Assignment-10CV45.pdf

Hydraulics and Hydraulic Machinery Assignment 10CV45
Department of Civil Engineering, SJB Institute of Technology, Bangalore Page 1
S J B INSTUTUTE OF TECHNOLOGY
BGS HEALTH CITY, UTTARHALLI – KENGERI ROAD, KENGERI, BANGALORE ‐ 60
DEPARTMENT OF CIVIL ENGINEERING
Sub: Hydraulic and Hydraulic Machinery Unit-1 Subject Code: 10CV45
1.Define dimensional analysis, homogeneity of an equation, and model analysis with an example
2. Describe the Rayleigh’ method and Buckingham’s π-theorem for dimensional analysis.
3. What do you mean by dimensionless numbers? Define and explain Reynolds’s number,
Froude’s number and Mach number.
4. Define the terms: Model, prototype, model analysis, hydraulic similitude and similarity laws
5. The pressure difference Δp 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.
6. Show that the power developed in a water turbine can be expressed as:
H
ND
N
D
B
D
D
N
P ,
,
2
5
3
Where D and B are diameter and width of the runner, N speed in RPM, H is the operating head,
µ and are coefficient of dynamic viscosity and mass density respectively
7. In 1 in 20 model of stilling basin, the height of hydraulic jump in the model is observed to be
20cm. What would be the corresponding height of jump in the prototype? If energy dissipation in
the model is 0.1kW, what would be the corresponding value in the prototype?
8. Water is flowing in an open channel at a depth of 1.5m with a velocity of 7.5m/s. At a
particular location, a hydraulic jump is formed and the depth increases to 2.2m, another channel
is built where a similar jump is formed. If the flow depth in the new dynamically similar channel
is 6m, estimate the flow velocity and the height of jump
9. A small flow meter is designed to measure gas flows in 1.25cm gas pipeline. For the flow rate
0.004m3
/s, the pressure drop across the meter is expected to be 4.8kPa. An enlarged
geometrically similar model of the prototype is tested in a 30 cm diameter water pipe. If
dynamically similarity is presumed, make calculations for the velocity and discharge. Also
calculate pressure drop in the model.
For gas : = 12kg/m3
, µ = 18× 10-6
Ns/m2
For water : = 1000kg/m3
, µ = 11.7× 10-4
Ns/m2

SJB Institute of Technology, Bangalore
DEPARTMENT OF CIVIL ENGINEERING Date: 23‐8‐2013
1. Define open channel flow with examples?
2. Briefly explain the importance of study of open channel flow
3. Compare the pressure flow with open channel flow
4. 9. A rectangular channel with a base width of 0.60 m carries a discharge of 100 LPS. The Chezy's
C is 60. If the depth of flow is 0.25 m, determine the bed slope of the channel.
5. A trapezoidal channel has side slopes of 1 horizontal to 2 vertical and the slope of the bed is 1 in
2000. The area of the section is 42 m2
. Find the dimensions of the section if it is to be most
economical. Determine the discharge of the most economical section given Chezy’s constant C=
60.
6. Define the following terms:
(i) Wide channel (ii) Hydraulic Mean depth (iii) Froude Number
7. Distinguish between the following:
(i) Uniform flow and Non- uniform flow
(ii) Steady and Unsteady flow
(iii)Prismatic and Non-prismatic channels
8. Determine the normal depth in a trapezoidal channel with bottom width 40 m and side slope 2
horizontal: 1 vertical when it carries 60 m3
/s of water discharge at a bed slope of 1 in 5000.
Assume Manning’s roughness coefficient as 0.015.
9. Find the depth of flow in the most efficient rectangular section carrying a discharge of 0.5 m3
/sec
on a slope of in 5000, Given Manning’s. Constant n= 0.012.
10. Find the depth of flow in the most efficient Triangular channel carrying a discharge of 0.2 m3
/sec
on a slope of in 2500, Given Manning’s. Constant n= 0.013. Angle of Notch is given as 45
11. Find the depth of flow in the most efficient Trapezoidal channel carrying a discharge of
0.25m3
/sec on a slope of in 7500, Given Chezy’s Constant C = 90, Side slope 1.5H:1V.

