5 m is required to transport an oil of specific gravity 0.90
and viscosity 3 * 10-2
poise at the rate 3000 litre / sec. Test where conducted on a
15cm diameter pipe using water at 20º C. Find the velocity and the rate of flow in
model. Viscosity of water at 20ºC = 0.01poise. [AU, Nov / Dec - 2012]
3.142) In order to predict the pressure in a large air duct model is constructed with linear
dimensions (1/10)th
that of the prototype and the water was used as the testing fluid.
If water is 1000 times denser than that of air and has 100 times the viscosity of air,
determine the pressure drop in the prototype, for the conditions corresponding to a
pressure drop of 70kPa, in the model. [AU, May / June - 2009]
3.143) In an aero plane model of size 1/10 of its prototype, the pressure drop is
7.5kN/m2
. The model is tested in water; find the corresponding drop in prototype.

Assume density of air = 1.24kg/m3
; density of water = 1000kg/m3
; viscosity of air =
0.00018 poise; viscosity of water = 0.01 poise. [AU, May / June - 2007]
3.144) The pressure drop in an airplane model of size 1/10 of its prototype is 80N/cm2
.
The model is tested in water. Find the corresponding pressure drop in the prototype.
Take density of air = 1.24 kg/m3
. The viscosity of water is 0.01 poise while viscosity
of air is 0.00018 poise. [AU, Nov / Dec - 2016]
3.145) A geometrically similar model of an air duct is built to 1/25 scale and tested with
water which is 50 times more viscous and 800 times denser than air. When tested
under dynamically similar conditions, the pressure drop is 200 kN/m2
in the model.
Find the corresponding pressure drop in the full scale prototype and express in cm
of water. [AU, Nov / Dec – 2010, May / June - 2014]
3.146) Model tests have conducted to study the energy losses in a pipe line of 1m
diameter required to transport kerosene of specific gravity 0.80 and dynamic
viscosity 0.02 poise at the rate of 2000 litre/sec. Tests were conducted on a 10cm
diameter pipe using water at 20°C. What is the flow rate in the model? If the energy
head loss in 30m length of the model is measured as 44cm of water, what will be the
corresponding head loss in the prototype? What will be the friction factor for the
prototype pipe. [AU, May / June - 2012]
3.147) In a geometrically similar model of spillway the discharge per meter length is
0.2m3
/sec. if the scale of the model is 1/36, find the discharge per meter run of the
prototype. [AU, May / June - 2014]
3.148) The ratio of lengths of a submarine and its model is 30: 1. The speed of the
prototype is 10 m/s. The model is to be tested in a wind tunnel. Find the speed of air
in wind tunnel. Also determine the ratio of the drag between the model and prototype.
Take values of kinematic viscosities of sea water and air as 0.012 stokes and 0.016
stokes respectively. The density of sea water and air is given as1030 kg/m3
and 1.24
kg/m3
respectively. [AU, Nov / Dec - 2015]
3.149) A 1:100 model is used for testing of ship. The model is tested in wind tunnel.
The length of the ship is 400m. The velocity air in the wind tunnel around the model
is 25m/s and the resistance is 55N. Determine the length of the model. Also find the
velocity of the ship as well as resistance developed. Take density of air and sea water

as 1.24kg/m3
and 1030kg/m3
. The kinematic viscosity of air and sea water are 0.018
stokes and 0.012 stokes respectively. [AU, April / May - 2017]
3.150) A spillway model is to be built to a geometrically similar scale of
1
50
- across a
flume of 600 mm width. The prototype is 15 m high and maximum head on it is
expected to be 1.5 m.
 What height of model and what head on the model should be used?
 If the flow over the model at a particular head is 12 litres per second, what
flow per metre length of the prototype is expected?
 If the negative pressure in the model is 200 mm, what is the negative
pressure in prototype? Is it practicable? [AU, May / June - 2013]
3.151) The characteristics of the spillway are to be studied by means of a geometrically
similar modal constructed to the scale ratio of 1:10.
 If the maximum rate of flow in the prototype is 28.3m3
, what will be the
corresponding flow in model?
 If the measured velocity in the model at a point on the spillway is 2.4m/s,
what will be the corresponding velocity in prototype?
 If the hydraulic jump at the foot of the model is 50mm high, what will be
the height of jump in prototype?
 If the energy dissipated per second in the model is 3.5Nm, what energy is
dissipated per second in the prototype? [AU, April / May - 2015]
3.152) Vortex shedding at the rear of a structure of a given section can create harmful
periodic vibration. To predict the shedding frequency, a smaller model is to be tested
in a water tunnel. The air speed is expected to be about 75 kmph. If the geometric
scale is 1 : 6.5 and the water temperature is 25°C determine the speed to be used in
the tunnel. Consider air temperature as 38°C. If the shedding frequency of the model
was 60 Hz, determine the shedding frequency of the prototype. The dimensions of
the structure are diameter 0.12 m and height 0.36 m. [AU, Nov / Dec - 2014]
3.153) An oil of specific gravity 0.92 and viscosity 0.03 poise is to be transported at the
rate of 2500 litres/sec. through a 1.2 m diameter pipe. Tests were conducted on a
12crn diameter pipe using water at 20°C. If the viscosity water at 20°C is 0.01poise,
find:

(i) Velocity of flow in the model
(ii) Rate of flow in the model [AU, May / June - 2016]
3.154) The model of tidal channel in a coastline study is scaled to 1/100 of actual size.
Fresh water is to be used in place of sea water in the model. Assuming the Reynolds
number must be matched, what model velocity is needed to ensure dynamic
viscosity? Will similarly also be achieved for free surface effects related to the
Weber and Froude numbers? In your calculations, note that the appropriate velocity
and length scales for the actual tidal channel are V = 0.5 m/s and L =10m,
respectively. [AU, May / June - 2016]
3.155) A solid sphere of diameter 100mm moves in water at 5m/s. Its experiences a
drag of magnitude 19.5N. What would be the velocity of 5m diameter sphere moving
in air in order to ensure similarity? What will be the drag experienced by it. Pwater =
1000 kg/m3
Pair = 1.2kg/m3
γair = 13γwater [AU, April / May - 2017]
3.156) An agitator of diameter D rotates at a speed N in a liquid of density ρ and
viscosity μ. Show that the power required to mix the liquid is expressed by a
functional form [AU, April / May - 2011]

UNIT – IV – PUMPS
PART - A
4.1) Define centrifugal pump.
4.2) Mention the main parts of the Centrifugal pump. [AU, Nov / Dec - 2012]
4.3) How centrifugal pumps are classified based on casing? [AU, May / June - 2006]
4.4) Define impeller.
4.5) Define casing.
4.6) List the commonly used casings in centrifugal pumps. [AU, Nov / Dec - 2010]
4.7) What is the function of volute casing? [AU, Nov / Dec - 2015]
4.8) What is the role of a volute chamber of a centrifugal pump?
[AU, Nov / Dec - 2005]
4.9) What precautions are to be taken while starting and closing the centrifugal pump?
[AU, May / June - 2012]
4.10) Define priming of centrifugal pump.
4.11) What is priming? [AU, Nov / Dec - 2010]
4.12) Why priming is necessary in a centrifugal pump?
[AU, May / June - 2007, April / May - 2010]
4.13) What is meant by priming of pumps? [AU, April / May - 2008]
4.14) What is priming? Why is it necessary? [AU, Nov / Dec - 2011]
4.15) What is meant by priming of a centrifugal pump? Why it is necessary?
[AU, Nov / Dec - 2016]
4.16) Define cavitation. [AU, Nov / Dec - 2008]
4.17) Define cavitation in a pump. [AU, May / June - 2007]
4.18) What is cavitation in pump? How it can be avoided? [AU, May / June - 2016]
4.19) What is the effect of cavitation in pump? [AU, April / May - 2011]
4.20) What are the effects of cavitation? Give necessary precautions against
cavitations? [AU, May / June - 2012]
4.21) What is cavitation? What causes it? [AU, Nov / Dec - 2013]
4.22) Explain the cavitation problem in Centrifugal pumps [AU, Nov / Dec - 2015]
4.23) Why is forward curved blading rarely used in pumps? [AU, May / June - 2016]
4.24) Define the characteristic curves of centrifugal pump.

4.25) List out the types of characteristic curves.
4.26) What are operating characteristics curves of centrifugal pump?
4.27) Define multistage centrifugal pump and give its function.
4.28) List the losses in centrifugal pump. [AU, Nov / Dec - 2014]
4.29) What are the advantages of centrifugal pump over reciprocating pumps?
[AU, May / June - 2009]
4.30) Tabulate the causes and remedies for a centrifugal pump, when pump fails to
pump the fluid. [AU, April / May - 2015]
4.31) What is a delivery pipe?
4.32) Define manometric efficiency and mechanical efficiency of a centrifugal pump.
4.33) What is the maximum theoretical suction head possible for a centrifugal pump?
4.34) Define suction head and manometric head of a centrifugal pump.
[AU, Nov / Dec - 2012]
4.35) Define - manometric head and write its mathematical equation.
[AU, Nov / Dec - 2013]
4.36) Define ‘Net Positive Suction Head’ [AU, Nov / Dec - 2014]
4.37) What do you mean by ‘Net Positive Suction Head’ (NPSH)?
[AU, May / June - 2014]
4.38) What is meant by NPSH? [AU, Nov / Dec - 2014]
4.39) How does the specific speed of a centrifugal pump differ from that of a turbine?
4.40) Write the equation for specific speed for pumps and also for turbine.
[AU, Nov / Dec - 2005]
4.41) Define specific speed as applied to pumps. [AU, May / June - 2009]
4.42) Define specific speed. [AU, Nov / Dec - 2007]
4.43) What is specific speed of a pump? How are pumps classified based on this
number? [AU, Nov / Dec - 2009]
4.44) Define specific speed of a centrifugal pump, giving its importance.
[AU, Nov / Dec - 2015]
4.45) Give examples of machines handling gases with high pressure rise.

