nagpurstudents - tgpcetb) in an inward flow reaction turbine the head on the turbine is 32 m. the...

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NRJ/KW/17/4425/4451 1 P.T.O

B.E. (Mechanical Engineering / Power Engineering) Fourth Semester (C.B.S.) Hydraulics Machines

P. Pages : 3 NRJ/KW/17/4425/4451

Time : Three Hours Max. Marks : 80

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Notes : 1. All questions carry marks as indicated.

2. Solve Question 1 OR Questions No. 2.






8. Assume suitable data whenever necessary.

9. Illustrate your answers whenever necessary with the help of neat sketches.

1. a) Derive the expression for sonic velocity for one dimensional flow with a neat sketch.

7

b) A gas with a velocity of 300 m/s is flowing through a horizontal pipe at a section where

pressure is 2m/kN78 absolute and temperature 40 ºC. The pipe changes in diameter and at

this section, the pressure is 2m/kN117 absolute. Find the velocity of the gas at this section

if the flow of the gas is adiabatic.

Take k.kg/J287R and 4.1 .

OR

7

2. a) Derive the expression for stagnation pressure in compressible flow with a neat sketch.

7

b) An aeroplane is flying at 1000 km/hr through still air having a pressure of 2m/kN5.78

(absolute) and temperature Cº8 . Calculate on the stagnation point on the nose of the

plane.

i) Stagnation pressure

ii) Stagnation temperature and

iii) Stagnation density.

7

3. a) Draw neat sketch for Pelton wheel bucket and Explain why jet is deflected through 160 to

170º?

6

b) A Pelton wheel is receiving water from a penstock with a gross head of 510 m. one third

of gross head is lost in friction in the penstock. The rate of flow through the nozzle fitted

at the end of the penstock is s/m2.2 3 . The angle of deflection of the Jet is 165º.

Determine

i) The power given by water to the runner and

ii) Hydraulic efficiency of the Pelton wheel.

Take coefficient of velocity - 1.0 and speed ratio = 0.45.

OR

7

4. a) Explain the elements of hydroelectric power plant with neat sketch indicating various

important heads.

6

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b) A Pelton wheel of 1.1 m mean bucket diameter works under a head of 500 m. The deflection

of jet is 165º and its relative velocity is reduced over the bucket by 15 percent due to friction.

If the diameter of Jet is 100 mm and the water is to leave the bucket without any whirl,

determine :

i) Rotational speed of wheel.

ii) Ratio of bucket speed to jet velocity.

iii) Impulsive force and power developed by wheel.

iv) Available power

v) Power input to buckets and

vi) Efficiency of the wheel with power input to bucket as reference point. Take .97.0Cv

7

5. a) Explain the role of following in reaction turbine.

i) Casing ii) Guide vanes

iii) Draft tube iv) Runner vanes

6

b) The following data pertain to an inward flow reaction turbine :

Net head = 86.4 m, speed of runner = 650 rpm, shaft power = 397 kW, Ratio of wheel width

to wheel diameter at inlet = 0.10, Ratio of inner diameter to outer diameter = 0.5, Flow ratio

= 0.17, Hydraulic efficiency = 95%, Overall efficiency = 85%, Flow velocity is constant,

discharge is radial. Neglecting blockage by blades, find the dimensions and blade angles of

the turbine.

OR

7

6. a) Derive the expression for draft tube efficiency and with neat sketch indicating various

heads.

6

b) The propeller reaction turbine of runner diameter 4.5 m is running at 48 rpm. The guide

blade angle at inlet is 145º and the runner blade angle is 25º to the direction of vane. The

axial flow area of water through the runner is 2m30 . If the runner blade angle at inlet is

radial.

Determine :

i) Hydraulic efficiency of the turbine.

ii) Discharge through the turbine, and

iii) Power developed by the runner.

7

7. a) Explain the components of centrifugal pump and installation with neat sketch.