1. Define specific energy and explain specific energy curve for a rectangular Channel of width
‘b’ and depth ‘y’
2. What do you mean by most economical section? Derive an expression for a trapezoidal section
of width B, depth y and side slope 2:1
3. List out various types of Gradually Varied Flow (GVF) profiles with neat sketch showing
critical and normal depth line along with profile?
4. A trapezoidal channel having a bottom width of 5.0 m and side slope 2: 1 is laid with a bottom
slope of 1/750. If it carries a uniform flow of 8m3
/s. Calculate the normal depth. Assume
Manning's n = 0.025.
5. A rectangular horizontal channel of 3.0 m wide carries a discharge of 10 m3
/s. Determine
whether hydraulic jump may occur at an initial depth of 0.50 m or not. If jump occurs determine
the sequent depth.
6. Derive an expression for energy loss in a hydraulic jump
7. Differentiate between ‘Alternate depth’ and ‘Sequent depth’
8. A 3m wide rectangular channel conveys 12m3/s of water at a depth of 2m. Calculate:
(i) Specific Energy and conjugate depth
(ii) Critical Depth, critical velocity and the minimum specific energy
(iv) Froude number and comment on the nature of flow
9. The specific energy for a 2.5m wide channel is to be 4N-m. Make calculations for the
maximum possible discharge
10. A concrete lined circular channel of diameter 3m has a bed slope of 1 in 500. Work out the
velocity and the flow rate for the conditions of (i) Maximum velocity (ii) Maximum discharge
11. Water flows at a steady and uniform depth of 2m in an open channel of rectangular cross-
section having base width equal to 5m and laid at a slope of 1 in 1000. It is desired to obtain
critical flow in the channel by providing a hump in the bed. Calculate the height of the hump and
sketch flow profile. Given Manning’s N = 0.02

1. Find the force exerted by a jet of water of diameter 100 mm on a stationary flat plate, when the jet
Strikes the plate normally with a velocity of 30 m/s. [7068.6 N]
2. A jet of water of diameter 50 mm moving with a velocity of 20 m/s strikes a fixed plate in such a
way that the angle between the jet and the plate is 60º. Find the force exerted by the jet on the plate (I)
in the directional normal to the plate, and (II) in the direction of the jet. [(I) 680.13 N, (II) 589 N]
3. A jet of water of 30 mm diameter, moving with a velocity of 15 m/s, strikes a hinged square plate
of weight 245.25 N at the centre of the plate. The plate is of uniform thickness. Find the angle
through which the plate will swing. [θ = 40º 25.6′]
4. A plate is acted upon at its center by a jet of water of diameter 20 mm with a velocity of 20 m/s.
The plate is hinged and is deflected through an angle of 15º. Find the weight of the plate. If the plate
is not allowed to swing, what will be the force required at the lower edge of the plate to keep the plate
in vertical position. [485.5 N, 62.8 N]
5. A jet of water of diameter 150 mm strikes a flat plate normally with a velocity of 12 m/s. The plate
is moving with a velocity of 6 m/s in the direction of the jet and away from the jet. Find: (I) the force
exerted by the jet on the plate, (II) work done by the jet on the plate per second, (III) power of the jet,
and (IV) efficiency of the jet. [(I) 636.3 N, (II) 3817.6 Nm/s, (III) 3.82 kW, (IV) 25%]
6. If in the problem 7, the jet strikes the plat in such a way that the normal on the plate makes an angle
of 30º to the axis of the jet, find: (I) the normal plate exerted on the plate, (II) power, and (III)
efficiency of the jet. [(I) 551 N, (II) 2.86 kW, (III) 18.74%]