4.46) What do you mean by manometric efficiency and mechanical efficiency of a
centrifugal pump? [AU, Nov / Dec - 2007]
4.47) Define pump.
4.48) What is the principle of pump? [AU, Nov / Dec - 2009]
4.49) Give the classification of pumps.
4.50) What is a positive displacement pump?
4.51) Define non - positive displacement pump (or) roto dynamic pump.
4.52) List the types of positive displacement pumps.
4.53) Write the classification of positive displacement rotary pumps.
[AU, Nov / Dec - 2016]
4.54) Under what conditions would you suggest use of double-suction pump and a
multistage pump? [AU, Nov / Dec - 2010]
4.55) What are roto dynamic pumps? Give examples. [AU, Nov / Dec - 2009]
4.56) List the types of roto dynamic pumps.
4.57) What is a reciprocating pump?
4.58) Why the reciprocating pump is called a positive displacement pump?
4.59) How are reciprocating pumps classified? [AU, Nov / Dec - 2011]
4.60) When will you select reciprocating pump for your use? [AU, Nov / Dec - 2015]
4.61) What are the materials used for manufacturing reciprocating pumps?
[AU, Nov / Dec - 2014]
4.62) Define a single acting reciprocating pump.
4.63) Define a double acting reciprocating pump.
4.64) Brief the working of double acting reciprocating pump.
4.65) List the advantages of double acting reciprocating pump.
[AU, Nov / Dec - 2014]
4.66) When will you select a reciprocating pump? [AU, Nov / Dec - 2005]
4.67) Draw the relationship between discharge and crank angle for a single acting
pump. [AU, Nov / Dec - 2013]
4.68) What is the function of non – return valve in a reciprocating pump?
[AU, May / June - 2012]

4.69) Distinguish between centrifugal pump and reciprocating pump.
[AU, Nov / Dec – 2005, 2012]
4.70) Mention the significance of 'back leakage'. [AU, Nov / Dec - 2013]
4.71) Define slip of a reciprocating pump. What is negative slip? When does negative
slip occur?
4.72) Define slip of reciprocating pump.
[AU, April / May - 2010, Nov / Dec – 2012, 2015]
4.73) When does negative slip occur?
[AU, Nov / Dec - 2008, May / June - 2016, April / May - 2017]
4.74) What is negative slip in a reciprocating pump? What are the causes for it?
[AU, May / June - 2013]
4.75) Define slip of a pump. When does negative slip occur? [AU, Nov / Dec - 2003]
4.76) Define slip. What conditions lead to a negative slip? [AU, Nov / Dec - 2015]
4.77) Define slip and percentage of slip of a reciprocating pump.
[AU, Nov / Dec – 2008, 2010]
4.78) Define slip, negative slip in reciprocating pump. [AU, May / June - 2014]
4.79) Define slip and percentage slip. [AU, Nov / Dec - 2011]
4.80) What is the % of slip in reciprocating pump? [AU, May / June– 2012]
4.81) Discuss – slip and volumetric efficiency. [AU, April / May - 2011]
4.82) Define slip in reciprocating machines. [AU, Nov / Dec - 2011]
4.83) Distinguish between pumps in series and pumps in parallel.
4.84) What is percentage slip in reciprocating pump? [AU, Nov / Dec - 2006]
4.85) Can actual discharge be greater than theoretical discharge in a reciprocating
pump? [AU, Nov / Dec - 2009]
4.86) Which factors determine the maximum speed of reciprocating pump?
[AU, Nov / Dec - 2009]
4.87) What factors govern the speed of reciprocating pump?
[AU, May / June - 2012]
4.88) Define co-efficient of discharge.
4.89) Brief on acceleration head. [AU, Nov / Dec - 2011]
4.90) Define rotary pump.

4.91) What are rotary pumps? Give examples [AU, April / May - 2003]
4.92) What is a rotary pump? Give its classification. [AU, April / May - 2011]
4.93) Define gear pump.
4.94) What is an air vessel?
4.95) What is the function of air vessel?
[AU, Nov / Dec – 2008, May / June - 2009, April / May - 2010]
4.96) What is the function of air vessel in reciprocating pumps? [AU, Nov / Dec - 2016]
4.97) What is an air vessel in reciprocating pump? [AU, May / June - 2006]
4.98) Explain the purpose of Air Vessel and in which pump it is used?
4.99) Mention the working principle of an Air-vessel. [AU, April / May - 2010]
4.100) What is an air vessel? List the objectives that would be fulfilled by the use of air
vessels. [AU, Nov / Dec - 2010]
4.101)What is an air vessel? What are its uses? [AU, May / June - 2012]
4.102)What is the use of an air vessel? [AU, April / May - 2017]
4.103)List importance of air vessels in reciprocating pump. [AU, May / June - 2016]
4.104)What are the uses of air vessels? [AU, May / June - 2014]
4.105) What are the advantages of air vessel? [AU, May / June - 2013]
4.106) State the advantages of fitting air vessels in reciprocating pumps.
[AU, May / June - 2009]
4.107) Define indicator diagram. State its uses. [AU, May / June, Nov / Dec - 2007]
4.108) What is indicator diagram? [AU, May / June - 2009]
4.109) Draw the ideal indicator diagram. [AU, April / May - 2010]
4.110) Write down the formula for discharge, work done and power required for a
double acting reciprocating pump.
4.111) What is the main difference between a single acting and double acting
reciprocating pump?
4.112) Give the types of rotary pumps.
4.113) What is the formula for work done by a reciprocating pump?
4.114) Give the formula for discharge through a double acting reciprocating pump.

4.115) A single acting reciprocating pump, running at 50rpm. The diameter of piston =
20cm and length = 40cm. Find the theoretical discharge of the pump.
4.116) A centrifugal pump delivers 20 litres/s of water against a head of 850 mm at 900
rpm. Find the specific speed of pump. [AU, April / May - 2010]
4.117) The following data refer to a centrifugal pump which is designed to run at 1500
rpm. D1
= 100 mm, D2
= 300 mm, B1
= 50 mm, B2
= 20 mm, Vf1
= 3 m/s. Find the
velocity of flow at outlet. [AU, April / May - 2010]
4.118) A pump is to discharge 0.82 m3
/s at a head of 42 m when running at 300 rpm.
What type of pump will be required? [AU, Nov / Dec - 2011]
PART - B
4.119) Draw typical velocity triangles for fluid motion along a series of moving curve
vanes and derive Euler’s equation of energy transfer. [AU, Nov / Dec - 2009]
4.120) Explain the construction and working of a centrifugal pump with a neat sketch.
4.121) Explain the working principle with the main parts of Centrifugal pump.
[AU, Nov / Dec - 2015]
4.122) Explain the operation of centrifugal pump with the help of a neat sketch. Write
short notes on different types of casing used in centrifugal pumps.
[AU, May / June - 2007]
4.123) Give the classification of turbo machines. Explain the working principle,
construction and operation of a centrifugal pump and also discuss the velocity
triangles for flow in a centrifugal pump. [AU, Nov / Dec - 2015]
4.124) What is the role of volute chamber of a centrifugal pump? Define manometric
head. [AU, Nov / Dec - 2009]
4.125) Sketch and briefly describe the volute diffusion type pumps. What function is
served by volute chamber in a centrifugal pump? [AU, May / June - 2012]
4.126) Compare the advantages and disadvantages of centrifugal, submersible and jet
pumps. [AU, April / May - 2008]
4.127) What is priming in a centrifugal pump? Why is it necessary?
[AU, Nov / Dec - 2005]

4.128) Obtain the expression for work done by impeller of a centrifugal pump on water
per second per unit weight of water. [AU, Nov / Dec – 2008, May / June - 2009]
4.129) Describe multi-stage pump with impeller in series and impellers in parallel.
[AU, May / June - 2014]
4.130) Define the manometric efficiency of a centrifugal pump?
[AU, Nov / Dec - 2006]
4.131) Define cavitation and discuss its causes, effects and prevention.
4.132) Define cavitation and its effects. [AU, April / May - 2017]
4.133) Define cavitation. What are the effects of cavitation? Give the necessary
precaution against cavitation. [AU, May / June – 2009, 2014]
4.134) Define cavitation and explain the various effects of cavitation.
4.135) Draw the velocity triangle for a centrifugal pump and obtain the expression for
the work done. [AU, April / May - 2011]
4.136) What is specific speed of pump?
[AU, April / May – 2004, May / June - 2009]
4.137) Define speed of a centrifugal pump. How does it differ from that of turbine?
[AU, May / June– 2007, 2012]
4.138) State the expression for the specific speed of a pump. What is its use?
[AU, Nov / Dec – 2007, 2012]
4.139) What do you understand by characteristics curves of a centrifugal pump? Explain
them with neat sketches. [AU, Nov / Dec - 2008]
4.140) Explain in detail about the performance curves for pumps and turbines.
4.141) Determine the minimum speed for starting a centrifugal pump.
[AU, Nov / Dec - 2009]
4.142) Explain briefly the following efficiencies of a centrifugal pump (i) Manometric
efficiency (ii) Volumetric efficiency [AU, May / June - 2014]
4.143) Discuss - characteristics of centrifugal pump at constant speed.
[AU, Nov / Dec - 2013]

4.144) Explain the characteristics curves of a centrifugal pump.
[AU, Nov / Dec - 2009]
4.145) Discuss on the performance characteristics of centrifugal pumps.
[AU, Nov / Dec - 2014]
4.146) Explain about the performance characteristics of centrifugal pumps.
[AU, Nov / Dec - 2014]
4.147) Define specific speed of a centrifugal pump. Derive expression for the same in
the terms of head ‘H’, discharge ‘Q’ and speed ‘N’ [AU, May / June - 2007]
4.148) Enumerate the losses that occur during the operation of the centrifugal pump.
[AU, May / June - 2009]
4.149) Distinguish between roto dynamic pump and positive displacement pump with
simple sketch. [AU, April / May - 2005]
4.150) How rotary pumps are classified. Explain the working principles of any one type
of rotary pump with the aid of a neat sketch.
[AU, Nov / Dec – 2008, May / June– 2012]
4.151) Discuss the working of rotary positive displacement pumps.
4.152) Discuss in detail about rotary positive displacement pumps.
[AU, Nov / Dec - 2011]
4.153) With neat sketches, discuss about the rotary positive displacement pump.
[AU, Nov / Dec - 2013]
4.154) With an example, explain in detail the working principle and construction of
rotary pumps with neat diagram. [AU, May / June - 2012]
4.155) Classify pumps. Explain the working of double acting reciprocating pump with
a neat diagram. [AU, Nov / Dec - 2009, April / May - 2010]
4.156) Discuss on the cascade theory. [AU, Nov / Dec - 2014]
4.157) Describe the working and principles of a reciprocating pump.
[AU, Nov / Dec – 2005, April / May - 2011]
4.158) What is a reciprocating pump? Describe the principle and working of a
reciprocating pump with a neat sketch.
4.159) Draw a neat sketch of reciprocating pumps. List the components and briefly
explain their functions. [AU, Nov / Dec - 2003]

4.160) Describe the principle and working of a reciprocating pump with a neat sketch.
[AU, Nov / Dec - 2008]
4.161) Explain the working principle of reciprocating pump with neat sketch.
[AU, Nov / Dec - 2008, 2015]
4.162) Explain the working principle of a reciprocating pump with neat diagram in
detail and state its advantages and disadvantages over centrifugal pump.
[AU, May / June - 2012]
4.163) Explain with a neat sketch the working of single – acting reciprocating pump.
Also obtain the expression for weight of water delivers by the pump per second.
4.164) With a neat sketch explain the working of double acting reciprocating pump with
its performance characteristics. [AU, Nov / Dec - 2011]
4.165) Derive an expression for acceleration head developed in a reciprocating pump.
4.166) Derive the expression for pressure head due to acceleration in the suction and
delivery pipes of the reciprocating pumps. [AU, Nov / Dec - 2016]
4.167) Explain the working principle of single and double acting reciprocating pumps
with neat diagram in detail. Also explain the effects of inertia pressure and friction
on the performance of the pump using indicator diagrams with and without air
vessel. [AU, Nov / Dec - 2010]
4.168) Sketch and describe the working principle of double acting reciprocating pump
with indicator diagram. [AU, Nov / Dec - 2009]
4.169) Differentiate between single acting and double acting pump.
[AU, Nov / Dec - 2009]
4.170) Discuss on the following: Working of double acting pump, indicator diagram,
acceleration head, friction head. [AU, Nov / Dec - 2013]
4.171) Explain the working principle of double acting reciprocating pump, external gear
pump and vane pump with neat diagram in detail [AU, Nov / Dec - 2015]
4.172) What are air vessels? Explain their purpose and principle of working. Derive an
expression for the work saved against friction in the case of single acting pump with
an air vessel [AU, Nov / Dec - 2015]
4.173) Define indicator diagram. Prove that the area of the indicator diagram is
proportional to the work done by the reciprocating pump. [AU, May / June - 2014]