6

b) A centrifugal pump has the following dimensions :

Inlet radius = 80 mm, outlet radius = 160 mm, width of impeller at the inlet = 50 mm, vane

angle of inlet 45.01 radians, vane angle at exit 25.02 radians, width of impeller at

outlet = 50 mm. Assuming shockless entry determine the discharge and head developed by

the pump when the impeller rotates at 90 rad/s.

OR

7

8. a) Explain the effect of outlet vane angle ( ) on manometric efficiency of centrifugal pump.

6

b) A three stage centrifugal pump has impellers 400 mm in diameter and 20 mm wide at outlet.

The vanes are curred back at the outlet at 45º and reduce the circumferential area by 10

percent, the manometric efficiency is 90% and the overall efficiency is 80%. The pump is

running at 1000 rpm and delivering s/m05.0 3 .

Determine :

i) Head generated by the pump and

ii) Shaft power required to run the pump.

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9. a) Derive the expression for percentage of work saved in pipe friction by fitting air vessels in

single acting reciprocating pump.

6

b) Determine the maximum speed at which a double acting reciprocating pump can be operated

under the following conditions

a) No air vessel on the suction side

b) A very large air vessel on the suction side, close to the pump.

The suction lift is 4 m, length of suction pipe 6.5 m, diameter of suction pipe 100 mm,

diameter of piston 150 mm and length of stroke is 0.45 m. Assume suitable harmonic

motion, atmospheric pressure head as 10.3 m of water and separation occurs at 2.6 m of

water absolute. Take Darcy's factor, f = 0.024.

OR

7

10. a) Explain the effect of acceleration in suction and delivery pipe on Indicator diagram for

reciprocating pump.

6

b) A single acting reciprocating pump running at 60 rpm, delivers 3m53.0 of water per minute.

The diameter of the piston is 200 mm and stroke length 300 mm. The suction and delivery

head are 4 m and 12 m respectively.

Determine :

i) Theoretical discharge

ii) Coefficient of discharge

iii) Percentage slip of the pump, and

iv) Power required to run the pump.

7

11. a) Explain different dimensionless numbers and their significance with mathematical

relations.

6

b) A hydraulic turbine is to develop 1015 kW when running at 120 rpm under a net head of

12m. work out the maximum flow rate and specific speed for the turbine if the overall

efficiency at the best operating point is 92%. In order to predict its performance, a 1 : 10

scale model is tested under a head of 7.2 m. What would be the speed, power output and

water consumption of the model if it runs under the conditions similar to the prototype.

OR

8

12. Write short note any three.

i) Air lift pumps.

ii) Submersible pumps

iii) Regenerative pump

iv) Similitude and types of similarities.

v) Hydraulic ram.

************

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10. Use of non programmable calculator is permitted.

1. a) What is sonic velocity? prove that velocity of sound wave in a compressible fluid is given

by :

d

dpC where, P is fluid pressure in pipe and is the density of the fluid.

7

b) A 120 mm dia. pipe reduces to 60 mm dia. through a sudden contraction. It carries air at

25º C under isothermal condition. The absolute pressures in the two pipes before and after

the contraction are 480 kN/m2 and 384 kN/m2 respectively.

Determine.

i) Densities at the two sections.

ii) Velocities at the two sections.

iii) Mass flow rate.

Take R = 287 J/kg.k

6

2. a) At some section in the convergent- divergent nozzle, in which air is flowing, pressure,

velocity, temperature and cross-sectional area are 200 kN/m2, 170 m/s, 200º C and

1000 mm2 respectively. If the flow conditions are isentropic, determine.

i) Stagnation temperature and stagnation pressure.

ii) Sonic velocity and Mach number at this section.

iii) Velocity, Mach number and flow area at outlet section where pressure is 110 kN/m2.

iv) Pressure, temperature, velocity and flow area at throat of the nozzle.

Take for air : R = 287 J/kgK.

CP = 1.0 kJ/kgk, and r = 1.4.

9

b) Discuss in detail, ''Normal shock wave'' with neat sketch.

4

3. a) Explain the elements of hydroelectric power plant with neat sketch.