S J B INSTUTUTE OF TECHNO LOGY
BGS HEALTH CITY, UTTARHALLI – KEN GERI ROAD, KENGERI, BA NGALORE ‐ 60
1. A jet of water of diameter 100 mm strikes a curved plate at its centre with a velocity of 15 m/sec.
curved plate is moving with a velocity of 7 m/s in the direction of the jet. The jet is deflected through
an angle of 150º. Assuming the plate smooth find :( I) force exerted on the plate in the direction of the
jet, (II) power of the jet, and (III) efficiency. [(I) 938 N, (II) 6.56 N, (III) 49.53]
2. A jet of water having a velocity of 30 m/s strikes a curved vane, which moving with a velocity of
15 m/s. The jet makes an angle of 30º with the direction of motion of vane at inlet and leaves at an
angle of 120º to the direction of the motion of vane at outlet. Calculate: (I) Vane angles, if the water
enters and leaves the vane without shock, (II) Work done per second per unit weight of water striking
the vanes per second. [(I) 53º 47.7′, 15º 41′, (II) 44.15Nm/N]
3. A jet of water of diameter 50 mm, having a velocity of 30 m/s strikes a curved vane which is
moving with a velocity of 15 m/s in the direction of the jet. The jet leaves the vane at an angle of 60º
to the direction of the motion of vanes at outlet. Determine: (I) the force exerted by the jet on the vane
in the direction of motion, (II) work done per second by the jet. [(I) 662.5 N, (II) 9937.5 Nm/s]
4. A jet of water having a velocity 20 m/s strikes a curved vane which moving with a velocity of 9
m/s. The vane is symmetrical and is so shaped that the jet is deflected through 120º. Find the angle of
the jet at inlet of the vane so that there is no shock. What is the absolute velocity of the jet at outlet in
magnitude and direction and the work done per second per unit weight of water striking? Assume the
vane to be smooth. [17º, 5.95 m/s, β = 79º 6′, 18.57 Nm/N]
5. A jet of water, having a velocity of 15 m/s, strikes a curved vane which is moving with a velocity
of 6 m/s in the same direction as that of the jet at inlet. The vane is so shaped that the jet is deflected
through 135º. The diameter of the jet is 150 mm. assuming the vane to be smooth, find: (I) the force
exerted by the jet on the vane in the direction of motion, (II) power of the vane, and (III) efficiency of
the vane. [(I) 2443.5 N, (II) 14.65 kW, (III) 49.16%]

6. If in the above problem, the jet of water instead of striking a single plate, strike a series of curved
vanes, find: (I) force exerted by the jet on the vanes in direction the motion, (II) power of the vane,
and (III) efficiency of the vane. [(I) 4072.5 N, (II) 24.43 kW, (III) 81.9%]
7. A jet of water having a velocity of 30 m/s strikes a series of radial curved vanes mounted on a
wheel which is rotating at 300 r.p.m. The jet makes an angle of 30º with the tangent to wheel at inlet
and leaves the wheel with a velocity of 4 m/s at an angle of 120º to the tangent to the wheel at outlet.
Water is flowing from outward in a radial direction. The outer and inner radii of the wheel are 0.6 m
and 0.3 m respectively. Determine: (I) vane angles at inlet outlet, (II) work done per second per kg of
water, and (III) efficiency of the wheel. [(I) 42º 10.7′, 27º 17.8′, (II) 52.92, (III) 56.5%]
8. A jet of water of diameter 100 mm moving with a velocity of 30 m/s strikes a curved fixed
symmetrical plate at the centre. Find the force exerted by the jet of water in the direction of the jet, if
the jet is deflected through and angle of 120º at the outlet of the curved plate. [10602.7 N]
9. A jet of water of the diameter 100 mm moving with a velocity of 20 m/s strikes a curved fixed
plate tangentially at one end at an angle of 30º to the horizontal. The jet leaves the plate at an angle of
20º to the horizontal. Find the force exerted by the jet on the plate in the horizontal and vertical
directions. [5672.34 N, 496.3 N]

