ASSIGNMENT-1 HYDROPOWER PLANT Power... · ASSIGNMENT-1 HYDROPOWER PLANT Theory ... inlet and outlet...

FLUID POWER ENGINEERING (2151903)

B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1

ASSIGNMENT-1 HYDROPOWER PLANT

Theory

1. Give classification of hydro electric power plant.

2. Write advantages, disadvantages and application of hydro electric power plant.

3. Explain general layout and essential components of hydro electric power plant.

4. Discuss the factors for site selection for hydro electric power plant.



ASSIGNMENT – 2 IMPACT OF JET

Theory

1. Derive an expression for force exerted by a jet of water on stationary plate for

following cases:

a) Stationary (fixed) vertical flat plate

b) Stationary inclined flat plate

c) Stationary curved plate

2. Derive an expression for force exerted by a jet of water on moving plate for

following cases:

a) Moving plate is vertical to the jet

b) Moving plate is inclined to the jet

c) Moving plate is curved

3. Derive an expression for the angle of swing of a vertical hinged plate.

4. Show that the efficiency of a free jet striking normally on a series of flat plates

mounted on the periphery of a wheel can never exceed 50%.

5. Prove an expression for work done equation and efficiency when jet striking on

series of radial curved vanes.

6. Explain jet propulsion. Also derive an expression for the work done and efficiency.

Examples

1. Water is flowing through a pipe at the end of which a nozzle is fitted. The diameter

of the nozzle is 100mm and the head of water at the centre of nozzle is 100m. Find

the force exerted by the jet of water on a fixed vertical plate. The co-efficient of

velocity is given as 0.95. [Ans: 13.907KN] [17.2; R. K. Bansal]

2. A jet delivers water at the rate of 60 liters per second with velocity 30m/s. The jet

strikes tangentially on the vane moving in the direction of the jet with the velocity of

15 m/s. The vane is so shaped that if stationary, it would deflect the jet through an

angle 50°. Calculate: (1) angle made by absolute velocity at outlet and (2) work done.

[GTU; JUN-2012]

3. A jet of water from a nozzle is deflected through 60˚ from its original direction by a

curved plate which it enters tangentially without shock with a velocity of 30 m/sec



and leaves with a mean velocity of 25 m/sec. If the discharge from the nozzle is 0.8

kg/sec, calculate the magnitude and direction of the resultant force on the vane, if

the vane is stationary. [Ans: 22.27N, 51.04°] [17.15; R. K. Bansal]

4. A jet of water of diameter 7.5 cm strikes a curved plate at its centre with a velocity of

20 m/sec. The curved plate is moving with a velocity of 8 m/sec in the direction of

the jet. The jet is deflected through an angle of 165˚. Assuming the plate smooth.

Find:

(1) Force exerted on the plate in the direction of jet,

(2) Power of the jet, and

(3) Efficiency of the jet. [Ans: 1.25KN, 10KW, 56.4%] [17.14; R. K. Bansal]

5. A jet of water having a velocity of 40 m/sec strikes a curved vane, which is moving

with a velocity of 20 m/sec. The jet makes an angle of 30˚ with the direction of

motion of vane at inlet and leaves at an angle of 90˚ to the direction of motion of

vane at output. Draw the velocity triangles at inlet and outlet and determine the

vane angles at inlet and outlet so that the water enters and leaves the vane without

shock. [Ans: 53.79°, 36.18°,] [17.19; R. K. Bansal]

6. A jet of water moving at 12 m/sec impinges on a concave shaped vane and is

deflected through an angle of 120˚. Assuming the vane to be symmetrical, find the

angle of jet for shock-less entry at inlet when vane velocity is 6 m/sec. Calculate

magnitude and direction of exit velocity and work done per unit mass per sec.

Assume 10% loss in relative velocity due to friction on moving plate. [24; V. L. Patel]

7. A horizontal jet of water with a velocity of 25 m/sec impinges on a moving curved

blade having velocity 10 m/sec. The blade is moving in the direction of a jet. The jet

leaves the blade at an angle of 60˚ with the direction of the motion of the blade.

Blade outlet angle is 40˚. Calculate :

(1) Percentage by which relative velocity is reduced at outlet

(2) Force per kg in the direction of motion if diameter of jet is 10 cm

(3) Work done per kg. [Ans: 41.4%, 2.56KN, 25.607KW] [25; V. L. Patel]

8. A 5 cm diameter horizontal jet of water with a velocity of 20 m/sec strikes a curved

vane tangentially at inlet tip. The vane is moving with 10 m/sec in the direction of

jet. The force experienced by the vane in the direction of motion is 295 N. Calculate

the angle made by absolute velocity of a jet at outlet with the direction of motion of

vane. [Ans: 60.08°] [28; V. L. Patel]



9. A jet of water of diameter 25mm strikes a 20cm x 20cm square plate of uniform

thickness with a velocity of 10 m/sec as the centre of the plate which is suspended

vertically by a hinge on its top horizontal edge. The weight of the plate is 98.1 N. The

jet strikes normal to the plate. What force must be applied at the lower edge of the

plate so that plate is kept vertical? If the plate is allowed to deflect freely, what will

be the inclination of the plate with vertical due to the force exerted by jet of water?

[Ans: 24.5N, 30°] [17.10; R. K. Bansal]

10. A metal plate of 6mm thickness and 150mm square swings about a horizontal edge.

A horizontal jet of water 12mm in diameter impinges with its axis perpendicular to

and 50mm below the edge of the hinge and keeps it steadily inclined at 30˚ to the

vertical. Find the velocity of jet, if the metal plate weighs 76875 N/m3.

[Ans: 8.29m/s] [6; V. L. Patel]

11. A jet of water having a velocity 20 m/sec strikes on a series of vanes moving with a

velocity 8 m/sec. The jet makes an angle of 30˚ with the direction of motion of vanes

when entering and leaves at an angle of 150˚ with the direction of motion. Sketch the

velocity triangles and calculate:

(1) Vane angles at inlet and outlet

(2) Work done when the vane discharging 300 lits/sec

Take loss due to friction over the vane as 10% of relative velocity.

