Upload
others
View
32
Download
6
Embed Size (px)
Citation preview
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.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1
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:
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2
(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]
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 3
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]
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1
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.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2
[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]
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1
ASSIGNMENT – 4 CENTRIFUGAL PUMPS
Theory
1. What is pump? Give classification of the pumps. Write down difference between
Positive displacement pumps and Rotodynamic pumps.
2. Explain how centrifugal pumps are classified? With neat sketch explain components
& working of centrifugal pump. Enlist and explain the various types of impeller used
in centrifugal pump.
3. Explain inlet & outlet velocity triangle for centrifugal pump & derive the work done
equation.
4. Describe various heads & efficiencies of centrifugal pump.
5. Derive an expression for pressure rise in the impeller of the centrifugal pump by
neglecting the frictional and other losses in the impeller.
6. Define the slip in Centrifugal pump. Explain briefly with sketch, the slip in
centrifugal pump. How it can be eliminated?
7. How will you obtain an expression for minimum starting speed for a centrifugal
pump?
8. Define and derive following terms for centrifugal pump:
1. Specific speed (Ns)
2. Maximum suction lift (hs)
3. Priming
9. Define and derive equation of NPSH in centrifugal pump? How its value significantly
affects efficiency of centrifugal pump.
10. Write brief notes on Multi-stage Centrifugal pump with neat sketch.
11. Discuss the various characteristic curves of a centrifugal pump.
12. What is cavitation? What are its causes? How it can be prevented in centrifugal
pump?
13. With neat sketch explain construction and working of submersible pump.
14. With neat sketch explain construction and working of Mud pump and Deep well
pump.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2
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 of
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/sec, 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
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 3
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 are 20 cm and 40 cm 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
Practice Examples
1. A centrifugal pump discharges 0.15 m3/sec of water against a head of 12.5 m, the
speed of the impeller being 600 rpm. The outer and inner diameters of impeller are
500mm and 250mm respectively and the vanes are bent back at 35˚ to the tangent at
exit. If the area of flow remains 0.07 m2 from inlet to outlet, calculate:
a. Manometric efficiency of the pump
b. Vane angle at inlet (Ө), absolute angle at the outlet (β)
c. Absolute velocity (V2) & relative velocity (Vr2 ) at the outlet
d. Width of the impeller at inlet and outlet
e. Work done by impeller on water per second
f. Loss of head at inlet to impeller when the discharge is reduced by 40% without
changing the speed. R.K Bansal 954/19.5
2. The external and internal diameter of an impeller of a centrifugal pump which is
running at 1000 rpm, are 200mm and 400mm respectively. The discharge through
pump is 0.04 m3/sec and velocity of flow is constant and equal to 2.0 m/sec. The
diameters of the suction and delivery pipes are 150mm and 100mm respectively
and suction and delivery heads are 6m (abs.) and 30 m (abs.) of water respectively.
If the outlet vane angle is 45˚ and power required to drive the pump is 16.186KW,
determine: R.K Bansal 959/19.8
a. Flow velocities in suction and delivery pipe
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 4
b. Manometric head and Manometric efficiency
c. The Mechanical efficiency and Overall efficiency of the pump
3. A three stage centrifugal pump has impellers 30 cm in diameter and 1.5 m wide at
outlet. The vanes are curved back at the outlet at 30ᵒ to the tangent at outlet and
occupy 8% of the outlet area. While running at 1000 rpm delivering 40 litres per sec
with manometric efficiency is 85% and the overall efficiency is 75%. Determine the
(i) head generated by the pump, (ii) Torque exerted by the impeller and shaft power.