4.174) Prove that work done by the pump is proportional to the area of the indicator
diagram. [AU, May / June - 2009]
4.175) Show that the work done by a reciprocating pump is equal to the area of the
indicator diagram. [AU, Nov / Dec - 2009, April / May - 2010]
4.176) Write briefly on the following.
 Rotary pumps and their classifications.
 Indicator diagram for reciprocating pump. [AU, April / May - 2011]
4.177) Define slip, percentage slip and negative slip of a reciprocating pump.
[AU, May / June - 2009]
4.178) Define: slope, % of slip and negative slop with respect to reciprocating pump.
[AU, May / June - 2009]
4.179) Define % of slip and indicator diagram, with respect to reciprocating pump.
[AU, May / June - 2007]
4.180) What is % of slip in reciprocating pump? [AU, April / May - 2010]
4.181) What is an air vessel? Describe the function of the air vessel for reciprocating
pumps.
4.182) What is an air vessel? What are the uses/advantages of fitting air vessel in a
reciprocating pump? [AU, May / June - 2007]
4.183) What is air vessel and write the expression for work done by reciprocating pump
fitted with air vessel. [AU, April / May - 2005]
4.184) What is an air vessel? Derive the expression for the percentage work saved by
using an air vessel. [AU, Nov / Dec - 2012]
4.185) What is an air vessel? What are the advantages of fitting air vessel in a
reciprocating pump? [AU, Nov / Dec - 2007]
4.186) Calculate the work saved by fitting an air vessel for a double acting single
cylinder reciprocating pump. [AU, April / May – 2008, May / June - 2013]
4.187) Describe the function of the air vessel.
[AU, Nov / Dec - 2008, May / June– 2012]
4.188) What are the functions of air vessel in a positive displacement pump?
[AU, Nov / Dec - 2009]
4.189) Explain in detail about the concept of pressure vessels with its characteristics.
[AU, Nov / Dec - 2014]

4.190) Determine the % of work saved in one cycle when air vessel is provided on the
delivery side of a single cylinder single acting reciprocating pump.
[AU, May / June - 2012]
4.191) Show that the maximum inertia head is a reciprocating pump without air vessel
is by 𝐻 𝑎 =
𝑙
𝑔
∗
𝐴
𝑎
∗ 𝜔2
𝑟 with usual notation. [AU, April / May - 2017]
4.192) Explain the various types of rotary pumps with its construction details and its
applications. [AU, Nov / Dec - 2014]
4.193) Explain the working principle of Gear pump with neat sketch.
[AU, Nov / Dec - 2008]
4.194) With a neat sketch, explain the working of a gear pump.
[AU, Nov / Dec - 2010]
4.195) Discuss the working of gear pump using it schematic. [AU, April / May - 2017]
4.196) Explain the construction and working of the following rotary pumps with neat
sketches. (a) Gear pump (b) Vane pump
4.197) Explain in detail the working principle and construction of rotary pumps with
neat sketch. [AU, May / June - 2013]
4.198) Explain the working of the following pumps with the help of neat sketches and
mention two applications of each.
(i) External gear pump (ii) Lobe pump (iii) Vane pump (iv) Screw pump.
4.199) Write a short note on following types of rotary pumps:
(i) Internal gear pump (ii) External gear pump
(iii) Vane pump (iv) Root pump [AU, April / May - 2015]
4.200) Discuss the working of Lobe and vane pumps. [AU, Nov / Dec - 2014]
4.201) Explain in detail the working of a gear pump with a neat sketch.
[AU, April / May, Nov / Dec - 2011]
4.202) Explain the working of vane pump with neat diagram.
[AU, May / June - 2012]
4.203) Discuss briefly the working principle of vane pump with a schematic diagram.
[AU, Nov / Dec - 2012]

4.204) Explain the working principle of screw pump and gear pump with neat diagram
in detail. [AU, Nov / Dec - 2010]
4.205) Draw and explain the indicator diagram for a reciprocating pump including the
effect of friction and acceleration.
4.206) Derive an expression for the percentage work saved by using an air vessel with
(i) single acting and (ii) double acting reciprocating pump.
PROBLEMS
4.207) A centrifugal pump is provided at a height of 5m above the sump water level and
the outlet of the delivery pipe is 10m above the sump. The vane angle at outlet is
50°. The velocity of flow through the impeller is constant at 1.6m/s. Find :
[AU, Nov / Dec - 2008]
 The pressure head at inlet to the wheel
 The pressure head at outlet of the wheel. Assume that the velocity of water
in the pipes is equal to the velocity of flow through the impeller. Ignore
losses
4.208) The following observations are made while conducting a performance test on
centrifugal pump. Determine the overall efficiency of the pump. Discharge of water
is 1.8m3
/s. Diameter of suction and delivery pipe are 15cm and 10cm respectively.
The suction and delivery gauge readings are 25cm of mercury and 175 kN/m2
respectively. The height of delivery gauge over suction gauge is 0.5m. The output
of driving motor is 9.555kW. [AU, April / May - 2005]
4.209) The head — discharge characteristics of a centrifugal pump is given below.
The pump delivers fresh water through a 500 m long, 15 cm diameter pipe line
having friction coefficient of f = 0.025. The static lift is 15 m. Neglecting minor
losses in the pipe flow, find (i) the discharge of the pump under the above conditions
(ii) driving power of the pump motor. Assume a pump efficiency of 72%.
[AU, Nov / Dec - 2010]

4.210) The internal and external diameters of the impeller of a centrifugal pump are
200mm and 400mm respectively. The pump is running at 1200 rpm. The vane angles
of the impeller at inlet and outlet are 20°and 30° respectively. The water enters the
impeller radically and the velocity of flow is constant. Determine the work done by
the impeller per unit weight of water. [AU, Nov / Dec – 2008, 2012]
4.211) The internal and external diameters of the impeller of a centrifugal pump are
300mm and 600mm respectively. The pump is running at 1000 rpm. The vane angles
of the impeller at inlet and outlet are 20°and 30° respectively. The water enters the
impeller radically and the velocity of flow is constant. Determine the work done by
the impeller per unit weight of water. Sketch the velocity triangle.
[AU, Nov / Dec - 2015]
4.212) The internal and external diameter of an impeller of a centrifugal pump which is
running at 1000 r.p.m, are 200 mm and 400 mm respectively. The discharge through
pump is 0.04 m3
/s and velocity of flow is constant and equal to 2.0 m/s. The
diameters of the suction and delivery pipes are 150mm and 100mm respectively and
suction and delivery heads are 6 m (abs.) and 30 m (abs.) of water respectively. If
the outlet vane angle is 45º and power required to drive the pump is 16.186 kW,
determine:
(i) Vane angle of the impeller at inlet,
(ii) The overall efficiency of the pump, and
(iii) Manometric efficiency of the pump. [AU, May / June - 2013]
4.213) The internal and external diameter of an impeller of a centrifugal pump which is
running at 1200 rpm are 300 mm and 600 mm. The discharge through the pump is
0.05 m3
/s and the velocity of the flow is constant and equal to 2.5 m/s. The diameters
of the suction and delivery pipes are 150 mm and 100 mm respectively and suction
and delivery heads are 6 m (abs) and 30 m (abs) of water. If the outlet vane angle is
45° and power required to drive the pump is 17 kW determine:
(i) Vane angle of the impeller at inlet,
(ii) The overall efficiency of the pump, and
(iii) Manometric efficiency of the pump. [AU, Nov / Dec - 2016]

4.214) A centrifugal pump with backward-curved blades has the following measured
performance when tested with water at 20°C :
Estimate the best efficiency point and the maximum efficiency. Also, estimate the most
efficient flow rate, and the resulting head and brake power, if the diameter is doubled
and the rotation speed is increased by 50%. [AU, Nov / Dec - 2011]
4.215) The impeller of a centrifugal pump is 300mm outside diameter and 150mm
inside diameter. The impeller vane angles are 30° and 25° at the inner and outer
peripheries respectively and the speed is 1450rpm. The velocity of the flow through
the impeller is constant. Find the work done by the impeller per N of water.
[AU, Nov / Dec - 2009]
4.216) A centrifugal pump running at 800rpm is working against a total head of 20.2m.
The external diameter of impeller is 480mm and the outlet width is 60mm. If the
vane angle at outlet is 40° and manometric efficiency is 70%, determine
 Flow velocity at outlet
 Absolute velocity of water leaving the vane
 Angle made by the absolute velocity at outlet with direction of motion
 Rate of flow through the pump
4.217) A centrifugal pump running at 1440rpm has an impeller diameter of 0.42m. The
backward curved blade outlet angle is 35° to the tangent. The flow velocity at outlet
is 10m/s. Determine the static head through which water will be lifted. In case a
diffuser reduces the outlet velocity to 40% of the velocity at the impeller outlet, what
will increase in the static head? [AU, April / May - 2011]
4.218) The dimensionless specific speed of a centrifugal pump is 0.06. Static head is 32
m. Flow rate is 50 1/s. The suction and delivery pipes are each of diameter 15 cm.
The friction factor is 0.02. Total length is 60 m other losses equal 4 times the velocity
head in the pipe. The vanes are forward curved at 120º. The width is one tenth of the
diameter. There is a 7% reduction in flow area due to the blade thickness. The

manometric efficiency is 80%. Determine the impeller diameter if inlet is radial.
[AU, Nov / Dec - 2014]
4.219) A centrifugal pump running at 1200rpm has a discharge of 13m3
/min. The pump
has manometric efficiency of 85% and working against a head of 22m. The impeller
has an outlet vane angle of 40º. If the velocity of the flow at the outlet is 2.6m/s.
Determine the diameter of the impeller and width of the impeller at the outlet.
[AU, Nov / Dec - 2012]
4.220) A centrifugal pump running at 920 rpm and delivering 0.32 m3
/s of water against
a head of 28 m, the flow velocity being 3 m/s. If the manometric efficiency is 80%
determine the diameter and width of the impeller. The blade angle at outlet is 25º.
[AU, Nov / Dec - 2014]
4.221) A centrifugal pump is to discharge 0.12 m3
/s at a speed of 1400rpm with a head
of 30m. The impeller diameter is 275mm, its width at outlet is 50mm. The
manometric efficiency is 78%. Calculate the vane angle at the outer periphery of the
impeller. [AU, April / May - 2011]
4.222) A Centrifugal pump impeller runs at 80 rpm and has outlet vane angle of 60°.
The velocity of flow is 2.5 m/s throughout and diameter of the impeller at exit is
twice that at inlet. If the manometric head is 20 m and the manometric efficiency is
75 percent, determine the diameter of the impeller at the exit and the inlet vane angle.
[AU, Nov / Dec - 2011]
4.223) A pump has to supply water which is at 70°C water at 90 m3
/min and 1800 rpm.
Find the type of pump needed, the power required, and the impeller diameter if the
required pressure rise for one stage is 200 kPa; and 1250 kPa.
[AU, Nov / Dec - 2011]
4.224) A centrifugal pump with an impeller diameter of 0.4 m runs at 1450 rpm. The
angle at outlet of the backward curved vane is 25º with tangent. The flow velocity
remains constant at 3 m/s. If the manometric efficiency is 84% determine the
fraction of the kinetic energy at outlet recovered as static head.
[AU, Nov / Dec - 2013]
4.225) A centrifugal pump has a head discharge characteristic given by H= 35-2200 Q2
,
where His head developed by pump in 'm' and Q is discharge in m3
/sec. The pump
is to deliver a discharge against a static head of 12 m. The suction pipe is 15 cm

diameter and 20m long with an f value of 0.018. The delivery pipe is 20 cm diameter
and 40 m long with an f value 0.02. Calculate the head and discharge delivered by
the pump. If the overall efficiency is 0.7, calculate the power supplied.
[AU, May / June - 2016]
4.226) The impeller of a centrifugal pump is 300mm in diameter and having a width of
50mm at the periphery. It has blades whose tip angles are inclined backwards at 60°
from the radius. The pump delivers 17m3
/min of water and the impeller rotates at
1000rpm. Assuming that the pump is designed to admit liquid radially, calculate
 Speed and direction of water as it leaves impeller
 Torque exerted by the impeller on water
 Shaft power required
 Lift of the pump
Assume the mechanical efficiency = 95% and the hydraulic efficiency = 75%
[AU, May / June – 2007, 2012]
4.227) A centrifugal pump discharges 2000 l/s of water per second developing a head
of 20m when running at 300rpm. The impeller diameter at the outlet ant the outflow
velocity is 1.5m and 3m/s respectively. It vanes are set back at an angle of 30° at the
outlet, determine
 Manometric efficiency
 Power required by the pump
If inner diameter is 750mm, find the minimum speed to start the pump.
[AU, May / June - 2012]
4.228) The impeller of a centrifugal pump has an external diameter of 450mm and
internal diameter of 200mm and it runs at 1440rpm. Assuming a constant radial flow
through the impeller at 2.5m/s and the vanes at exit are set back at an angle of 25°.
Determine
 Inlet vane angle
 The angle, absolute velocity of water at exit makes with the tangent
and
 The work done per N of water. [AU, Nov / Dec - 2006]