[Ans: 47.01°, 11.02°, 51.33KW] [29; V. L. Patel]

12. A wheel having radial blades has 1 m diameter at inlet and 70 cm diameter at outlet.

Water enters the wheel at a velocity of 40 m/sec at an angle of 30˚ with the tangent

of vane tip velocity and leaves with a velocity of flow 5 m/sec. If the blade angles at

inlet and outlet are 35˚ and 40˚ respectively find

(1) The speed of wheel

(2) The work done per kg of water and

(3) Efficiency. [Ans: 116RPM, 115.06N-m/kg, 14.38%] [31; V. L. Patel]



ASSIGNMENT – 3 HYDRAULIC TURBINES

Theory 1. Give the classification of hydraulic turbines.

2. Define below terms:

a) Gross head

b) Net head

c) Hydraulic efficiency

d) Volumetric efficiency

e) Mechanical efficiency

f) Overall efficiency

g) Speed ratio

h) Jet ratio

3. Differentiate between:

a) The impulse and reaction turbine

b) Radial and axial flow turbine

c) Inward and outward radial flow turbine

d) Kaplan and propeller turbine.

4. Explain the components and working of a Pelton wheel. Give an expression for the

work done equation & expression for maximum efficiency of the Pelton wheel.

5. Explain the components & working of the Francis turbine with the help of a neat

sketch.

6. What is the function of draft tube? Explain various types of draft tube.

7. Explain various components & working of Kaplan turbine with the help of a neat

sketch.

8. Derive an expression for specific speed of a hydraulic turbine.

9. Explain the “Governing of Pelton turbine & Francis turbine”.

10. What is Cavitation? What are the effects & precaution of cavitation in hydraulic

turbine?

Examples Impulse Turbine / Pelton Wheel

1. A Pelton wheel is required to develop 8000 kW while working under head of 380m

at a speed of 500 rpm. If overall efficiency is 88%, find: a. Flow rate through the turbine, b. Runner diameter, c. No. of nozzles and d. No. of buckets in runner.

Assume jet ratio of 10, co-efficient of velocity as 0.97 and speed ratio of 0.46. [Jan – 2013]

2. The following data relate to a Pelton wheel:

Tangential velocity of bucket = 25 m/s

Head of water = 65 m

Deflection of jet on bucket = 165°

Discharge through the nozzle=110 litres/sec

Co-efficient of nozzle=0.95

Determine the power developed by the runner and the efficiency. [Nov-2011]



3. The gross available head for a Pelton wheel is 600m, out of which one third is lost

due to friction in the penstock which takes water to the nozzle of the Pelton wheel.

The rate of flow of water through the nozzles fitted at the end of the penstock is 2

m³/s. The angle of deflection of jet is 165°. The reduction in relative velocity while

passing through buckets as 15%.

Take speed ratio, Ku = 0.45 and co-efficient of velocity Cv = 0.978, D/d = 1/10,

mechanical efficiency = 95%,

Determine,

a) Power developed by the turbine,

b) Hydraulic efficiency,

c) The unit power, and

d) The dimensionless specific speed.

[Dec-2013]

Reaction Turbine

4. The internal and external diameters of an outward flow reaction turbine are 2m and

2.75m respectively. The turbine is running at 250 rpm and rate of flow of water

through the turbine is 5 m3/s. The width of the runner is constant at inlet and outlet

and is equal to 250mm. The head on the turbine is 150m. Neglecting thickness of the

vanes and taking discharge radial at outlet determine:

a. Vane angles at inlet and outlet

b. Velocity of flow at inlet and outlet.

[18.22; R. K. Bansal][Answer: 6.072°, 3.68°, 3.183m/s, 2.315m/s]

5. A Francis turbine develops 160 kW at 150 rpm under head of 10 m. The peripheral

velocity at inlet and flow velocity at inlet of runner are 0.3(2gH)0.5 and 0.9(2gH)0.5

respectively. The overall efficiency of turbine is 78% and hydraulic efficiency is 82%.

Assuming radial discharge at outlet, find (i) Guide blade angle and runner vane angle

at inlet and (ii) Diameter and width of runner at inlet. [Jan-2013]

OR

5. Francis turbine designed to develop 160 kW working under a head 10 m and

running at 200 rpm. The hydraulic losses in turbine are 15% of available energy. The

overall efficiency of turbine is 80%. Assume flow ratio=0.94 and speed ratio=0.25.

Calculate: (1) Guide blade angle and runner vane angle at inlet and (2) Diameter and

width at inlet. [Jun-2012]

6. A Kaplan Turbine produces 25MW operating under a head of 40 m. The blade tip

diameter is 2.5 times the hub diameter and the overall efficiency is 0.9. If the speed

and flow ratio are 2.0 and 0.6 respectively, calculate the diameter and speed of the

turbine. [May-2013]

7. A turbine is to operate under a head of 25 m at 200rpm. The discharge is 9 m3/sec. If

the efficiency is 90% determine, specific speed of machine, power generated, type of

turbine and performance under head of 20 m.

[Dec-2010][Reference: 18.37; R. K. Bansal]



ASSIGNMENT – 4 CENTRIFUGAL PUMPS

Theory

1. Give classification of the pumps. With neat sketch explain components & working of

centrifugal pump. Enlist and explain the various types of impeller used in centrifugal

pump.

2. Explain inlet & outlet velocity triangle for centrifugal pump & derive the work done

equation.

3. Describe various heads & efficiencies of centrifugal pump.

4. Derive an expression for pressure rise in the impeller of the centrifugal pump by

neglecting the frictional and other losses in the impeller.

5. How will you obtain an expression for minimum starting speed for a centrifugal

pump?