6

b) A Pelton wheel is receiving water from a penstock with gross head of 510 m. one-third of

gross head is lost is friction in the penstock. The rate of flow through the nozzle fitted at

the end of the penstock is 2.2 m3/s. The angle of deflection of the jet is 165º. Determine.

i) The power given by water to the runner and.

ii) Hydraulic efficiency of the pelton wheel.

Take. 0.1Cv and speed ratio = 0.45.

8

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4. a) A Pelton wheel is designed for following specification: ,kW9560Power

,rpm750Speed,m350Head

Overall efficiency = 85%

jet diameter is not to exceed 1/6th of the wheel diameter.

Determine the following.

i) Wheel diameter.

ii) Diameter of Jet.

iii) No. of Jets required.

Take : 45.0ratioSpeed,985.0Cv .

9

b) Explain with neat sketches performance characteristic curves for Pelton turbine.

5

5. a) Explain the governing of a reaction turbine with a neat sketch.

6

b) In an inward flow reaction turbine the head on the turbine is 32 m. The external and

internal diameters are 1.44 m and 0.72 m respectively. The velocity of flow through the

runner is constant and equal to 3 m/s. The guide blade angle is 10º and the runner vanes

are rigid at inlet. If the discharge at outlet is radial, determine.

i) The speed of the turbine.

ii) The vane angle at outlet of the runner, and.

iii) Hydraulic efficiency.

8

6. a) What are the functions of Draft Tube? Explain different types of draft tubes with suitable

sketches.

6

b) The hub diameters of Kaplan turbine working under a head of 12 m, is 0.35 times the

diameter of runner. The turbine is running at 100 rpm. If the vane angle of the extreme

edge of the runner at outlet is 15º and flow ratio is 0.6, find.

i) Diameter at runner.

ii) Diameter of boss

iii) Discharge through runner.

The velocity of whirl at outlet is given as zero.

8

7. a) With a neat Sketch explain different components of a centrifugal pump.

6

b) A Centrifugal pump is running at 1000 rpm. The outlet vane angle of the impeller is 45º

and velocity of flow at outlet is 2.5 m/s. The discharge through the pump is 200 litres/s

when the pump is working against a total head of 20 m. If the manometric efficiency of

pump is 80%, determine.

i) Outside diameter of impeller.

ii) Width of impeller at outlet.

7

8. a) What is multi-staging in centrifugal pumps? Explain with neat sketches pumps in series

and in parallel.

6

b) A centrifugal pump has discharge of 1565 liters/sec against a mean lift of 6.1 m. When it

rotates at 200 rpm. The impeller diameter is 1.22 m and the area at outer periphery is

6450 cm2. If the vanes are set back at an angle of 26º at the outlet, determine.

i) Hydraulic efficiency.

ii) Power required to drive the pump.

iii) Minimum Speed to start pumping if the ratio of external to internal diameter is 2.

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9. a) Explain the Indicator diagram of reciprocating pump with neat sketch.

6

b) A single acting reciprocating pump having a bore of 150 mm and a stroke of 300 mm is

raising water to a height of 20 m above the sump level. It has actual discharge of

0.0052 m3/s and efficiency 70%. If the speed of the pump is 60 rpm, determine.

i) Theoretical discharge.

ii) Theoretical power.

iii) Actual power.

iv) Percentage slip.

7

10. a) Explain Air vessels with neat sketch.

6

b) A 'Three throw' pump has cylinders of 250 mm diameter and stroke of 500 mm each. The

pump is required to deliver 0.1 m3/s at a head of 100 m. friction losses are estimated tobe

1m in sanction pipe and 19 m in Delivery pipe. Velocity of water in delivery pipe is 1 m/s,

overall efficiency is 85% and the slip is 3%.

Determine.

i) Speed of the pump, and.

ii) Power required to run pump.

7

11. a) Explain any three dimensionless numbers with mathematical formula and their

significance.

5

b) Two geometrically Similar Pumps are running at the same speed of 1000 rpm. one pump

has an impeller diameter of 0.30 m and lifts water at the rate of 20 litres/sec against a head

of 15 m. Determine the head and impeller diameter of the other pump to deliver half the

discharge.