4.229) A centrifugal pump has 30 cm and 60 cm diameters at inlet and outlet. The inlet
and outlet vane angles are 30° and 45° respectively. Water enters at a velocity of
2.5 m/s radially. Find the speed of impeller in rpm and the power of the pump if the
flow is 0.2 m3
/s. [AU, April / May - 2008]
4.230) A centrifugal pump has an impeller diameter 500mm in diameter running at 40
rpm. The discharge at the inlet is entirely radial. The velocity of the flow at outlet is
1m/s. The vanes are curved backwards at outlet at 30º to the wheel tangent. If the
discharge of the pump is 0.14m3
/s, calculate the impeller power and the torque on
the shaft. [AU, April / May - 2015]
4.231) A centrifugal pump is required to deliver 300 litres of water per second against
a head of 20m. If the vanes of the impeller are radial at outlet and the velocity of
flow is constant and equal to 2m/s find the proportions of the pump. Assume
manometric efficiency as 80% and the ratio of breadth to diameter at outlet as 0.1.
4.232) A centrifugal pump delivers water against a net head of 14.5 meters and a design
speed of 1000 rpm. The vanes are curved back to an angle of 30° with the periphery.
The impeller diameter is 300 mm and outlet width 50 mm. Determine the discharge
of the pump if the manometric efficiency is 95%. [AU, Nov / Dec - 2007]
4.233) A centrifugal pump with 1.2m diameter runs at 200rpm and discharge 1880
litres/s, against an average lift of 6m. The angle which the vanes make at exit with
the tangent to the impeller is 26° and the radial velocity of the flow is 2.5m/s. Find
the manometric efficiency and at least speed to start the pump against the head of
6m. Assume the inner diameter of the impeller as 0.6m. [AU, May / June - 2009]
4.234) A single stage centrifugal pump with impeller diameter of 30cm rotates at
2000rpm and lifts 3m3
of water per second to a height of 30m with an efficiency of
75%. Find the number of stages and diameter of each impeller of a similar multistage
pump to lift 5m3
of water per second to a height of 300m when rotating at 1500rpm.
[AU, May / June - 2009]
4.235) A centrifugal pump having an outer diameter equal to two times the inner
diameter and running at 1000 rpm. Works against a total head of 40m. The velocity
of flow through the impeller is constant and equal to 2.5m/sec. The vanes are set

back at an angle of 40° at outlet. If the outer diameter of the impeller is 500mm and
width at outlet is 50mm, determine the
i) Vane angle at inlet
ii)Manometric efficiency
iii) Work done by impeller on water per second. [AU, April / May - 2017]
4.236) The outer diameter of an impeller of a centrifugal pump is 400mm and outlet
width is 50mm. The pump is running at 800rpm and working against a total head of
15m. The vanes angle at outlet is 40° and the manometric efficiency is 75%.
Determine the velocity of flow at inlet, velocity of water leaving the vane, angle
made by the absolute velocity at outlet with direction of motion at outlet, and the
discharge. [AU, Nov / Dec – 2007, 2012]
4.237) The centrifugal pump has the following characteristic. Outer diameter of
impeller = 800mm; width of the impeller vane at outlet = 100mm; angle of the
impeller vanes at outlet = 40°. The impeller runs at 550 rpm and delivers 0.98 m3
/s
under an effective head of 35m. A 500 kW motor is used to drive the pump.
Determine the manometric, mechanical and overall efficiencies of the pump.
Assume waters enter impeller vanes radially at inlet.
[AU, April / May – 2003, 2010]
4.238) A centrifugal pump delivers water against a net head of 14.5m and design speed
of 1000rpm. The vanes are curved back angle of 30° with the periphery. The
impeller diameter is 300mm and the outlet width 50mm. Determine the discharge of
the pump if manometric efficiency is 95%. [AU, Nov / Dec - 2007]
4.239) A centrifugal pump, in which water enters radially, delivers water to a head of
165m. The impeller has a diameter of 360mm and width 180mm at inlet and the
corresponding dimensions at the outlet are 720mm and 90mm respectively. Its
rotational speed is 1200 rpm. The blades are curved backward at 30° to the tangent
at exit and discharge is 0.389 m3
/s. Determine [AU, May / June - 2007]
 Theoretical head developed
 Manometric efficiency
 Pressure rise across the impeller assuming losses equal to 12% of velocity
head at exit.

 Pressure rise and the loss of head in the volute casing
 The vane angle at inlet and
 Power required to drive the pump assuming an overall efficiency of 70%.
What would be the corresponding mechanical efficiency?
4.240) Compute the overall efficiency of a centrifugal pump from the following test
data. Suction gauge reading = 27.5kPa(vac) and delivery gauge reading =
152(gauge) height of the delivery gauge over suction gauge is 0.4m, discharge is
2100mm. Diameter of the suction pipe is 15cm and diameter of delivery pipe is
10cm. the motor power = 12MHP and fluid water. [AU, Nov / Dec - 2009]
4.241) A centrifugal pump id to discharge 0.118m3
/s at a speed of 1450rpm against a
head of 25m. The impeller diameter is 25cm, its width at outlet is 5cm and
manometric efficiency is 75%. Determine the vane angle at the outer periphery of
the impeller and draw its velocity triangle. [AU, April / May - 2011]
4.242) A centrifugal pump delivers 0.18 m3
/s of water against a head of 12 m and runs
at 620 rpm. The outer and inner diameters of impeller are 0.4 m and 0.2 m
respectively and the vanes are bent back at 38º C to the tangent at exit. If the area of
flow remains at 0.1 m2
from inlet to outlet, calculate manometric efficiency, vane
angle at inlet and loss of head at inlet to impeller when the discharge is reduced by
40% without changing the speed. [AU, Nov / Dec - 2014]
4.243) A centrifugal pump delivers 400 litres/s of water to a height of 20m through a
pipe diameter 15cm and length 100m. The pump has an overall efficiency of 70%
and the friction coefficient is 0.15. Determine the power required to drive the pump.
[AU, Nov / Dec - 2010]
4.244) A radial flow impeller has a diameter 25 cm and width 7.5 cm at exit. It delivers
120 lps of water against a head of 24 m at 1440 rpm. Assuming that the vanes block
the flow area by5 percent and the hydraulic efficiency as 0.8, estimate the vane angle
at exit. Also calculate the torque exerted on the driving shaft if the mechanical
efficiency is 95 percent.
4.245) An axial flow pump running at 620 rpm deliver 1.5 m3
/s against a head of 5.2 m.
The speed ratio is 2.5. The flow ratio is 0.5. The overall efficiency is 0.8. Determine
the power required and the blade angles at the root and tip and the diffuser blade
inlet angle. Inlet whirl is zero. [AU, May / June - 2016]

4.246) A single acting reciprocating pump, running at 50rpm, delivers 0.01m3
/sec of
water. The diameter of the piston is 200mm and stroke length 400mm. Determine
the
 theoretical discharge of the pump
 co-efficient of discharge
 slip and the percentage slip of the pump
[AU, Nov / Dec – 2007, 2008, May / June– 2012, April / May - 2017]
4.247) A single acting reciprocating pump, running at 60rpm, delivers 0.02m3
/sec of
water. The diameter of the piston is 250mm and stroke length 450mm. Determine
the
 theoretical discharge of the pump
 co-efficient of discharge
 slip and the percentage slip of the pump [AU, Nov / Dec - 2015]
4.248) For a single acting reciprocating pump, piston diameter is 150 mm, stroke length
is 300 mm, and rotational speed is 50 r.p.m. The pump is required to lift water to a
height of 18 m. Determine the theoretical discharge. If the actual discharge is 4.0
lit/sec, and the mechanical efficiency is 80% determine the volumetric efficiency,
slip,theoretical power and the actual power required. [AU, Nov / Dec - 2010]
4.249) A single – acting reciprocating pump has a plunger diameter of 250mm and
stroke of 450mm. It is driven at 60rpm and undergoes SHM. The length and
diameter of the delivery pipe are 60m and 100mm respectively. Determine the power
saved in overcoming the friction in the delivery pipe, due to fitting of an air vessel
on the delivery side of the pump. Assume the friction factor f = 0.01 the pipe friction
formula hf=(flv2
/2gd) [AU, Nov / Dec - 2007]
4.250) A single – acting reciprocating pump has a plunger diameter of 400mm and
stroke of 700mm. The delivery pipe is 80m long and 120mm diameter. Find the
power saved by installing an air vessel near the pump. If the pump runs at 50rpm.
Assume f = 0.02. [AU, April / May - 2017]
4.251) A single acting reciprocating pump is to raise a liquid of density 1200kg/m3
through a vertical height of 11.5m, from 2.5m below pump axis to 9m above it. The
plunger which moves in SHM, has diameter 125mm and stroke 225mm. The suction
and delivery side pipes are 75mm diameter and 3.5 and 13.5m long, respectively.

There is a large air vessel fitted on the delivery pipe near to the pump axis. But there
is no air vessel on the suction pipe. If separation takes place at 8.829 N/cm2
below
atmospheric pressure, find the maximum speed at which the pump can run without
separation taking place and the power required to drive the pump. Assume there is
no slip in the pump and f = 0.08 the pipe friction formula hf=(flv2
/2gd)
[AU, Nov / Dec - 2007]
4.252) A single acting reciprocating pump has a plunger of diameter 30 cm and stroke
of 20 cm. If the speed of the pumps is 30 rpm and it delivers to6.5 lit/s of water, find
the coefficient of discharge and the percentage slip of the pump.
4.253) The piston area of a single acting reciprocating pump 0.15 m2
and stroke is 30
cm. The water is lifted through a total head of 15 m. The area of delivery pipe is
0.03 m2
. If the pump is running at 50rpm, find the percentage slip, coefficient of
discharge and the power required to drive the pump. The actual discharge is 35 litres
per second. Take mechanical efficiency is 0.85. [AU, Nov / Dec - 2011]
4.254) A single acting reciprocating pump has a diameter (piston) of 150mm and stroke
length 350 mm. The center of the pump is 3.5 m above the water surface in the sump
and 22 m below the delivery water level. Both the suction and delivery pipes have
the same diameter of 100 mm and are 5 m and 30 m long respectively. If the pump
is working at 30 rpm determine the pressure heads on the piston at the beginning,
middle and end of both suction and delivery strokes.
[AU, Nov / Dec - 2011]
4.255) Calculate the rate of flow in and out of the air vessel on the delivery side in a
single acting reciprocating pump of 220 mm bore and 330 mm stroke running at 50
rpm. Also find the angle of crank rotation at which there is no flow into or out of the
air vessel. [AU, Nov / Dec - 2011]
4.256) In a single acting reciprocating pump the bore and stroke are 100 and 150 mm.
respectively. The static head requirements are 4 m suction and 18 m delivery. If the
pressure at the end of delivery is atmospheric calculate the operating speed. The
diameter of the delivery pipe is 75 mm and the length of the delivery pipe is 24 m.
Determine the acceleration head at θ = 33 from the start of delivery.
[AU, Nov / Dec - 2011]

