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?
[AU, Nov / Dec - 2008, 2012, April / May - 2017]
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.
[AU, May / June - 2006, Nov / Dec – 2009, 2015]
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.
[AU, Nov / Dec – 2008, May / June - 2009]
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.

CE6451 - FLUID MECHANICS AND MACHINERY

CE6451 - FLUID MECHANICS AND MACHINERY

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CE6451 - FLUID MECHANICS AND MACHINERY