6. Explain following terms in detail for centrifugal pump:

1. Specific speed (Ns)

2. Net positive suction head (NPSH)

3. Maximum suction lift (hs)

4. Priming

7. Write notes on Multi-stage Centrifugal pump with neat sketch.

8. Discuss the various characteristic curves of a centrifugal pump.

9. Explain the Cavitation in pumps.

Examples

1. A centrifugal pump has the following dimensions: inlet radius = 80 mm, outer radius

= 160 mm, width of impeller at the outlet = 50 mm, β1 = 0.45 radians, β2 = 0.25

radians, width of the impeller at the outlet = 50 mm. assuming shockless entry

determine (i) the discharge, (ii) pressure rise through the impeller, (iii) % of total

work converted into kinetic energy and (iv) the head developed by the pump when

the impeller rotates at 90 radians/second. R.K Bansal 957/19.7

2. Find the power required to drive the centrifugal pump which delivers 0.04 m3/s 0f

water to a height of 20 m through a 15 cm diameter pipe and 100 m long. The overall

efficiency of the pump is 70% and coefficient of friction is 0.15. R.K Bansal 961/19.9



3. The axis of centrifugal pump is 2.5 m above the water level in the sump and the

static lift from the pump centre is 32.5 m. The friction losses in the suction and

delivery pipes are 1 m and 8 m respectively; suction and delivery pipes are each 12

cm diameter at outlet, the diameter and width of the impeller are 30 cm and 1.8 cm

respectively and the vanes are set back at an angle of 30ᵒ with tangent to the wheel.

For a speed of 1800 rpm, mechanical efficiency 0.75 and manometric efficiency 80%.

Make calculation for the discharge and the power required to drive the pump.

Assume radial entry. D.S Kumar 1070/17.6

4. A centrifugal pump impeller has diameter of 60 cm and width of 6 cm at the outlet.

The pumps runs at 1450 rpm and delivers 0.8 m3/s against head of 80 m .the leakage

loss after the impeller is 4% of discharge, the external mechanical loss is 10 kW and

the hydraulic efficiency is 80%. Determine the blade angle at outlet, the power

required and the overall efficiency of the pump. D.S Kumar 1072/17.8

5. A centrifugal pump with 1.2 m outlet diameter and 0.6 m inner diameter runs at 200

rpm and pumps 1880 Liters/s, the average lift being 6 m. the angle which the vanes

make at exit with the tangent to the impeller is 26ᵒ and the radial velocity of flow is

2.5 m/s. determine the (i) manometric efficiency and (ii) the least speed to start

pumping against head of 6 m. R.K Bansal 967/19.15

6. The impeller of the centrifugal pump is 30 cm diameter and 5 cm width at the

periphery, and has blades whose tip angles backwards 60 from the radius. The

pump delivers 17 m3/min and the impeller rotates at 1000 rpm. Assuming that the

pump is designed to admit radially, calculate (i) speed and direction of water as it

leaves the impeller (ii) torque exerted by the impeller on water (iii) shaft power

required (iv) lift of the pump. D.S Kumar 1075/17.12

7. The following requirements are to be satisfied by a centrifugal pump whose impeller

has internal and external diameters respectively. Suction and delivery heads = 5 m

and 20 m, diameter of suction and delivery pipes = 12 cm and 8 cm, discharge =

0.035 m3/s while running at 950 rpm. If the vane outlet angle is 45ᵒ, the flow

velocity is constant and equal to 1.8 m/s and power required to drive the pump is 15

kW, make calculations for (i) the vane angle of impeller at inlet, (ii) the overall and

manometric efficiency of the pump. D.S Kumar 1078/17.16



ASSIGNMENT – 5 RECIPROCATING PUMPS

Theory

1. Give classification of the Reciprocating pumps. With neat sketch explain

construction & working of single acting reciprocating pump.

2. What is an air vessel? Explain with a neat sketch the working of air vessel in

reciprocating pump.

3. Give expression for discharge, work done power and slip of reciprocating pump.

4. Compare the reciprocating pump with centrifugal pump. Draw theoretical indicator

diagram of reciprocating pump.

Examples

1. The cylinder bore diameter of a single acting reciprocating pump is 150 mm and its

stroke is 300 mm. The pump runs at 50 rpm and lifts water through a height of 25 m.

The delivery pipe is 22 m long and 100 mm in diameter. Find the theoretical

discharge and theoretical power required to run the pump. If the actual discharge is

4.2 litres/sec. Find the % slip and acceleration head at the beginning and middle of

the delivery stroke.

2. The length and diameter of a suction pipe of a single acting reciprocating pump are 5

m and 10 cm respectively. The pump has a plunger of diameter a5 cm and a stroke

length of 35 cm. the Centre of the pump is 3 m above the water surface in the pump.

The atmospheric pressure head is running at 35 rpm. Determine: (1) Pressure head

due to acceleration at the beginning of the suction stroke, (2) Maximum pressure

head due to acceleration and (3) Pressure head in the cylinder at the beginning and

at the end of the stroke.



ASSIGNMENT– 6 RECIPROCATING COMPRESSOR

Theory

1. Discuss the application of compressed air and give detail classification of air

compressors. 2. Define below terms:

a. Brake power

b. Indicated power

c. Frictional power

d. Mechanical efficiency

e. Compression ratio (Pressure

ratio)

f. Free air delivered

g. Single-double acting

h. Isothermal efficiency

i. Overall Isothermal efficiency

j. Adiabatic efficiency

3. Explain principle of working of single stage single acting reciprocating air

compressor with schematic diagram. 4. Prove the work done equation for compression of single stage single acting

reciprocating compressor neglecting (without) clearance volume for following three

mode of compression:

I. Polytropic compression (PVn = C)

II. Adiabatic compression (PVγ = C)

III. Isothermal compression (PV = C)

OR

Prove that the work done/kg of air in single stage single acting reciprocating air

compressor without clearance is given by,

[(

)

]

5. What are the methods used to approach approximate isothermal compression?

6. Why clearance volume is provided in reciprocating air compressor? Prove the work

done equation for compression of single stage single acting reciprocating air

compressor with clearance volume for polytropic compression (PVn = C).