8

12. Write short notes on any three.

i) Air lift pump.

ii) Specific speed for turbine and pump.

iii) Submersible pump.

iv) Cavitation in Reciprocating pump.

13

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B.E. (Mechanical Engineering / Power Engineering) Fourth Semester (C.B.S.) Hydraulics Machines Paper - III

P. Pages : 3 TKN/KS/16/7373/7399


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8. Due credit will be given to neatness and adequate dimensions.



1. a) Derive an expression for area velocity relationship for a compressible fluid in the form

1MV

dV

A

dA 2 .

6

b) Determine the speed and Mach number of a supersonic aircraft flying at an attitude of 1000

m where the temperature is 280 K. Sound of the aircraft is heard 2.15 seconds after the

passage of air craft over the head of an observer.

Take Y = 1.41 and R = 287 J/kg K.

OR

7

2. a) What do you mean by compressibility correction factor? Find an expression for

compressibility factor.

6

b) Air flows through a convergent – divergent nozzle. At some section in the nozzle pressure

= 2 bar, velocity = 170 m/s, and temp = 200ºC and cross sectional area = 1000 mm2.

Assuming isentropic flow conditions determine :

a) Stagnation temperature and pressure.

b) Sonic velocity and Mach number at this section.

c) Velocity, Mach number and flow area at outlet section where pressure is 1.1 bar.

d) Pressure, temperature, velocity and flow area at throat of the nozzle

Take R = 287 J/kgK

Cp = 1000 J/kg K and

Y = 1.4

7

3. a) Draw a neat sketch and explain the characteristic features of pelton wheel bucket.

What are the limitations in keeping the deflection angle of the jet less than 180º?

6

b) A Pelton wheel is required to develop 6 MW under a head of 300 m. If rotates with a

speed of 550 rpm. Assuming Jet ratio as 10 and over all efficiency as 85%.

Determine :

i) Diameter of wheel

ii) Quantity of water required.

iii) Number of jets.

Take : Cv = 0.98 and Ku = 0.46.

OR

7

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4. a) Draw a general layout of a hydroelectric power plant using impulse turbine and explain

briefly its construction and working.

6

b) A single jet Pelton wheel runs at 300 rpm under a head of 510 m. The jet diameter is 200

mm, its deflection inside the bucket is 165º and its relative velocity is reduced by 15% due

to friction. Determine

i) Water power

ii) Resultant force on the bucket

iii) Overall efficiency.

Take Co – efficient of velocity = 0.98 and speed ratio = 0.46

7

5. a) What is cavitation? How can it be avoided in reaction turbines.

7

b) The following data pertains to an inward flow reaction turbine.

Net head = 86.4 m. Speed = 650 rpm

Output power = 397 KW

Hydraulic efficiency = 95%


Flow ratio = 0.17 Breadth Ratio = 0.1

Ratio of inner diameter to outer diameter = 0.5

Flow velocity constant and

Discharge radial.

Neglecting blockage by blades,

Find dimensions and blade angles of the turbine.

OR

7

6. a) What is governing and how it is accomplished in Reaction turbines?

7

b) A Kaplan turbine develops 22000 KW at an average head of 35m. Assuming a speed ratio

of 2, flow ratio of 0.6 diameter of boss equal to 0.35 times the diameter of the runner and

overall efficiency of 88 percent, Calculate the diameter, speed and specific speed of the

turbine.

7

7. a) Show that the pressure rise of a centrifugal pump when frictional and other losses are

neglected is given by 222

22

21

cosecfVufVg2

1

where 21 fV,fV velocities of flow at inlet and outlet respectively.

2u tangential velocity at outlet

vane angle at outlet.

7

b) A centrifugal pump is required to discharge 0.118 m3 of water per second against a head of

25m. When rotating at 1500 rpm. The manometric efficiency is 75%. The impeller diameter

is 250 mm and its width at outlet is 50 mm. Determine the vane angle at the outer periphery

of the impeller.