4.257) A double - acting reciprocating pump, running at 40rpm is discharging 1m3
of
water per minute. The pump has a stroke of 400mm. The diameter of the piston is
200mm. The delivery and suction heads are 20m and 5m respectively. Find the slip
of the pump and the power required to drive the pump.
4.258) The cylinder bore diameter of a single acting reciprocating pump is150mm and
its stroke length is 300mm. The pump runs at 50 rpm and lifts water through a height
of 25m. The delivery pipe is 22m long and 100mm in diameter. Find the theoretical
discharge and the theoretical power required to run the pump. If the actual discharge
is 4.2 litres/s. Find the percentage of slip.
[AU, April / May - 2004, Nov / Dec - 2005, 2012]
4.259) The cylinder bore diameter of a single acting reciprocating pump is150mm and
its stroke length is 300mm. The pump runs at 50 rpm and lifts water through a height
of 25m. The delivery pipe is 22m long and 100mm in diameter. Find the theoretical
discharge and the theoretical power required to run the pump. If the actual discharge
is 4.2 litres/s. Find the percentage of slip. Also determine the acceleration head at
the beginning and middle of the delivery stroke. [AU, Nov / Dec - 2016]
4.260) The diameter and stroke of a single acting reciprocating pump are 120 mm and
300 mm respectively. The water is lifted by a pump through a total head of 25 m.
The diameter and length of delivery pipe are 100 mm and 20 m. respectively. find
out:
(i) Theoretical discharge and theoretical power required to run the pump
if its speed is60 rpm.
(ii) Percentage slip, if the actual discharge is 2.95 1/s and
(iii) The acceleration head at the beginning and middle of the delivery stroke.
4.261) The length and diameter of a suction pipe of a single acting reciprocating pump
are 5 m and 10 cm respectively. The pump has a plunger of diameter 150 mm and
a stroke length of 300 mm. The center of the pump is 4 m above the water surface
in the sump. The atmospheric pressure head is 10.3m of water and the pump runs
at 40 rpm. Determine the
i)Pressure head due to acceleration at the beginning of the suction stroke.

ii)Maximum pressure head due to acceleration.
iii) Pressure head in the cylinder at the beginning and at the end of the stroke.
4.262) A single acting reciprocating pump has following dimensions:
Piston diameter = 25cm
Stroke = 35cm
Speed = 40rpm
Suction head = 4.5m
Delivery head =18m
Suction pipe: Diameter = 15 cm; length = 9 m
Delivery pipe: Diameter =12 cm; length =32m
Coefficient of friction = 0.028
Atmospheric pressure = 10.3 m of water
Find (i) pressure head on the piston at the beginning, middle and end of the suction
and delivery strokes, (ii) HP required to driving the pump. [AU, May / June - 2016]
4.263) Consider a double acting reciprocating pump running at 40rpm. The pump
delivers 1m3
/min of water. The piston diameter is 20cm and the stroke length is
40cm. The delivery and the suctions heads are 20m and 5m respectively. Calculate
the % slip and the power required to drive the pump. [AU, Nov / Dec - 2010]
4.264) The diameter and the stroke of a single acting reciprocating pump are 200mm
and 400mm respectively, the pump runs at 60 rpm and lifts 12 litres of water per
second through a height of 25m. The delivery pipe is 20m long and 150mm in
diameter. Find (i) theoretical power required to run the pump (ii) % of slip and (iii)
acceleration head at the beginning and middle of the delivery stroke.
[AU, Nov / Dec - 2003]
4.265) The diameter and stroke length of a single acting reciprocating pump are 75 mm
and 150 mm respectively. Supply of water to the pump is from a sump 3 m below
the pump through a pipe of 5 m long and 40 mm in diameter. The pump delivers
water to a tank located at 12 m above the pump through a pipe 30 mm in diameter
and 15 m long. Assuming that a separation of flow occurs at 75 kN/m2
(below the
atmospheric pressure), find the maximum speed at which the pump may be operated
without any separation. [AU, May / June - 2007]

4.266) The cylinder of a single- acting reciprocating pump is 15 cm in diameter and 30
cm in stroke. The pump is running at 30 r.p.m. and discharge water to a height of 12
m. The diameter and length of the delivery pipe are 10 cm and 30 m respectively. If
a large air vessel is fitted in the delivery pipe at a distance of 2 m from the centre of
the pump, find the pressure head in the cylinder.
(i) At the beginning of the delivery stroke, and
(ii) In the middle of the delivery stroke. Take f = 0.01.
[AU, May / June - 2013]
4.267) A double acting pump with 35 cm bore and 40 cm stroke runs at 60 strokes per
minute. The suction pipe is 10m long and delivery pipe is 200m long. The diameter
of the delivery pipe is 15 cm. The pump is situated at a height of 2.5 m above the
sump; the outlet of the delivery pipe is 70 m above the pump. Calculate the diameter
of the suction pipe for the condition that separation is avoided. Assume separation
to occur at an absolute pressure head is 2.5m of water. Find the Horsepower required
to drive the pump neglecting all losses other than friction in the pipes assuming
friction factor f as 0.02. [AU, Nov / Dec - 2008]
4.268) A double acting reciprocating pump is running at 30rpm. Its bore and stroke are
250mm and 400mm respectively. The pump lift water from sump 3.8m below and
delivers it to a tank located at 65m above the axis of the pump. The lengths of suction
and delivery pipes are 6m and 150m respectively. The diameter of the delivery pipe
is 100mm. if an air vessel of adequate capacity has been fitted on the delivery side
of the pump, determine
 The minimum diameter of the suction pipe to prevent separation of flow,
assuming the minimum head to prevent occurrence of separation is 2.5m
4.269) The maximum gross head against which the pump has to work and the
corresponding power of motor. Assume the mechanical efficiency = 78% and slip =
1.5%; Hatm = 10m; F=0.012. [AU, May / June - 2007]
4.270) The plunger diameter and the stroke length of a single acting reciprocating pump
are 300mm and 500mm respectively. The speed of the pumps is 60rpm. The
diameter and length of the delivery pipe are 150mm and 60m respectively. If the
pump is equipped with an air vessel at delivery side at the center line of the pump,
find the power saved in overcoming friction in delivery pipe. Assume Darcy’s

friction factor as 0.04, and plunger undergoes a simple harmonic motion.
[AU, May / June - 2009]
4.271) The plunger diameter and the stroke length of a single acting reciprocating pump
are 300mm and 500mm respectively. The speed of the pumps is 50rpm. The
diameter and length of the delivery pipe are 150mm and 55m respectively. If the
pump is equipped with an air vessel at delivery side at the center line of the pump,
find the power saved in overcoming friction in delivery pipe. Assume Darcy’s
friction factor as 0.01. [AU, May / June - 2014]
4.272) Determine the maximum speed in rpm at which a single acting reciprocating
pump without an air vessel of the following details can be operated without causing
separation at any stage during the operation of the pump. Compute the discharge at
this speed. What would be the speed and discharge if air vessel is fitted near the
pump on the suction side? The fluid is water. Assume f= 0.01 for the pipes. Diameter
of plunger = 15cm, stroke = 22.5cm, Suction pipe diameter = 10cm, length = 50m,
static suction head = 4m, static delivery head = 25m, atmospheric pressure = 101kPa
and vapor pressure of water = 25.5kPa(abs) [AU, April / May - 2015]
4.273) A double acting reciprocating pump has a bore of 150mm and stroke of 400mm.
The suction pipe has a diameter of 150mm and is fitted with an air vessel. Find the
rate of flow into or from the air vessel when the crank makes angles of 30°, 90° and
120° with the inner dead centre. The speed is 120rpm and the plunger has simple
harmonic motion. [AU, April / May - 2017]
4.274) The diameter and length of a single acting reciprocating pump are 100mm and
200mm respectively. The pump is used to deliver water to the tank 14m above the
pump through a pipe of 30mm in diameter and 18m long by taking its supply from
the sump 2m below the pump, through a pipe 40mm in diameter and 6m long. If
separation occurs at 78.48kN/m2
, below the atmospheric pressure find the maximum
speed at which the pump can be operated without separation. Assume 1 atm pressure
= 10.3m of water column and the plunger undergoes simple harmonic motion.
[AU, May / June - 2009]
4.275) A single acting reciprocating pump has a plunger 10cm diameter and stroke of
length 200mm. The centre of the pump is 4m above the water level in the sump and
14m below the level of water in a tank to which water is delivered by the pump. The

diameter and length of the suction pipe are 40mm and 6m while of the delivery pipe
are 30mm diameter and 18m respectively. Determine the maximum speed at which
the pump may run without separation, if separation occurs at 7.848 N/cm2
below the
atmospheric pressure. Take atmospheric pressure head = 10.3m of water.
[AU, Nov / Dec - 2016]
4.276) Determine the maximum operating speed in rpm and the maximum capacity in
lps of a single acting reciprocating pump with the following details. Plunger
diameter = 25cm, stroke = 50cm, suction pipe diameter = 15cm, length = 9cm,
delivery pipe diameter = 10cm, length = 36cm, static suction head = 3m, static
delivery head = 20m, atmospheric pressure = 76cm of mercury, vapour pressure of
water = 25kPa. [AU, Nov / Dec - 2009]
4.277) A reciprocating pump handling water with a bore of 110mm and stroke of
205mm runs at 38rpm. The delivery pipe is of 90mm diameter and 30m long. An air
vessel of sufficient volume is added at a distance of 2.5m from the pump. Determine
the acceleration head with and without air vessel. [AU, April / May - 2011]
4.278) Discuss about air vessel used with reciprocating pump. A single acting
reciprocating pump handles water. The bore and stroke of the unit are 22 cm and 32
cm. The suction pipe diameter is 12 cm and length is 10m. The delivery pipe
diameter is 12 cm and length is 30m. Take frictional factor as 0.02. The speed of
operation is 32 rpm. Determine the friction power with and without air vessels.
[AU, May / June - 2016]
4.279) A single cylinder double acting reciprocating pump has a piston diameter of
300mm and stroke length of 400mm. When the pump runs at 45rpm, it discharges
0.039m3
/s under a total head of 15m. What will be the volumetric efficiency, work
done per second and power required if the mechanical efficiency of the pump is
75%. [AU, May / June - 2012]
4.280) The indicator diagram of a single acting reciprocating pump gives effective
delivery head of 5m and 23m with crank at inner and outer dead center respectively.
What is the static delivery head of reciprocating pump? [AU, April / May - 2005]

UNIT – V – TURBINES
PART - A
5.1) Define turbo machines.
5.2) Define turbine.
5.3) What is a pump turbine? Is it the same as turbine pump? [AU, April / May - 2015]
5.4) Classify fluid machines. [AU, April / May - 2010]
5.5) Give the classification of turbines.
5.6) How are hydraulic turbines classified
[AU, May / June - 2009, 2014, Nov / Dec - 2009 April / May - 2011]
5.7) How do you classify turbines based on flow direction and working medium?
5.8) What are high head turbines? Give example. [AU, Nov / Dec - 2009]
5.9) State the principles on which turbo-machines are based. [AU, Nov / Dec - 2010]
5.10) Explain specific speed. [AU, Nov / Dec - 2005]
5.11) Define specific speed. [AU, Nov / Dec - 2009]
5.12) Define specific speed of a turbine. [AU, Nov / Dec – 2003,
2008, 2009, May / June–2007, 2009, April / May –2010, 2011]
5.13) Define specific speed of a turbine. What is its usefulness?
[AU, Nov / Dec - 2007]
5.14) How is specific speed of a turbine defined? [AU, May / June - 2006]
5.15) What is meant by specific speed of a turbine? [AU, April / May - 2010]
5.16) Why not the specific speed of a hydraulic turbine is calculated using watts, instead
of metric horse power? [AU, April / May - 2015]
5.17) Write the equation for specific speed for pumps and also for turbine.
[AU, Nov / Dec - 2012]
5.18) Define specific speed and unit speed of a turbine. [AU, April / May - 2015]
5.19) List the range of head for various turbines. [AU, April / May - 2015]
5.20) What is hydraulic turbine? [AU, May / June - 2006]
5.21) State and concise on Euler turbine equation. [AU, Nov / Dec - 2014]
5.22) Classify turbines according to flow. [AU, Nov / Dec - 2005]
5.23) Define impulse turbine and give examples.