OR

Derive an expression for indicated work of reciprocating air compressor considering

its clearance.

7. Define volumetric efficiency. Derive the expression for volumetric efficiency referred

to suction and ambient conditions. Discuss the factors affecting on it.

8. Justify the need for multi-staging in reciprocating air compressor. Discussed

advantages and disadvantages of multi-stage compression.

9. Explain the working of two stage reciprocating air compressor and give the

expression of work done of two stage single acting reciprocating air compressor



neglecting (without) clearance volume for perfect (complete) and imperfect

(incomplete) intercooling with P-V and T-S diagram.

OR

Why intercooling is employed in multistage compression? Give explanation.

10. Derive an expression of work done for two stage single acting reciprocating air

compressor with clearance volume for perfect and imperfect intercooling with P-V

and T-S diagram.

11. Show that for a two stage reciprocating air compressor with complete intercooling

the total work of compression becomes minimum (maximum efficiency) when the

pressure ratio in each stage is equal.

OR

Derive an expression for the optimum value of the intercooler pressure (condition of

minimum work) in a two stage reciprocating air compressor for perfect intercooling

condition.

OR

Show that for multi stage compression, the intermediate pressure for optimum

condition is to be geometric mean of its two neighboring pressures OR √

12. Derive an expression for optimum intermediate pressure and work done in two

stage reciprocating air compressor with imperfect intercooling with ideal

intercooler pressure.

OR

Show that optimum intermediate pressure for two stage air reciprocating

compressor neglecting clearance with incomplete intercooling is given by,

√ ( )

13. Describe the methods of controlling output of reciprocating air compressor.



Examples

CASE (A) –: Single-Multi Stage, Single-Double acting Compression

without Clearance Volume

1. A single stage, single acting reciprocating compressor compresses 1.8 m3 of air per

min from 1 bar and 20°C to 8 bar delivery pressure. Determine each of the below

neglecting clearance, when compression takes place polytropically (PV1.3=

constant), adiabatically (PV1.4 = constant), and isothermally (PV = constant).

1) Mass of the air inducted in kg/min

2) Temperature and volume of air at the end of compression

3) Indicated power

4) Heat transfer during compression

5) Brake power of compressor if the mechanical efficiency is 85%

6) Isothermal efficiency, adiabatic efficiency

7) Size of the cylinders if compressor runs at 220 rpm and piston speed 130

m/min. Provide your explanation on the answers with P-V and T-S diagram.

Answers: (a) Polytropic compression: (1) m = 2.140 kg/min (2) T2 = 473.45 K, V2 =

0.36 m3/min (3) I.P = 8.006 kW (4) Q = 1.539 kW (5) B.P = 9.419 kW, (6) ηiso =

77.92%, ηad = 93.96%, (7) D = 0.187 m, L = 0.295 m

(b) Adiabatic compression: (1) m = 2.140 kg/min (2) T2 = 530.75 K, V2 = 0.40

m3/min (3) I.P = 8.520 kW (4) Q = 0 kW (5) B.P = 10.023 kW

(c) Isothermal compression: (1) m = 2.140 kg/min (2) T2= T1= 293 K, V2 = 0.225

m3/min (3) I.P = 6.238 kW (4) Q = I.P = 6.238 kW (5) B.P = 7.338 kW

[Attention Note: If above compressor is employed with two stage compression with

perfect intercooling to achieve same delivery pressure then what will be consequence

on brake power consumption in case?] V.L Patel- Page 6.62/10

2. In a two stage single acting air compressor the L.P cylinder draws in 0.15 m3 of air

at a temperature of 15°C and a pressure of 1 bar. It is compressed adiabatically to 2

bar and then delivered to a intercooler where the air is cooled at constant pressure

to 15°C. This air is then drawn in to the H.P cylinder and compressed adiabatically to

4 bar and delivered to the receiver. Calculate,

1) Indicated power required when compressor running at 100 rpm

2) Indicated power during single stage compression

3) Saving in power if compressor runs at two stage considering complete

intercooling

Answers: (1) I.P (for two stage) = 38.33 kW, (2) I.P (for single stage) = 42.52 kW, (3)

Saving in power = 9.86% V.L Patel- Page 6.59/7

3. A two stage single acting RAC takes in air at a pressure 1 bar, 20°C and compresses

to pressure of 55 bar. The air is cooled in intercooler at constant pressure of 10 bar

to a temperature of 40°C. The diameter of L.P cylinder is 175 mm and both the



cylinder have 225 mm stroke. If the compression follow the law of PV1.25 = C. Find

indicated power if the compressor runs at 150 rpm.

Answers: I.P = 6.89 kW

4. Determine the size of L.P and H.P cylinders of a compound double acting RAC which

runs at 100 rpm and requires 75 kW indicated power. The suction and delivery

pressures are 0.985 bar and 8.45 bar respectively and the intercooler pressure is 2.8

bar. The piston speed is 137.1 m/min and polytropic index is 1.35. Assume perfect

intercooling between two stages.

Answers: dLP = 0.41 m, dHP = 0.24 m

5. A three stage single acting RAC is required to compress 8 m3/min of air from 1 bar,

300 K to a final pressure of 81 bar, assuming intercooling is perfect in between

stages and the compressor is design for minimum work. Determine, (1)

Dimensions of each cylinder for the speed of 900 rpm. Take polytropic index = 1.25

throughout. Given that the stroke of the compressor is equal to the diameter of L.P

cylinder, (2) Theoretical power required to drive compressor.