OR

7

8. a) What do you mean by "NPSH' Net positive suction heads? What is its importance.

7

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b) A three stage centrifugal pump has impellers 400 mm in diameters and 20 mm wide at

outlet. The vanes are curved back at the outlet at 450 and reduce the circumferential area by

10%. The manometric efficiency is 90% and the overall efficiency is 80%. The pump is

running at 1000 rpm. and delivering s/m05.0 3 .

Determine :

i) Head generated by the pump and

ii) Shaft power required to run the pump.

7

9. a) Define indicator diagram. Prove that work done by the reciprocating pump is proportional

to the area of indicator diagram.

6

b) A three throw has cylinder of 250mm diameter and stroke of 500 mm each. The pump is

required to deliver s/m1.0 3 at a head of 100 m. Friction losses are estimated to be 1m in

suction pipe and 19 m in delivery pipe. Velocity of water in delivery pipe is 1 m/s, overall

efficiency is 85% and slip is 3%.

Determine :

i) Speed of the pump and

ii) Power required to drive the pump.

OR

7

10. a) What is negative slip in reciprocating pump? Explain with neat sketches the function of air

vessels in reciprocating pump.

6

b) The bore and stroke of a reciprocating pump are 250 mm and 500 mm respectively. The

pump delivers water trough a 100 mm delivery pipe to a tank located at 14 m above it and

27 m horizontally from it. If separation occures at 2m/KN22 absolute, find the safe speed

at which pump should run when

i) The delivery pipe is horizontal from the pump and then vertical upto the tank. and

ii) The delivery pipe is vertical from the pump and then horizontal upto the tank. The

atmospheric pressure is 10.3 m of water.

7

11. a) What are the various methods of dimensional analysis to obtain a functional relationship

between various parameters affecting a physical phenomenon.

6

b) A model turbine constructed to a scale of 1 : 10 when tested under a head of 8 m and 400

rpm. Gave an efficiency of 77 percent. Determine the rpm of the prototype and the ratio of

powers developed by the model and prototype. If the prototype works under a head of

400 m?

OR

7


i) Air Lift Pump. ii) Hydraulic Ram

iii) Submersible Pump. iv) Regenerative Pump.

*********

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P. Pages : 3 NJR/KS/18/4425/4451


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1. a) Prove that the velocity of sound wave in a compressible fluid is given by C k= where

k and are the bulk modules and density of fluid respectively.

6

b) A supersonic aircraft flies at an altitude of 1.8km where temperature is 4ºC. Determine the

speed of an aircraft if its sound is heard 4 seconds after its passage over the head of an

observer.

Take R = 287 J/kg k y = 1.4.

7

OR

2. a) Derive an expression for area velocity relationship for a compressible fluid in the form.

( )2dA dvM 1

A v= − .

6

b) A tank fitted with a convergent nozzle contains air at a temperature of 20ºC. The diameter

at the outlet of the nozzle is 25mm. Assuming adiabatic flow find the mass flow rate of flow

air through the nozzle to the atmosphere when the pressure in the tank is.

i) ( )2140 kN m abs ii) 2300 kN m

Take for air R = 287 J/kg k, y = 1.4, Barometric Pressure = 100 2kN m .

7

3. a) Draw neat sketch of Pelton wheel bucket and explain why undercut is provided? Why jet

is not deflected through 180º?

7

b) A Pelton wheel is to be designed for following specifications.

Shaft Power = 9560kW

Head = 350 Meters

Speed = 750 RPM


Jet dia - Not to exceed 1/6th of the wheel diameter

Determine the following.

i) The wheel diameter ii) The diameter of jet

iii) Number of jets required.

Take VC = 0.985 Speed Ratio = 0.45.

7

OR

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4. a) Derive an expression for maximum efficiency of a Pelton Wheel.

7

b) A Pelton wheel is required to develop 4000 kW under a head of 350m. There are two equal

jets and the bucket deflection angle is 165º, overall efficiency - 85%, vC =0.97, nK 0.46=

and relative velocity at exit reduces by 14% the relative velocity at inlet.