5.24) Explain the working of impulse turbine. [AU, April / May - 2011]
5.25) Define reaction turbine and give examples.
5.26) What is reaction turbine? Give examples [AU, April / May - 2003]
5.27) Differentiate between reaction turbine and impulse turbine.
[AU, Nov / Dec - 2003, April / May - 2008, 2015, 2017, May / June - 2012]
5.28) List down the main components of pelton wheel. [AU, May / June - 2016]
5.29) What is a ‘breaking jet’ in Pelton wheel/turbine?
5.30) Draw velocity triangle diagram for Pelton wheel turbine.
[AU, Nov / Dec - 2008, 2014]
5.31) Define tangential flow turbine.
5.32) Define radial flow - turbine.
5.33) Define axial flow turbine.
5.34) Define mixed flow turbine.
5.35) What is the difference between radial flow and axial flow turbo machines?
[AU, Nov / Dec - 2016]
5.36) In what respects outward flow reaction turbine differs from inward flow reaction
turbine? Which one is better and why? [AU, May / June - 2016]
5.37) Define the flow ratio of reaction radial flow turbine. [AU, Nov / Dec - 2012]
5.38) Draw a sketch of a Francis turbine and name its components.
5.39) Francis turbine is not used as a high head turbine? [AU, May / June - 2016]
5.40) Explain the type of flow in Francis turbine. [AU, Nov / Dec - 2016]
5.41) List the main parts of Kaplan turbine. [AU, Nov / Dec - 2012]
5.42) Differentiate between Kaplan turbine and propeller turbine.
[AU, May / June - 2016]
5.43) What is draft tube? [AU, Nov / Dec – 2012, 2016]
5.44) What is a draft tube? Explain why it is necessary in reaction turbine.
5.45) What is draft tube? In which type of turbine is mostly used?
[AU, Nov / Dec - 2003]
5.46) Write the function of draft tube in turbine outlet?
[AU, April / May - 2005, 2008, Nov / Dec - 2011]

5.47) What is the function of draft tube?
[AU, May / June– 2007, Nov / Dec - 2009]
5.48) What are the different types of draft tubes? [AU, Nov / Dec - 2009]
5.49) Write short notes on draft tube. [AU, Nov / Dec - 2015]
5.50) Why does a Pelton wheel not possess any draft tube? [AU, May / June - 2012]
5.51) Mention the importance of Euler turbine equation. [AU, Nov / Dec - 2011]
5.52) What are the different efficiencies of turbine to determine the characteristics of
turbine? [AU, May / June – 2012]
5.53) Define hydraulic efficiency of turbine [AU, Nov / Dec - 2016]
5.54) Define hydraulic efficiency and jet ratio of a Pelton wheel.
[AU, Nov / Dec - 2010]
5.55) Define hydraulic efficiency and axial thrust of a roto-dynamic hydraulic machine.
[AU, May / June - 2013]
5.56) What is meant by hydraulic efficiency of turbine?
[AU, Nov / Dec – 2012, 2013]
5.57) Define hydraulic efficiency and overall efficiency of a turbine.
[AU, Nov / Dec - 2012]
5.58) Define -volumetric efficiency of turbine. [AU, Nov / Dec – 2014, 2015]
5.59) What are the different efficiencies of turbine to determine the characteristics of
turbine? [AU, Nov / Dec - 2006]
5.60) Define overall efficiency and plant efficiency of turbines.
[AU, May / June– 2007, 2012]
5.61) Draw the characteristics curves of a turbine with head variation.
5.62) What is meant by Governing of Turbines? [AU, April / May - 2017]
5.63) What is the difference between a turbine and a pump?
5.64) Differentiate between pumps and turbines.
[AU, May / June, Nov / Dec – 2007, 2008]
5.65) A shaft transmits 150 Kw at 600 rpm. What is the torque in Newton –meters?

5.66) The mean velocity of the buckets of the Pelton wheel is 10 m/s. The jet supplies
water at 0.7 m3
/s at a head of 30 m. The jet is deflected through an angle of 160° by
the bucket. Find the hydraulic efficiency. Take CV = 0.98.
5.67) A water turbine has a velocity of 8.5m/s at the entrance of draft tube and velocity
of 2.2m/s at exit. The frictional loss is 0.15m and the tail race water is 4m below the
entrance of draft tube. Calculate the pressure head at entrance.
PART – B
5.68) Derive the general equation of turbo machines and draw the inlet and outlet
triangles. [AU, April / May - 2011]
5.69) How will you classify the turbines? [AU, Nov / Dec - 2008]
5.70) Enumerate the differences between an impulse turbine and reaction turbine.
5.71) Describe briefly the function of the various main components of a Pelton wheel
turbine with neat sketches.
5.72) Describe briefly the functions of various components of Pelton turbine with neat
sketches. [AU, Nov / Dec - 2008]
5.73) Explain the component parts and working of a Pelton wheel turbine.
5.74) Define and derive an expression for specific speed of a turbine.
5.75) Explain the terms unit power, unit speed and unit discharge with reference to a
turbine.
5.76) Explain the hydraulic efficiency of a turbine. [AU, Nov / Dec - 2009]
5.77) Sketch the velocity triangles at inlet and outlet of a Pelton wheel.
5.78) Draw inlet and outlet velocity triangles for a Pelton turbine and indicate the
direction of various velocity components. Also obtain the expression for the work
done per second by water on the runner of the Pelton wheel. [AU, April / May - 2015]
5.79) What is breaking jet in Pelton wheel turbine?
[AU, April / May – 2004, Nov / Dec - 2005, May / June– 2012]

5.80) Differentiate Pelton wheel turbine with Francis turbine.
5.81) Distinguish between reaction turbine and impulse turbine.
[AU, May / June - 2013]
5.82) Give the comparison between impulse and reaction turbine.
[AU, Nov / Dec - 2005]
5.83) With the help of neat diagram explain the construction and working of a Pelton
wheel turbine. [AU, Nov / Dec - 2005]
5.84) With a neat sketch, explain the working of a Pelton wheel.
5.85) With a neat sketch, explain the working of a Pelton wheel. Also obtain the
expression of the work done. [AU, Nov / Dec - 2012]
5.86) Obtain an expression for power developed in a reaction turbine.
[AU, Nov / Dec - 2011]
5.87) What is the condition for hydraulic efficiency of a Pelton wheel to be maximum?
[AU, Nov / Dec - 2005]
5.88) Explain the construction and working of the following turbines with neat
sketches.
(i) Pelton wheel turbine (ii) Francis turbine (iii) Kaplan turbine
5.89) Compare radial flow and axial flow turbo machines.
5.90) Draw the inlet and outlet velocity triangles for an inward flow reaction turbine
indicating the various components. [AU, Nov / Dec - 2009]
5.91) Derive an expression for the maximum hydraulic efficiency of an impulse turbine.
5.92) Obtain an expression for the work done per second by water on the runner of a
Pelton wheel. Hence derive an expression for maximum efficiency of the Pelton
wheel giving the relationship between the jet speed and bucket speed.
[AU, Nov / Dec - 2007]
5.93) Obtain the expression for the work done per second by water on the runner of a
Pelton wheel and draw inlet and outlet velocity triangles for a Pelton turbine and
indicates the direction of various velocities. [AU, May / June - 2009]

5.94) Derive the velocity triangle for Pelton wheel and obtain the expression for the
work done. [AU, Nov / Dec - 2010, April / May - 2011]
5.95) Sketch the velocity triangles at inlet and outlet of Pelton wheel.
[AU, Nov / Dec - 2006]
5.96) Derive the expression for efficiency and work done for a Pelton wheel and draw
the velocity triangles. [AU, May / June - 2012]
5.97) Explain how the net head on the reaction turbine is increased with the use of draft
tube. [AU, April / May - 2008]
5.98) Derive Euler’s equation of motion for turbines and obtain the components of
energy transfer with a construction of velocity triangles. [AU, May / June - 2012]
5.99) An inward flow reaction turbine has inlet and outlet vane angles φ and Ф are both
equal to 90°. If H = head of the machine, α = guide vane angle and C = ratio of
velocity of flow at outlet and inlet, show that the peripheral velocity and hydraulic
efficiency are given by [AU, Nov / Dec - 2009]
5.100) Show that the hydraulic efficiency for a Francis turbine having velocity flow
through runner as constant given by relation. [AU, April / May - 2011]
5.101) An inward flow reaction turbine discharges radially and the velocity of flow is
constant, show that the hydraulic efficiency can be expressed by
Where α and θ are the guide and vane angles at inlet. [AU, May / June - 2012]
5.102) Write a short note on Governing of Turbines. [AU, Nov / Dec - 2008]

5.103) Classify hydraulic machines and give one example for each.
[AU, Nov / Dec - 2008]
5.104) Explain the working principle of Kaplan turbine and derive the working
proportion of its design. [AU, Nov / Dec - 2008]
5.105) Draw a neat sketch of Kaplan turbine, name the parts and briefly explain the
working. [AU, May / June - 2007]
5.106) Draw a schematic diagram of a Kaplan turbine and explain its construction and
Working. [AU, May / June - 2014]
5.107) Explain with help of a diagram, the essential features of Kaplan turbine.
[AU, Nov / Dec - 2009]
5.108) Draw a schematic diagram of a Kaplan turbine and explain briefly its
construction and working. Obtain an expression for work done by the runner.
[AU, Nov / Dec - 2011]
5.109) Discuss about construction details of Kaplan turbine with a neat sketch.
[AU, Nov / Dec - 2014]
5.110) Explain the working of Kaplan turbine. Construct its velocity triangles.
[AU, Nov / Dec - 2016]
5.111) Describe the efficiencies of a turbine. [AU, Nov / Dec - 2016]
5.112) What is function draft tube in Francis turbine?
[AU, April / May – 2003, 2010]
5.113) Discuss about draft tube and its types. [AU, Nov / Dec - 2014]
5.114) Derive an expression for the efficiency of draft tube. [AU, Nov / Dec - 2006]
5.115) Derive an expression for specific speed. What is the significance of specific
speed of turbine? [AU, May / June - 2009]
5.116) How is a specific speed of the turbine, defined? [AU, May / June - 2009]
5.117) Write a note on performance curves of turbine. [AU, April / May - 2010]
5.118) Explain the performance characteristics curves of turbine.
5.119) Show that the overall efficiency of a hydraulic turbine is the product of
volumetric, hydraulic and mechanical efficiencies. [AU, May / June - 2007]
5.120) Define: Hydraulic efficiency and overall efficiency with respect to turbines.
[AU, Nov / Dec - 2007]