Answers: (1) dLP = 0.2245 m, dIP = 0.1080 m, dHP = 0.0519 m, (2) I.P = 68.08 kW

CASE (B) –: Single-Multi Stage, Single-Double Acting Compression with

Clearance Volume

6. A 23 kW electric motor drives a single cylinder, single acting reciprocating air

compressor running at 300 rpm. Mechanical efficiency = 87%. The air inlet

conditions are 1.013 bar and 15°C respectively, delivery pressure = 8 bar, index of

compression and re-expansion = 1.3. Clearance volume is 7% of the stroke

volume. Diameter of cylinder is same as its stroke length. Calculate,

1) FAD in m3 of air per minute

2) Volumetric efficiency

3) Cylinder dimensions V.L Patel- Page 6.74/18

Answers: (1) V1-V4 = 4.476 m3/min, (2) ηv = 72.70%, (3) d = l = 0.296 m

7. A single stage, single acting reciprocating air compressor delivers air at 7 bar. The

pressure and temperature at the end of suction are 1 bar and 27°C. It delivers 2.3

m3of free air per minute when speed is 150 rpm. If clearance volume of 5 % of the

stroke volume, ambient pressure and temperature are 1.013 bar and 15°C. Take n =

1.25. Determine,

1) Indicated power

2) Power required to run the compressor if mechanical efficiency is 80%

3) Mean effective pressure in bar


5) Cylinder size if stroke to bore ratio 1.3.

Answers: (1) I.P = 9.606 kW, (2) B.P = 12.007 kW, (3) Pm = 1.933 bar, (4) ηv = 81.28

%, (5) d = 0.269 m, l = 0.3498 m V.L Patel- Page 6.84/25



8. A single stage, single acting reciprocating air compressor has bore of 127.5 mm,

stroke of 115 mm, clearance volume is 70 cm3, suction pressure and temperature

are 1.013 bar, 20°C respectively, delivery pressure is 5.2 bar, speed of compressor is

105 rpm, polytropic index is 1.32 for compression and expansion. Determine,

1) Delivery of air in kg/min

2) Indicated power if the delivery pressure increased to 25 bar by the addition of

a H.P cylinder of same stroke together with an intercooler which reduces

temperature to 38°C.

3) Bore of the H.P cylinder allowing clearance volume to 6 % of the swept

volume and same index 1.32. V.L Patel- Page 6.99/35

Answers: (1) mad = 0.164 kg/min, (2) I.P = 0.4612 kW, (3) dHP = 0.0586 m

9. A single acting two stage compressor with complete intercooling delivers 6 kg/min

of air at 16 bar. Assuming intake at 1 bar and 15°C and compression and expansion

with the law PV1.3 = C. Calculate,

1) Power required to run the compressor

2) Isothermal efficiency

3) Free air delivery in m3/min

4) Volumetric efficiency and swept volumes of each cylinder, if the clearance

volume ratios for L.P and H.P cylinders are 0.04 and 0.06 and speed of

compressor is 420 rpm.

Answers: (1) I.P = 27 kW, (2) ηiso = 84.88 %, (3) Va (FAD) = 4.259 m3/min, (4) ηVLP =

92.38 %, ηVHP = 88.57 %, VSLP = 0.0128 m3, VSHP = 0.00333 m3

10. A single acting, two stage reciprocating air compressor running at 5 rps delivers air

at a pressure of 18 bar while suction pressure is 98 kPa and 300 K. intermediate

pressure is 4 bar, while the temperature of air after the intercooler is 305 K.

Clearance volume of L.P cylinder is 5% of swept volume. Capacity of compressor

under free air delivery at 1 bar, 15:C is 2.25 m3/min. Find:


2) Work supplied

3) Dimension of L.P cylinder if bore = stroke length

4) Isothermal efficiency

Answers: (1) ηv = 90.49 %, (2) W = 13.7547 kW, (3) dLP = 0.2239 m, (4) ηiso = 82.65 %

[Note: how volumetric efficiency is affected at higher altitude?]

11. A two stage reciprocating air compressor takes air at 1 bar, 20°C and delivers it at

15 bar runs at 300 rpm. There is 10% pressure drop in the intercooler. If the

compression and expansion follow the law PV1.4 = constant in the both the cylinder.

If the L.P cylinder has a bore of 22 cm and stroke of 33 cm and there is perfect

intercooling. Clearance volume is 6 % of stroke volume in L.P cylinder. If

Clearance volume in H.P cylinder is 3% of stroke volume and the bore to stroke in

H.P cylinder is 1:1.5. Determine,

1) Minimum power required



2) Bore and stroke of the H.P cylinder V.L Patel- Page 6.131/AE-4

Answers: (1) Pmin = 19.458 kW, (2) dHP = 0.1399 m, l = 0.21 m

[Note: If there is an ideal intercooler pressure then what will be influence on power

required to run the compressor?]



ASSIGNMENT – 7 ROTARY COMPRESSORS

Theory

1. Discuss the basic principle and classification of rotary air compressor.

2. Describe the working of root blower with neat sketch and P-V diagram.

3. Explain vane type compressor with neat sketch and P-V diagram.

4. Describe the working of a screw compressor and list its applications.

5. Describe the working of scroll compressor with neat sketch. State its advantages.

6. Give compare reciprocating compressor with rotary compressor.

7. Give compare scroll compressor with rotary compressor.

Examples

1. A two lobe root blower compresses 0.05 m3 of air from 1 bar to 1.5 bar per

revolution if the speed is 220 rpm. Calculate the root efficiency, volume of air

handled per cycle and power required to drive the blower.

Answer: 86%, 0.0125 m3/cycle, 5 kW V.L Patel- Page 9.4/1

2. A vane type rotary compressor has a free air delivery of 0.05 m3 per revolution

when it compressed air from 1 bar to 1.5 bar. Determine the work expended/rev

in driving the compressor and the efficiency of compressor when the ports are so

placed that (i) there is no internal compression (ii) there is 35 % pressure rise

due to internal compression before back flow occurs. Also determine power

required to drive the compressor. If the speed is 120 rpm in each case.