Calculate:

i) Diameter of the bucket ii) Diameter of Jet

iii) Hydraulic efficiency of the turbine

7

5. a) What is governing and how it is accomplished in Reaction Turbines?

6

b) The following data is given for Francis turbine.

Net Head = 60m, Speed = 750RPM, Shaft Power = 295kW, o h84% 93%, = = Flow

Ratio = 0.2, Breadth Ratio = 0.1,

Outer diameter = 2 x inner diameter, Thickness of vanes occupy 5% of area, Velocity of

flow is constant and Discharge from turbine is Radial.

Determine:

i) Guide blade angle

ii) Runner vane angle at inlet & outlet

iii) Dia of runner at inlet & outlet

iv) Width of wheel at inlet.

7

OR

6. a) What are the functions of Draft tube? Explain different types of draft tube with suitable

sketches.

6

b) A Kaplan turbine runner is to be designed to develop 7357.5kW of power. The net head

available is 10m. Assume speed ratio is 1.8 and flow ratio is 0.6.

If the overall efficiency is 70% and the diameter of the boss is 0-4 times the diameter

of runner

Find:

i) The diameter of Runner

ii) Speed of the Runner and

iii) Specific Speed

7

7. a) Show that the pressure rise in the centrifugal pump is given by:

2 2 2 21 2 2

1Vf , U Vf cosec

2g + −

Where 1 2Vf , Vf → velocities of flow at inlet and outlet

2U → Velocity of Vane at outlet

→ Vane angle at outlet.

6

b) The impeller of a centrifugal pump having external and internal diameter 50cm and 25cm

respectively, width at outlet is 5cm and running of 1200RPM, it works against a head of

48m. The velocity of flow through impeller is constant and equal to 3 m/s. The Vanes are

set back at an angle of 40º at outlet. Determine.

i) Inlet Vane angle

ii) Work done by the Impeller and

iii) Manometric efficiency.

7

OR

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8. a) What is multistaging in centrifugal pumps? Explain with neat sketches pumps in series

and in parallel.

6

b) A centrifugal pump impeller has an outlet diameter of 360mm and width 60mm. The Vanes

are curved backwards at 35º. and thickness of Vanes occupy 20% of the area of flow, the

velocity of flow is constant from inlet to outlet. The pump rotates at 800 RPM. If the rate

of flow through the pump is 30.13m s . Determine.

i) Pressure rise in the impeller

ii) The percentage of total work converted to kinetic energy.

7

9. a) Define Indicator diagram prove that work done by reciprocating pump is proportional to

the area of indicator diagram.

7

b) A single acting reciprocating pump has the plunger diameter of 20cm and stroke of 30cm.

The pump discharges 30.53m min at 60 rpm.

Find the theoretical discharge, co-efficient of discharge, and percentage slip of pump.

Further if suction and delivery heads are 4m and 12m respectively work out power required

to drive the pump.

7

OR

10. a) What is negative slip? Explain with neat sketches the function of air vessels in reciprocating

pump.

7

b) A single acting reciprocating pump has a diameter of Piston 15cm and stroke length of

35cm. the centre of the pump is 3.5m above the water surface in sump and 22m below the

delivery water level. Both the suction and delivery pipes have the same diameter of 10cm

and are 5m and 30m long respectively. If the pump is working at 30rpm.

Determine:

i) The pressure heads on the Piston at the beginning, middle and end of both suction and

delivery strokes.

ii) The Power required to drive the pump.

7

11. a) What are the various methods of dimensional analysis to obtain a functional relationship

between various parameters affecting a physical phenomenon.

6

b) A centrifugal pump is discharging 0-025 3m s of water against a total head of 18m. The

diameter of the impeller is 0.4m and it is rotating at 1400 r.p.m. Calculate the head,

discharge and ratio of powers of a geometrically similar pump of diameter 0.25m when it

is running at 2800 r.p.m.

7

OR


i) Air Lift Pump ii) Submersible pump

iii) Regenerative Pump iv) Hydraulic Ram

v) Specific speed for Turbine and Pump

13

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