5.121) Explain the different types of the efficiency of a turbine.
[AU, Nov / Dec - 2008]
5.122) Explain the load efficiency characteristics of hydraulic turbines with a diagram.
[AU, Nov / Dec - 2013]
5.123) Mention three to four most striking characteristics of Pelton wheel, Francis
turbine and Kaplan turbine. [AU, April / May - 2015]
5.124) Discuss the performance characteristics of reaction turbine in detail.
5.125) Discuss briefly the characteristics curves of hydraulic turbines.
[AU, Nov / Dec - 2010]
PROBLEMS
5.126) A turbine develops 9000kW when running at speed of 140rpm and under a head
of 30m. Determine the specific speed of the turbine. Derive the expression used in
above problem. [AU, Nov / Dec - 2008]
5.127) A Pelton wheel is to be designed for the following specifications :
a. Shaft power =11,772 KW ; head = 380 metres; speed = 750 rpm,
b. Overall efficiency=86%. Jet diameter is not to exceed one-sixth of the wheel
diameter. Determine the
i) Wheel diameter ii) Number of jets required
iii) Diameter of the jet. [AU, Nov / Dec - 2012]
5.128) A Pelton wheel is to be designed for a head of 60m when running at 200 rpm.
The Pelton wheel develops 95.6475 kW shaft power. The velocity of the buckets is
equal to 0.45 times the velocity of the jet. Overall efficiency = 0.85 and co-efficient
of velocity is equal to 0.98.
5.129) A Pelton wheel has to be designed for the following data. Power to be developed
= 6000kW; Net head available = 300m; Speed = 550rpm; Ratio of jet diameter to
wheel diameter = 1/10 and overall efficiency = 85%. Find the no of jets, diameter of
jet, diameter of wheel and quantity of water required. [AU, Nov / Dec - 2006]
5.130) A Pelton wheel is to be designed for the following specifications:
Shaft power = 11,772 kW
Head (H) = 380m
Speed = 750rpm

Overall efficiency (η0) = 86%
Jet diameter > 1/6 wheel diameter.
Determine: The wheel diameter, the number of jets required and diameter of the
jet. [AU, Nov / Dec - 2007]
5.131) A Pelton wheel has to be designed for the following data:
HP to be developed = 8500
Net head available = 280m
RPM = 650
Ratio of jet diameter to wheel diameter = 119
Mechanical efficiency = 88%
Find the number of jets, diameter of jet, diameter of wheel and quantity of water
required. [AU, May / June - 2016]
5.132) For a high head storage capacity dam of net head 800m, it is been decided to
design and install a Pelton wheel for generating power of 13,520 kW running at a
speed of 600 rpm, if the coefficient of the jet is 0.97 Speed ratio = 0.46 and Ratio of
jet diameter is 1/15 of the wheel Calculate (i) Number of Jets (ii) Diameter of the
Jets (iii) Diameter of the Pelton wheel (iv) No of Buckets and (v) Discharge of one
jet. [AU, April / May - 2017]
5.133) Design a Pelton wheel for a head of 400m when running at 750 rpm. The pelton
wheel develops 12,110 kW shaft power. The ratio of Jet diameter to the wheel
diameter is 1/6. The overall efficiency, ηo = 0.86, Coefficient of velocity Cv =0.985
and Speed ratio, ϕ = 0.45. [AU, Nov / Dec - 2015]
5.134) A single jet Pelton wheel runs at 300 rpm under a head of 510 m. The jet
diameter is 200 mm and its deflection inside the bucket is 165°. Assuming that its
relative velocity is reduced by 15% due to friction, determine (i) water power (ii)
resultant force on bucket and (iii) overall efficiency.
[AU, May / June - 2007, 2012]
5.135) Determine the rpm, work done per second, power and overall efficiency of a
Pelton wheel from the following data. Head = 150m, Wheel diameter = 0.75m, Jet
diameter =4cm, Deflection angle of buckets = 172º, Cv of nozzle = 0.98, Speed ratio
= 0.42 and surface roughness factor of vanes = 0.97. [AU, April / May - 2015]

5.136) A Pelton wheel supplied water from reservoir under a gross head of 112m and
the friction losses in pen stock amounts to 20m of head. The water from pen stock is
discharged through a single nozzle of diameter of 100mm at the rate of 0.30m3
/s.
Mechanical losses due to friction amounts to 4.3kW of power and the shaft power
available is 208kW. Determine velocity of jet, water power at inlet to runner, power
losses in nozzles, power lost in runner due to hydraulic resistance.
[AU, May / June - 2007]
5.137) A Pelton wheel is having a mean bucket diameter of 1 m and is running at 1000
rpm. The net head on the Pelton wheel is 700 m. If the side clearance angle is 15°and
the discharge through the nozzle is 0.1m3
/sec, find the i) power available at the
nozzle and ii) hydraulic efficiency of the turbine. Take CV=1.
[AU, Nov / Dec - 2007]
5.138) A Pelton wheel has a mean bucket speed of 12 m/s and supplied with water at
the rate of 0.7 m3
/s under a head of 300 m. If the buckets deflect the jet through an
angle of 160°, find the power developed and hydraulic efficiency of the turbine.
5.139) A Pelton wheel has a mean bucket speed of 10m/s with a jet of water flowing at
the rate of0.7 m3
/s under a head of 30m. The buckets deflect the jet through an angle
of 160°. Calculate the power given by the water to the runner and the hydraulic
efficiency of the turbine. Assuming the coefficient of velocity as 0.98
[AU, April / May - 2004, Nov / Dec - 2005, 2010, 2012, May / June - 2009]
5.140) A Pelton wheel which is receiving water from a penstock with a gross head of
510m. One - third of Gross head is lost in the penstock. The rate of flow through the
nozzle fitted at the end of the penstock is 2.2 m3
/sec. The angle of deflection of the
jet is 165°. Determine (1) The power given by the water to the runner (2) Hydraulic
efficiency of the Pelton wheel. Take Cv=1 and speed ratio =0.45
[AU, May / June - 2014]
5.141) A Pelton turbine is required to develop 9000 kW when working under a head of
300m the impeller may rotate at 500 rpm. Assuming a jet ratio of 10 and overall
efficiency of 85% calculate [AU, Nov / Dec - 2003, 2016]
(i) Quantity of water required

(ii) Diameter of the wheel
(iii) Number of jets
(iv) Number and size of the bucket vanes on the runner
5.142) The nozzle of a Pelton wheel gives a jet of 9cm diameter and velocity 75m/s.
Coefficient of velocity is 0.978. The pitch circle diameter is 1.5m and the deflection
angle of the buckets is 170°. The wheel velocity is 0.46 times the jet velocity.
Estimate the speed of the Pelton wheel turbine in rpm, theoretical power developed
and also the efficiency of the turbine. [AU, April / May - 2005, Nov / Dec - 2009]
5.143) A Pelton turbine having 1.6m bucket diameter develops a power of 3600kW at
400rpm, under a net head of 275m. If the overall efficiency is 88%, and the
coefficient of velocity is 0.97, find speed ratio, discharge, diameter of the nozzle and
specific speed. [AU, May / June - 2007]
5.144) A Pelton wheel has a mean bucket speed of 12m/s and supplied with water at
the rate of 0.7m3/s under a head of 300m. If the buckets deflect the jet through an
angle of 160° find the power developed and hydraulic efficiency of the turbine.
5.145) A Pelton turbine is to produce 18MW under a head of 450 m when running at
480 rpm. If D/d ratio is 10, determine the number of jets required.
[AU, Nov / Dec - 2011]
5.146) At a location selected to install a hydroelectric plant, the head is estimated as
540 ms. The flow rate was determined as 22 m3
/s. The plant is located at a distance
of 2 km from the entry to the penstock pipes along the pipes. Two pipes of 2 m
diameter are proposed with a friction factor of 0.03. Additional losses amount to
about 1/4th
of frictional loss. Assuming an overall efficiency of 85%, determine how
many single jet unit running at 330 rpm will be required. [AU, May / June - 2016]
5.147) Consider an impulse wheel with a pitch diameter of 2.75m and a bucket angle
of 170°. If the velocity is 58m/s, the jet diameter is 100mm, and the rotational speed
is 320rpm, find the force on the buckets, the torque on the runner, and the power
transferred to the runner. Assume v2 = 0.9v1. [AU, April / May - 2011]
5.148) A gas turbine operates between 1000k and 650 k temperature limits taking in air
20 kg/s at 125 m/s and discharging at 300 m3/s. Estimate the power developed by
the turbine. Given Cp=995 J / Kg.K. [AU, April / May - 2011]

5.149) A reaction turbine at 450rpm, head 120m, diameter at inlet 120cm flow area
0.4m2 has angles made by absolute and relative velocities at inlet 20° and 60°
respectively. Find volume flow rate, H.P and efficiency. [AU, Nov / Dec - 2009]
5.150) An inward flow reaction turbine has internal and external diameter as 0.85m and
1m respectively. The hydraulic efficiency of turbine is 0.92 under a head of 60m.
The velocity of flow at outlet is 3m/s and discharge at outlet is radial. The vane angle
at the outlet is 18° and width of the wheel is 75mm. Calculate the guide blade angle,
turbine speed, vane angle at inlet and power developed by the turbine.
5.151) An inward flow reaction turbine has external and internal diameters as 0.9m and
0.45m respectively. The turbine is running at 200 rpm and width of the turbine at
inlet is 200mm. The velocity of flow through the runner is constant and is equal to
1.8m/sec. The guide blades make an angle of 10° to the tangent of the wheel and the
discharge at the outlet of the turbine is radial. Determine the
i) Absolute velocity of water at inlet of runner
ii) Velocity of whirl at inlet
iii) Relative velocity at inlet
iv) Runner blade angles
v) Width of the runner at outlet
vi) Mass of water flowing through the runner per second
vii) Head at the inlet of the turbine
viii)Power developed and hydraulic efficiency of the turbine.
5.152) An inward flow reaction turbine having an overall efficiency of 80% is required
to deliver 136 kW. The head H is 16 m and the peripheral velocity is 3.3 √H. The
radial velocity of flow at inlet is 1.1√H. The runner rotates at 120 rpm. The hydraulic
losses in the turbine are 15% of the flow available energy. Determine (i) diameter of
the runner, (ii) guide vane angle, (iii) the runner blade angle at inlet and (iv) the
discharge through the turbine. [AU, Nov / Dec - 2010]
5.153) An inward flow reaction turbine is required to produce a power of 280 kW at
200rpm. The effective head on the turbine is 20m. The inlet diameter is twice as the
outlet diameter. Assume hydraulic efficiency as 80%. The radial velocity is 3.5m/s

and is constant. The ratio of breadth to wheel diameter is 0.1 and 5% of the flow area
is blocked by vane thickness. Determine the inlet and outlet diameters, inlet and exit
vane angle and guide blade angle at the inlet. Assume radial discharge.
[AU, Nov / Dec - 2015]
5.154) In an outward flow reaction turbine, the internal and external diameters are 2m
and 2.7m respectively. The turbine speed is 275rpm and the water flow rate is
5.5m3
/s. The width of the runner is constant at the inlet and outlet and equal to
250mm. The head acting on the turbine is 160m. The vanes have negligible thickness
and the discharge at the outlet is radial. Determine the vane angles and velocity of
the flow at inlet and outlet. [AU, Nov / Dec - 2012]
5.155) In a hydroelectric station, water is available at the rate of 175m3
/s under head of
18m. The turbine run at a speed of 150 rpm, with overall efficiency of 82%. Find the
number of turbines required, if they have the maximum specific speed of 460.
[AU, Nov / Dec - 2005]
5.156) A radial flow impeller has a diameter 25 cm and width 7.5 cm at exit. It delivers
120 liters of water per second against a head of 24 m at 1440 rpm. Assuming the
vanes block the flow area by 5% and hydraulic efficiency 0.8, estimate the vane
angle at exit. Also calculate the torque exerted on the driving shaft in the mechanical
efficiency is 95% [AU, Nov / Dec - 2003]
5.157) A 50m/s velocity jet of water strikes without shock, a series of vanes moving at
15m/s. The jet is inclined at an angle of 20° to the direction of motion of vanes. The
relative velocity of jet at outlet is 0.9 times of the values at inlet and the absolute
velocity of water exit is to be normal to the motion of vanes. Determine the vane
angle at entrance and exit. Also determine work done on vanes per second N of water
supplied by the jet. [AU, April / May - 2005]
5.158) In an inward radial flow turbine, water enters at an angle of 22° to the wheel
tangent to the outer rim and leaves at 3 m/s. The flow velocity is constant through
the runner. The inner and outer diameters are 300 mm and 600 mm respectively.
The speed of the runner is 300 rpm. The discharge through the runner is radial. Find
the
(i)Inlet and outlet blade angles.