Answer: (i) 86%, 5 kW (ii) 94.6%, 4.546 kW V.L Patel Page 9.15/2

3. Compare the work inputs required for roots blower and a vane type compressor

having same induced volume of 0.03 m3 per revolution. The inlet pressure being

1.013 bar and the pressure ratio is 1.5. For the vane type assume that the internal

compression takes place through half of the pressure range.

V.L Patel- Page 9.17/4

Answer: Root blower W = 1.521 kJ, vane type W = 1.352 kJ/rev

4. A vane type rotary compressor has an air delivery of 0.01 m3per revolution when

it compressed air from 1 bar to 2 bar. Determine the efficiency of compressor

when the ports are so placed that (i) there is no internal compression (ii) there is

45 % pressure rise due to internal compression before back flow occurs.



Answer: (i) 76.65% (ii) 94.19% R.N Patel- Page 9.19/8

5. A vane type rotary compressor work between pressure limits of 1 bar and 1.5 bar

and gives 4 m3/min free air delivered when running at 200 rpm. Determine the

power required to drive the compressor when the ports are so placed that (i)

there is no internal compression (ii) there is 50 % pressure rise due to internal

adiabatic compression before back flow occurs.

Answer: (i) 1.535 kW (ii) 2.955 kW R.N Patel-Page 9.19/9

6. Determine the compression efficiency of roots blower if it compressors 0.06 m3

of air per revolution of the rotor to raise the pressure of air from 1.013 bar to

2.026 bar.

Answer: 68.74% R.N Patel Page 9.20/10



ASSIGNMENT – 8 CENTRIFUGAL COMPRESSORS

Theory

1. Describe with neat sketch the principle of operation and essential parts of

centrifugal compressors and state its advantages with applications.

OR

Describe principle construction and working of centrifugal compressor.

2. Explain static and stagnation (total head) properties with T-S diagram.

3. Explain inlet and outlet velocity triangles for the centrifugal compressor.

4. Define below terms.

a. Isentropic efficiency

b. Slip factor

c. Power input factor

d. Pressure (loading) coefficient

e. Static and stagnation property

5. Define degree of reaction for centrifugal compressor stage and prove its expression.

6. Explain the phenomenon of surging, choking and stalling in centrifugal compressor.

7. What are the various losses occurring in centrifugal compressor?

Examples

1. Following data relates to the Centrifugal compressor.

Speed = 7000 RPM

Impeller tip diameter = 50 cm

Static temperature of air at inlet= 282 K

Axial velocity of air at inlet = 120 m/s

Slip factor = 0.9

Power input factor = 1.04

Isentropic efficiency = 82%

Specific heat of air = 1005 J/kg K

Assume no whirl at inlet. Determine the pressure ratio developed and power

required per kg of air to drive the compressor. Repeat the example if there is no slip

and power input factor is unity.

Answers: Case-a: (1) P02/P01 = 1.346, P = 31431.40 J/kg, Case-b: (1) P02/P01 = 1.09, P

= 33580 J/kg


Free air delivered = 1200 m3/min

Pressure ratio = 1.5

Index of compression = 1.5

Speed = 5000 RPM

Velocity of flow at inlet and outlet= 3600 m/min

Width of impeller at inlet and outlet= 177 mm and 67.5 mm

Assuming all pressure rise to take place in impeller. Find, (1) the angle at which air

from

impeller enters the casing, (2) impeller blade angle at inlet.



Answers: (1) α2 = 10.81:, (2) β1 = 20.9:

3. Following data refers to the Centrifugal compressor.

Speed = 16000 RPM

Isentropic efficiency = 0.82

Inducing temperature of air = 17:C

Impeller mean eye diameter = 200 mm

Work done by impeller = 175 kJ/kg

Absolute velocity at inlet = 120 m/s

Slip factor = 0.78

If guide vanes at inlet give the air a prewhirl of 20⁰. Determine (1) the total pressure

ratio, (2) impeller tip diameter, (3) absolute angle at inlet and angle at which air

enters the casing, (4) blade angle at impeller inlet and outlet, (5) relative velocity at

inlet and outlet.

Answers: (1) P02/P01 = 3.95, (2) D2 = 0.576 m, (3) α1 = 70:, α2 = 16.66:, (4) β1 =

41.71:, β2 = 46.70:, (5) Cr1 = 169.465 m/s, Cr2 = 154.922 m/s

4. A single sided Centrifugal compressor is required to deal with following data.

Mass flow rate = 10 kg/s

Total head pressure ratio = 4.5

Speed = 270 rps

Ambient air conditions at entry = 1 bar, 30:C


Slip factor = 0.94


Specific heat of air = 1005 J/kg K

If the air enters without prewhirl. Calculate, (1) rise in total temperature, (2) tip

diameter of impeller, (3) inlet eye annulus area, (4) impeller tip speed, (5) power

required to drive the compressor.

Answer: (1) T02-T01= 203.3 K, (2) D2 = 0.55 m, (3) Ae = 0.0637 m2, (4) u2 = 466.2

m/s, (5) P = 2043.16 kW


Total pressure ratio = 4


Speed = 11000 RPM

Inducing air temperature = 288 K

Mean eye diameter = 400 mm


Impeller tip diameter = 750 mm

Angle of prewhirl = 20:

Calculate the number of impeller radial vanes by using Stanitz formula.

Answer: Z ≈ 16

6. The air entering the impeller of a centrifugal compressor has an absolute axial

velocity of 100 m/s. At the impeller exit the relative air angle measured from the



radial direction is 26: 36’. The radial component of the velocity is 120 m/s, the tip

speed of the radial vanes is 500 m/s, air flow rate is 2.5 kg/s, mechanical efficiency is

95%, the eye of the impeller has a hub to tip radius ratio of 0.3, the total to total

efficiency is 80%, stagnation pressure and temperature at the compressor inlet are

1.013 bar and 288 K.. Determine (1) the power required to drive the compressor, (2)

the suitable inlet diameter assuming the inlet flow is incompressible and (3) overall

total pressure ratio assuming velocity at exit from the diffuser is negligible.