1. A Pelton wheel is revolving at a speed of 200r.p.m and develops 5886 kW S.P. When
working under a head of 200 m with an overall efficiency of 80%. Determine the unit speed,
unit discharge and unit power. The speed ratio for the turbine is given as 0.48. Find the
speed; discharge the power when this turbine is working under a head of 150 m.
[14.14, 0.265 m3
/s, 2.08 kW and 173.2r.p.m, 3.247 m3/s, 3823 kW]
2. A Pelton wheel has a mean bucket speed of 35 m/s with a jet of water flowing at the rate of 1
m3/s under a head of 270 m. The buckets deflect the jet through an angle of 170º. Calculate
the power delivered to the runner and the hydraulic efficiency of the turbine. Assume co-
efficient of velocity at 0.98. [2523.8 kW, 95.3%]
3. A Pelton wheel is to be designed for the following specification. Power = 735.75 kW S.P.
Head = 200 m, Speed = 800 r.p.m., ηo = 0.86 and jet diameter is not to exceed one –tenth the
wheel diameter. Determine: (I) Wheel diameter, (II) The number of jets required, and (III)
Diameter of the jet. Take Cv =0.98 and speed ratio = 0.45. [(I) 0.673 m, (II) 2, (III) 67.3]
4. A Pelton wheel is having a mean bucket diameter of 0.8 m and is running at 1000 r.p.m. The
net head on the Pelton wheel is 400 m. If the side clearance angle is 15º and discharge
through nozzle is 150 liters/s, find: (I) Power available at the nozzle, and (II) Hydraulic
efficiency of the turbine. [(I) 588.6 kW, (II) 98%]
5. Two jets strike at buckets of a Pelton wheel, which is having shaft power as 14,715 kW. The
diameter of each jet is given as 150 mm. If the net head on the turbine is 500 m, find the
overall efficiency of the turbine. Take Cv= 1.0. [85.7%]
6. Design a Pelton wheel for a head of 80 m and speed 300r.p.m. The Pelton wheel develops
103 kW S.P. Take Cv= 0.98, speed ratio = 0.45 and overall efficiency = 0.80.
[D = 1.135 m, d = 72.6 mm, size = 36.3×87, Z = 23]

7. The following data is related to the Pelton wheel:
Head at the base of the nozzle =110 m,
Diameter of the jet =7.5 cm,
Discharge of the nozzle =200 liters/s,
Shaft power =191.295 kW,
Power absorbed in mechanical resistance =3.675 kW.
Determine: (I) power lost is nozzle and, (II) Power lost due to hydraulic resistance in the
runner.
[(I) 10.874 kW, (II) 9.97 kW]
8. Explain step-wise procedure for design of Pelton wheel Turbine including working proportion
of Pelton wheel Bucket

1. A Kaplan turbine working under a head of 29 m develops 1287.5 kW S.P. If the speed ratio
is equal to 2.1, flow ratio = 0.62, diameter of boss = 0.34 times the diameter of the runner
and overall efficiency of the turbine = 89%, find the diameter of the runner and the speed of
the turbine. [0.705 m, 1162.3]
2. A Kaplan turbine working under a head of 25 m develops 16000 kW shaft power. The outer
diameter of the runner is 4 m and hub diameter is 2 m. The guide blade angle is 35º. The
hydraulic and overall efficiency are 90% and 85% respectively. If the velocity of the whirl is
zero at outlet, determine runner vane angles at inlet and outlet, and speed of the turbine.
[35º 27′, 88º 36′, 9.236]
3. A conical draft tube having inlet and outlet diameters 0.8 m and 1.2 m discharges water at
outlet with a velocity of 3 m/s. The total length of the draft tube is 8 m and 2 m of the length
of draft tube is immersed in water. If the atmospheric pressure head is 10.3 m of water and
loss of head due to friction in the draft tube is equal to 0.25 times the velocity head at outlet
of the tube, find: (I) Pressure head at inlet, and (II) Efficiency of the draft tube.
[(I) 2.551 m, (II) 75.3%]
4. A Kaplan turbine develops 9000 kW under a net head of 7.5 m. Mechanical efficiency of the
wheel is 86%. The speed ratio is based on the outer diameter is 2.2 and the flow ratio is 0.66.
Diameter of the boss is 0.35 times the external diameter of the wheel. Determine the diameter
of the runner and the specific speed of the runner.
5. A Kaplan turbine working under a head of 15 m develops 7357.5 kW shaft power. The outer
diameter of the runner is 4 mm and hub diameter 2 m. The guide blade angle at the extreme
edge of the runner is 30º. The hydraulic and overall efficiencies of the turbine are 90% and
85% respectively. If the velocity of whirl is zero at outlet, determine: (I) runner vane angles
at inlet and outlet at the extreme edge of the runner and (II) speed of the turbine.
[(I) 103º 10′, 26º 58.5′, (II) 58.5]