(ii) Taking inlet width as 150 mm and neglecting the thickness of the blades,
find the power developed by the turbine. [AU, April / May - 2010]
5.159) The velocity of the whirl at the inlet to the runner of an inward flow reaction
turbine is 3.15√H m/s and the velocity of flow at inlet is 1.05√H m/s. The velocity
of whirl at exist is 0.22√H m/s in the same direction as at inlet and the flow at exist
is 0.83√H m/s, where H is head of water 30m. The inner diameter of the runner is
0.6 times the outer diameter. Assuming hydraulic efficiency of 80%. Compute angles
of the runner vanes at inlet and exist. [AU, April / May – 2003, 2010]
5.160) Design a Francis Turbine runner with the following data: Net head = 70m speed
N = 800 rpm. Output power 400 Kw Hydraulic efficiency = 95% Overall efficiency
= 85% Flow ratio = 0.2 Breadth ratio = 0.1 Inner diameter is 1/3 outer diameter.
Assume 6% circumferential area of the runner to be occupied by the thickness of the
vanes. The flow is radial at exit and remains constant throughout.
[AU Nov / Dec - 2008]
5.161) A Francis turbine developing 16120 kW under a head of 260 m runs at 600 rpm.
The runner outside diameter is 1500 mm and the width is 135 mm. The flow rate is
7 m3
/s. The exit velocity at the draft tube outlet is 16 m/s. Assuming zero whirl
velocity at exit and neglecting blade thickness determine the overall and hydraulic
efficiency and rotor blade angle at inlet. Also find the guide vane outlet angle.
[AU, Nov / Dec - 2014]
5.162) A Francis turbine working under a head of 20m is supplied with 1.5 m3
/sec of
water. Wheel diameter at the entrance and exit are 1m and 0.6 m respectively. It is
developing 300 HP at 300 rpm. Velocity of water at exit is 3 m/sec. Assuming wheel
width constant, find (i) theoretical hydraulic efficiency (ii) actual efficiency (iii)
suitable angles of guide vanes and runner vanes at inlet. [AU, May / June - 2016]
5.163) Calculate guide blade angles, vane angles, runner diameters at inlet and outlet
and width of the wheel at outlet for a Francis turbine with the following data: Net
head: 70 m; Speed: 720 rpm; Shaft Power: 310 kW; Overall efficiency: 0.85;
Hydraulic efficiency: 0.9; Flow ratio: 0.2; Breadth ratio: 0.1; OD/ID ratio: 1.8; The
thickness of vanes occupy 7.5% of circumferential area of runner velocity of flow is
Constant and discharge is radial at outlet. [AU, Nov / Dec - 2014]

5.164) The following data is given for a Francis Turbine Net head = 60m speed N =
700 rpm. Shaft power 294.3 kW Hydraulic efficiency = 93% Overall efficiency =
84% Flow ratio = 0.2 Breadth ratio = 0.1 Inner diameter is 1/2 outer diameter.
Assume 5% circumferential area of the runner to be occupied by the thickness of the
vanes. Velocity of flow is constant at inlet and outlet and discharge is radial outlet.
Determine [AU, Nov / Dec - 2012, 2016, April / May - 2017]
 Guide blade angle
 Runner vane angle at inlet and outlet
 Diameter of the runner at inlet and outlet
 Width of the wheel at inlet
5.165) The inner and outer diameters of an inward flow reaction turbine are 50 cm and
100 cm respectively. The vanes are radial at inlet and discharge is also radial. The
inlet guide vanes angle is 10°. Assuming the velocity of flow as constant and equal
to 3 m/s, find the speed of the runner and the vane angle at the outlet.
5.166) A reaction turbine 0.5m diameter when running at 500rpm develops 265KW,
the flow through the turbine in 0.9m3
/s. The pressure head at entrance to the turbine
is 28m, the elevation of the turbine above the tail water level is 1.5m and the velocity
of slow at the entrance of the turbine in 3.5m/s. Assuming the runner vane angle at
inlet as 90°, calculate the effective head on the turbine and the efficiency.
5.167) A reaction turbine works at 450rpm under a head of 120metres. Its diameter at
inlet is 120cm and the flow area is 0.4m2
. The angles made by absolute and relative
velocities at inlet are 20° and 60° respectively with the tangential velocity.
Determine the
 Volume flow rate
 Power developed
 Hydraulic efficiency. [AU, Nov / Dec - 2007]
5.168) A turbine is to operate under a head of 25m at 200rpm. The discharge is 9cumec.
If the efficiency is 90%, determine the
i) Specific speed of the turbine

ii) Power generated
iii) Type of turbine
5.169) A Francis turbine with overall efficiency of 75% is required to produce
149.26kN. It is working against a head of 7.62m. The peripheral velocity is
0.26√(2gH) and the radial velocity of flow at inlet is 0.96√(2gH). The wheel runs at
150rpm and the hydraulic losses in the turbine account for 22% of the available
energy. Assume radial discharge; determine the guide blade angle, the wheel vane
angle at inlet, diameter of the wheel at inlet and width of the wheel at inlet.
[AU, May / June – 2009, 2013]
5.170) A Francis turbine with overall efficiency of 76% and hydraulic efficiency of
80% is required to produce 150kW. It is working against a head of 8m. The
peripheral velocity is 0.25√(2gH) and the radial velocity of flow at inlet is
0.95√(2gH). The wheel runs at 150rpm. Assume radial discharge; determine the
guide blade angle, the wheel vane angle at inlet, diameter of the wheel at inlet and
width of the wheel at inlet. [AU, Nov / Dec – 2009, April / May - 2010]
5.171) A Francis turbine with an overall efficiency of 70% is required to produce147.15
kW. It is working under a head of 8m. The peripheral velocity = 0. 30√2𝑔𝐻 and the
radial velocity of the flow at inlet is 0.96√2𝑔𝐻. The wheel runs at 200rpm and the
hydraulic losses in the turbine are 20% of the available energy. Assume radial
discharge, determine (i) guide blade angle, (ii) wheel vane angle at inlet, (iii)
diameter of wheel at inlet and (iv) width of wheel at inlet. Draw the suitable velocity
triangle. [AU, Nov / Dec - 2015]
5.172) A dam on a river is being sited for a hydraulic turbine. The flow rate is 1600
m3
/h, the available head is 25 m, and the turbine speed is to be 460 rpm. Discuss the
estimated turbine size and feasibility for a Francis turbine; and a Pelton wheel.
[AU, Nov / Dec - 2011]
5.173) A turbine is to operate under a head of 25m at 200rpm. The discharge is 9 cumec.
If the efficiency is 90%, determine the performance of the turbine under a head of
20 meters. [AU, Nov / Dec - 2007]
5.174) A reaction turbine works at 450 rpm under a head of 120 m. Its diameter at inlet
is 120 cm and the flow area is 0.4 m2
. The angles made by the absolute and relative

velocity at inlet are 20° and 60° respectively, with the tangential velocity. Determine
the volume flow rate, the power developed and the hydraulic efficiency.
[AU, Nov / Dec - 2007]
5.175) Calculate the diameter and speed of the runner of a Kaplan turbine
developing6000 kW under an effective head of 5 m. Overall efficiency of the turbine
is 90% and the diameter of the boss is 0.4 times the external diameter of the runner.
The turbine speed ratio is 2.0. And flow ratio is 0.6. [AU, Nov / Dec - 2006]
5.176) A Kaplan turbine runner is to be designed to develop 7357.5kW shaft power.
The net available head is 5.50m. Assume that the speed ratio is 2.09 and flow ratio
is 0.68, and the overall efficiency is 60%. The diameter of the boss is 1/3rd
of the
diameter of the runner, its specific speed. [AU, May / June - 2009]
5.177) A Kaplan turbine runner is to be designed to develop 7360kW. The net available
head is 5.5m. Assuming the speed ratio is 2.09 and the flow ratio is 0.68 and the
overall efficiency is 60%. The diameter of the boss is one third of the diameter of the
runner. Find the diameter of the runner, its speed and its specific speed.
[AU, Nov / Dec - 2009]
5.178) A Kaplan turbine working under a head of 20 m develops 15 MV brake power.
The hub diameter and runner diameter of the turbine are 1.5 m and 4 m respectively.
The guide blade angle at the inlet is 30°. The discharge is radial. Find the runner
vane angles and turbine speed. Take hydraulic and overall efficiency as 90% and 80
% [AU, April / May - 2010, Nov / Dec - 2011]
5.179) A Kaplan turbine is to be designed to develop 9100kW. The net available head
is 5.6m. If the speed ratio is 2 and flow ratio is 0.68, overall efficiency 86% and the
diameter of the boss is 1/3 the diameter of the runner. Find the diameter of the runner,
its speed and specific speed of turbine. [AU, April / May - 2011]
5.180) A Kaplan turbine is to be designed to develop 9100kW. The net available head
is 5.6m. If the speed ratio is 2.09 and flow ratio is 0.68, overall efficiency 86% and
the diameter of the boss is 1/3 the diameter of the runner. Find the diameter of the
runner, its speed and specific speed of turbine. [AU, April / May - 2017]
5.181) A Kaplan turbine delivers 10 MW under a head of 25 m. The hub and tip
diameters are 1.2 m and 3 m. Hydraulic and overall efficiencies are 0.90 and 0.85. If

both velocity triangles are right angled triangles, determine the speed, guide blade-
outlet angle and blade outlet angle. [AU, Nov / Dec – 2013, 2014]
5.182) A Kaplan turbine delivering 40 MW works under a head of 40 m and runs at 150
rpm. The hub diameter is 3 m and runner tip diameter is 6 m. The overall efficiency
is 90%. Determine the blade angles at the hub and tip and also at a diameter of 4 m.
Also find the speed ratio and flow ratio based on tip velocity. Assume hydraulic
efficiency as 95%. [AU, May / June - 2016]
5.183) A Kaplan turbine develops a 20000 kW at a head of 35m and at rotational speed
of 420rpm. The outer diameter of the blades is 2.5m and the hub diameter is 0.85m.
If the overall efficiency is 88%. Calculate the discharge, the inlet flow angle and the
blade angle at inlet. [AU, Nov / Dec - 2016]
5.184) The hub diameter of a Kaplan turbine working under a head of 12m, is 0.35
times the diameter of the runner. The turbine is running at 100 rpm. If the vane angle
of the extreme edge of the runner at outlet is 15º and the flow ratio is 0.6, find the
diameter of the runner, diameter of the boss and the discharge through the runner.
The velocity at the whirl at outlet is given as zero. [AU, April / May - 2015]

CE6451 - FLUID MECHANICS AND MACHINERY

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