Answer: (1) P = 578.947 kW, (2) Det = 5.273 m, (3) P02/P01 = 5.273

7. The following data refers to a single sided centrifugal compressor.

Overall diameter of the impeller= 50 cm

Eye tip diameter = 30 cm

Eye root diameter = 15 cm

Rotational speed = 15000 RPM

Air mass flow rate = 10 kg/s

Inlet total head temperature = 300 K

Power input factor = 1.04

Slip factor = 0.9

Total head isentropic efficiency = 80%

Find, (1) the total head pressure ratio (2) power required to drive the compressor

(3) the inlet angle of the vanes at the root and tip of impeller eye.

Answer: (1) P02/P01 = 3.11, (2) P = 1443.18 kW, (3) β1t = 32.48:, βr1 = 51.85:

8. Following data relates to the centrifugal compressor.

Volume flow rate = 10 m3/s

Speed = 6000 RPM

Pressure ratio = 4


Velocity of flow at inlet and outlet = 60 m/s

Outer diameter to inner diameter = 2

Slip factor = 0.9

Blade area coefficient = 0.92 at inlet

Determine: (1) theoretical power required, (2) impeller diameter at inlet and outlet,

(3) width of impeller at inlet, (4) impeller blade angle at inlet, and (5) diffuser blade

angle at inlet.

Answer: (1) P = 2050.3 kW (2) D1 = 0.705 m, D2 = 1.41 m (3) b1 = 0.0817 m (4) β1 =

15.15: (5) α2 = 7.7:

9. Following operating conditions are relates to the centrifugal compressor.


Diameter at inlet = 450 mm

Diameter at outlet = 800 mm

Radial component of velocity at impeller exit = 52 m/s

Slip factor = 0.9

Impeller speed = 10000 RPM



Static pressure at impeller exit = 2.2 bar

Stagnation pressure and temp. at inlet = 1.013 bar, 288 K

If the air leaving the guide vanes has a velocity of 90 m/s at 75: to the tangential

direction. Determine (1) the relative Mach number assuming frictionless flow

through the guide vane, (2) impeller total head isentropic efficiency and (3) power

required to drive the compressor.

Answer: (1) M1r = 0.679, (2) ηc = 0. 935, (3) P = 1218.86 kW

10. In a radial blade Centrifugal compressor has following data:

Speed = 16000 RPM

Total head pressure ratio = 4

Atmospheric pressure and temperature are= 1 bar, 27:C

Diameter of hub at impeller eye = 15 cm

Axial velocity at inlet = 120 m/s

Absolute velocity at the diffuser exit = 120 m/s


Total to total adiabatic efficiency = 80%

Pressure coefficient = 0.72

Find: (1) eye tip diameter, (2) impeller tip diameter, (3) power required to drive the

compressor and (4) static conditions at exit.

Answer: (1) Det = 0.316 m, (2) D2 = 0.538 m, (3) P = 1467.3 kW, (4) T3 = 475 K, P3 =

3.793 bar.

11. A 580 kW motor drives a centrifugal compressor of 480 mm outer diameter at a

speed of 2000 rpm. At the impeller outlet the blade angle is 26.5° measured from the

radial direction and the flow velocity at exit from the impeller is 122 m/s. If a

mechanical efficiency is 95% is assumed. Assume there is no slip and the flow at

inlet is incompressible and ambient air conditions are 1.013 bar and 288 K.

Determine: (1) the air flow is to be expected, (2) the eye tip and hub diameters if a

radius ratio of 0.3 is chosen for the impeller eye and if the velocity at inlet is 95 m/s

with zero whirl, (3) overall total to total isentropic efficiency If an overall total

pressure ratio of 5.5 is required.

Answer: (1) m = 2.481 m/s, (2) Dt = 0.172 m, Dh = 0.0517 m, (3) ηo = 0.818

12. A single sided centrifugal compressor delivers 8.15 kg per second with a total

pressure ratio 4.4. The compressor runs at 18000 RPM. The entry to the eye for

which the internal diameter is 12.7 cm is axial and the mean velocity at the eye

section is 148 m/s with no prewhirl. Static conditions at the eye section are 15:C and

1 bar. The slip factor is 0.94 and the isentropic efficiency is 0.785. Neglecting losses

calculate, (1) the rise in total temperature during compression, (2) the tip speed of

the impeller eye and tip speed of the impeller outlet, (3) impeller tip diameter, (4)

power required to drive the compressor, (5) eye external diameter.

Answer: (1) T02 – T01 = 201.9 K, (2) uet = 256.3 m/s, u2 = 464.6 m/s, (3) 0.272 m, (4)

1653.7 kW, (5) Det = 0.272 m



13. A two stage centrifugal compressor delivers air with an overall pressure ratio of 12:1

without intercooling between stages. The pressure and temperature of the

surrounding air are 1 bar and 22:C respectively. The overall isentropic efficiency is

72% while that of the first stage is 77%. If the actual works done in both the stages

are equal. Determine: (1) the pressure and temperature at the exit from the first

stage, (2) the approximate tip velocity of the first stage impeller assuming

approximate value for the pressure coefficient.

Answer: (1) P02 = 4.666 bar, To2 = 233.8:C, (2) u2 = 467.5 m/s



ASSIGNMENT – 9 AXIAL COMPRESSORS

Theory

1. What is an axial flow compressor? With suitable sketch explain working and

construction of axial compressor.

2. Explain inlet and exit velocity triangles for axial flow compressor stage.

3. Explain aerofoil blading & Lift and Drag coefficient for blade.

4. State advantages of an axial flow compressor. Give comparison between centrifugal and

an axial flow compressor.

5. Discuss performance characteristic of an axial flow compressor.

Examples

1. An axial flow compressor of 50% reaction design has blades inlet and outlet angles of

45: and 10: respectively. The compressor is to be produced a stagnation pressure ratio

of 7.5 with an overall total head efficiency of 0.85 when inlet stagnation is 37:C. The

blade speed and axial velocity of flow are constant throughout the compressor. The

work done factor is 0.87. Taking the value of 200 m/s for blade speed. Find the number

of stages required.