6. A Kaplan turbine runner is to be designed to develop 7357.5 kW S.P. The net available head
is 10 m. Assume that the speed ratio is 1.8 and flow ratio 0.6. If the overall efficiency is 70%
and diameter of the boss is 0.4 times the diameter of the runner, find the diameter of the
runner, its speed and specific speed. [4.39 m, 109.63r.p.m, 528.82]
7. What are functions of a draft tube? Derive an expression for efficiency of draft tube
8. What is a Hydraulic turbine
9. Sketch a layout of a Hydroelectric power plant and name its components

1. The internal and external diameters of the impeller of a centrifugal pump are 300 mm and 600
mm respectively. The pump is running at 1000r.p.m. The vane angles at inlet and outlet are 20º
and 30º respectively. The water enters the impeller radially and velocity of flow is constant.
Determine the work done by the impeller per unit weight of water. [68.89 Nm/N]
2. A centrifugal pump having outer diameter equal to two times the inner diameter and running
at 1200r.p.m. works against a total head of 75 m. The velocity of flow through the impeller is
constant and equal to 3 m/s. The vanes are set back at an angle of 30º at outlet. If the outer
diameter of the impeller is 600 mm and width at outlet is 50 mm, determine:
(a) vane angle at inlet, (b) work done per second by impeller, (c) manometric efficiency
[(a) 9º 2′, (b) 346.37 kW, (c) 60%]
3. A centrifugal pump is running at 1000r.p.m. The outlet vane angle of the impeller is 30º and
velocity of flow at outlet is 3 m/s. The pump is working against a total head of 30 m and the
discharge through the pump is 0.3m3
/s. If the manometric efficiency of the pump is 75%,
determine: (I) the diameter of the impeller, and (II) the width of the impeller at outlet.
[(I) 43.1 cm, (II) 7.4 cm]
4. Find the power required to drive a centrifugal pump which delivers 0.02m3
/s of water to a
height of 30 m through a 10 cm diameter pipe and 90 m long. The overall efficiency of the pump
is 70% and f = 0.009 in the formula hf = 4lV2
/d× 2g [11.5 kW]
5. Find the rise in pressure in the impeller of a centrifugal pump through which water is flowing
the rate of 15 liter/s. The internal and external diameters of the impeller are 20 cm and 40 cm
respectively. The widths of impeller at inlet outlet are 1.6 cm and 0.8 cm. The pump is running at
1200r.p.m. The water enters the Impeller radially at inlet and impeller vane angle at outlet is 30º.
[31.85 m]

6. The diameters of an impeller of a centrifugal pump at inlet outlet are 20cm and 40cm
respectively. Determine the minimum speed for starting the pump if it works against a head of
25m. [1221.2r.p.m.]
7. The diameter of an impeller of a centrifugal pump at inlet and outlet are 300 mm and 600 mm
respectively. The velocity of flow at outlet is 2.5 m/s and vanes are set back at an angle of 45º at
outlet. Determine the minimum starting speed of the pump if the manometric efficiency is 75%.
[159.31r.p.m.]
8. A three stage centrifugal pump has impeller 40 cm in diameter and 2.5 cm wide at outlet. The
vanes are curved back at the outlet at 30º and reduce the circumferential area by 15%. The
manometric efficiency is 85% and overall efficiency is 75%. Determine the head generated by
the pump when running at 1200r.p.m. and discharging 0.06m3
/s. find the shaft power also.
[138.75 m, 108.89 kW]
9. Find the number of pumps required to take water from a deep well under a total head of
156 m. Also the pumps are identical and are running at 1000r.p.m. The specific speed of each
pump is given as 20 while the rated capacity of each pump is 150litre/s. [3]
10. What is Cavitation? What are its causes and prevention?
11. What are the different types of Heads in centrifugal pump?
12. Define the different types of efficiencies in centrifugal pump.
13. What is priming? Why is it necessary?
14. Define the specific speed of centrifugal pump? Derive it.
15. What are multistage centrifugal pumps? Explain multistage centrifugal pumps with high
discharge

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