Answer: Number of stages = 12 R.L Patel 11.47/1

2. An axial flow compressor has 8 stages and the following data apply to each stage at the

mean diameter.

Blade speed = 210 m/s

Degree of reaction = 0.5

Stage efficiency = 0.85

Polytropic efficiency = 0.88

Angle of absolute air velocity at rotor inlet = 15:

Angle of absolute air velocity at rotor inlet = 45:

Work done factor = 0.86

Inlet stagnation pressure = 1 bar

Inlet stagnation temperature = 27:

Determine the total pressure ratio of the first stage and overall static pressure ratio.

Answer: (i) 1.233 (ii) 3.98 R.L Patel 11.48/2

3. First stage of an axial flow compressor delivers 20 kg/s of air at 9000 rpm.Stage

temperature rise is 150 m/s. the work done factor is 0.96 and blade occupies 10% of the

axial area of flow. Taking 50% reaction, calculate

(i) Inlet and outlet blade angles of moving blades and fixed blades

(ii) Blade height at entry

Assume ambient condition as 288 K and 1 bar.

Answer: (i) inlet blade angles α1= 12: β1 = 44.64:, outlet blade angles α2 = 44.64, β2 =

12: (ii) h = 0.1132 m R.L Patel 11.50/3

4. The following data refers to an axial flow compressor.



The total pressure ratio = 4

Overall total head isentropic efficiency = 0.85

Inlet stagnation temperature = 290 K

The inlet and outlet angles from the rotor blades = 45: and 10:


Assuming blade speed is 220 m/s. The rotor and stator blades are symmetrical. The

mean blade speed and axial velocity remain constant through the compressor. Find,

(i) Polytropic efficiency

(ii) Number of stages required

(iii) Inlet Mach number relative to rotor at the mean blade height of the first stage.

Answer: (i) 6 stages (ii) 0.8 R.L Patel 11.54/5

5. A multi stage axial flow compressor absorbs 2211 kW when delivering 10 kg/s of air

from stagnation conditions 1bar and 15C:. If the polytropic efficiency of the compressor

is 0.9 and the stage stagnation pressure ratio is constant. Calculate,

(i) The number of stages

(ii) Final delivery pressure

(iii) Overall isentropic efficiency of the compressor.

Answer: (i) 9 stages (ii) 5.975 bar (iii) 87.2% R.L Patel 11.59/8

6. The following data refers toan axial flow compressor.

Pressure of air at inlet ofan axial flow compressor = 768 mm of Hg

Temperature of air at inlet ofan axial flow compressor = 41C:

Diameter at mean blade section = 500 mm

Peripheral velocity = 100 m/s

Mass flow rate through the stage = 25 kg/s


Mechanical efficiency = 92%

Stage efficiency = 88%

If air angles are β1 = 51:, α1 = α3 =7:and the air is turned through 42: through the rotor.

Determine,

(i) Air angle at the stator entry

(ii) Blade height at entry

(iii) Hub to tip ratio

(iv) Stage loading coefficient

(v) Power input

(vi) Stage pressure ratio R.L Patel 11.61/9

Answer: (i) α2 =50.18: (ii) h = 19 cm (iii) 0.449 (iv) 0.7532 (v) 204.692 kW (vi) 1.0754

7. Each stage of an axial flow compressor is of 0.5 reaction, has the same mean blade speed

and the same flow outlet angle of 30:relativ to the blades. The mean flow coefficient is

constant for all stages at 0.5. At inlet to the first stage the stagnation temperature and

pressure is 278 K, stagnation pressure is 1.013 bar, the static pressure is 0.873 bar and

the floe area is 0.372 m2. Determine the axial velocity, mass flow rate and power



required to drive the compressor when there are 8 stages and the mechanical efficiency

is 99%.

Answer: (i) 132.1 m/s (ii) 56.1 kg/s (iii) 10030 kW Page 11.69/12

8. The following data refers toan axial flow compressor.

Stage stagnation temperature rise = 22 K

Mass flow of air = 25 kg/s

Rotational speed = 150 rev/s

Axial velocity through the stage = 157 m/s

Mean blade speed = 200 m/s


Reaction at mean radius = 50%

Rotor blade aspect ratio = 3

Inlet stagnation pressure and temperature = 1.013 bar, 288 K

Solidity = 0.8

Determine,

(i) The blade and air angle at the mean radius

(ii) The mean radius

(iii) The blade height

(iv) The pitch and chord

(v) The number of blades

Answers: (i) β1 = 45.2:, β2 = 14.93:(ii) 0.2122 m (iii) h = 0.11 m (iv) S = 0.02928 m,

0.0366 m (v) 45.53

9. An axial flow air compressor stage has a mean diameter of 60 cm. and runs at 15000

rpm if the actual temperature rise and pressure ratio developed are 30°C and 1.35

respectively. Determine, (I) Power required to drive the compressor while delivering 57

kg/s of air, if the mechanical efficiency is 86 percent and inlet temperature rise is 35 °C,

(II) The stage loading coefficient and ,(III) The degree of reaction if the temperature at

the rotor exit is 55 °C.



ASSIGNMENT 10 MISCELLANEOUS HYDRAULIC MACHINES

Theory

1. Explain construction and working of below miscellaneous machines with

diagram.

a) Hydraulic press

b) Hydraulic accumulator

c) Hydraulic intensifier

d) Hydraulic crane

e) Hydraulic jack

f) Hydraulic lift

g) Hydraulic ram

h) Fluid couplings

i) Fluid torque converter

j) Air lift pump

ASSIGNMENT-1 HYDROPOWER PLANT Power... · ASSIGNMENT-1 HYDROPOWER PLANT Theory ... inlet and outlet...

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