D.S Kumar 1069/17.4
4. A centrifugal pump of 1.25 m diameter is designed to pump 1.5 m3/s through 75 m
height whilst running at 600 rpm. At outlet the vanes are set back at angle of 25 with
tangent to the wheel. If the measured power is 1325 kW and the pump has an
effective circumferential area of 0.4 m2 at outlet, workout: (i) theoretical head with
the assumption of infinite number of vanes, (ii) theoretical head with the
assumption that the net power imparted to the water flowing through the impeller
gets transformed into head without any hydraulic loss, and (iii) hydraulic & overall
efficiencies if external mechanical loss is equivalent to 45 kW and the leakage loss
amounts to 4%. D.S Kumar 1071/17.7
5. A centrifugal pump having impeller diameter of 1 m has backward curved vanes
which make angle of 25ᵒ with the wheel tangent at the blade tip is 10 m/s and the
slip coefficient is 0.85. Determine: (i) actual work input/kg of water flow (ii)
absolute velocity of fluid at the impeller tip and (iii) hydraulic efficiency, considering
that kinetic energy at the outlet is wasted. How the hydraulic efficiency would
change if the pump is fitted with a diffusion chamber of 75% efficiency so that exit
velocity is reduced to 12m/s. D.S Kumar 1073/17.9
6. The Impeller of the centrifugal pump has a diameter of 10cm and breadth 3.5 cm at
the inner periphery; the corresponding dimensions at the outer periphery are 20 cm
and 1.7 cm respectively. The pump runs at 1500 rpm, has 7 vanes at entry and exit
angles equal to 16 and 30 respectively. Calculate (i) theoretical discharge for
shockless entry, (ii) the theoretical head developed, (iii) the actual head produced,
the losses and power required to drive the pump. D.S Kumar 1074/17.11
7. Water enters radially through a centrifugal pump whose impeller has a diameter of
30 cm and breadth 15 cm; the corresponding dimensions at the outer periphery are
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 5
60 cm and 7.5 cm. the blades are curved backward at 30 to the tangent at exit and
the discharge is 225 lit/sec. if the rotational speed of the impeller is 1200 rpm and
the pump delivers water to a height of 115 m, calculate: (i) the theoretical head
develop (ii) the pressure rise across the impeller assuming losses are equal to 10%
of velocity head at the exit, (iii) the pressure rise and the loss of head in the volute
casing, (iii) power required to drive the pump assuming 65% overall efficiency, (iv)
mechanical efficiency. D.S Kumar 1079/17.17
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1
ASSIGNMENT – 5 RECIPROCATING PUMPS
Theory
1. Give classification of the Reciprocating pumps. With neat sketch explain
construction & working of single acting single stage reciprocating pump.
2. Explain function of an air vessel? Explain with neat sketch the working of
reciprocating pump with an air vessel.
3. Give expression for discharge, work done and power of reciprocating pump.
4. Define (i) slip (ii) % slip (iii) negative slip in relation with reciprocating pump.
5. Prove from the first principles that the work saved in a single–acting reciprocating
pump by fitting an air vessel is 84.8%.
6. Draw theoretical indicator diagram of reciprocating pump.
7. Draw an indicator diagram for single acting reciprocating pump by considering
effect of acceleration and friction in suction and delivery pipes. Find an expression
for the work done per second for it.
8. Compare the Reciprocating pump with Centrifugal pump.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2
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 (i) % slip and (ii) acceleration head at
the beginning and middle of the delivery stroke. GTU May 2016
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 5 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.
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1
ASSIGNMENT– 6 RECIPROCATING COMPRESSOR
Theory
1. Classify air compressors and state applications of compressed air.
2. Explain principle of working of single stage single acting reciprocating air compressor
with schematic diagram.
3. Prove that the work done/kg of air in single stage single acting reciprocating air
compressor without clearance is given by,
[(
)
]
4. Why clearance volume is provided in reciprocating air compressor? Derive an
expression for indicated work of reciprocating air compressor considering its clearance.
OR
5. Define volumetric efficiency. Derive the expression for volumetric efficiency referred to
suction and ambient conditions. Discuss the factors affecting on it.
6. Justify the need for multi-staging in a reciprocating air compressor. What are its merits
and demerits over single stage compression? Show this process on P – V diagram.
7. Explain the working of two stage reciprocating air compressor and give the expression
of work done without clearance volume for perfect (complete) and imperfect
(incomplete) intercooling with P-V and T-S diagram.
8. 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
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2
In a two stage air compressor in which intercooling is perfect prove that the work done
in compression is minimum when pressure in the intercooler is geometric mean
between initial and final pressure √ .
OR
Draw P-V diagram for two stage reciprocating air compressor. Write equation for
indicated work per cycle and find out optimum intermediate pressure for minimum
work supply.
Examples
1. A single stage, single acting reciprocating air compressor takes in air 5 m3/min at 1 bar
and 27°C and compresses to a delivery pressure of 7 bar. Determine each of the below
neglecting clearance with the help of P-V and T-S diagram, when compression takes
place (a) polytropically (PV1.3 = constant), (b) adiabatically (PV1.4 = constant), and (c)
isothermally (PV = constant). Take ambient conditions 1.013 bar and 15°C.
(1) Mass of the air measured at suction condition per minute
(2) Temperature and volume of air at the end of compression
(3) Work done by air during suction, work done on air during compression, work
done on air during delivery and net work done on air (I.P)
(4) Heat transfer and change in internal energy during compression
(5) Brake power of compressor if the mechanical efficiency is 80%
(6) Isothermal efficiency and adiabatic efficiency
[Attention Note: State the remarkable conclusions and implications from above results]
2. In a two stage single acting reciprocating air compressor, the pressure and
temperature in the cylinder at the start of compression are 1 bar and 35°C respectively.
The diameter of L.P cylinder is twice that of H.P cylinder. The air enters the H.P cylinder
at 40°C and is then compressed to 17.5 bar. The law of compression is PV1.22 = C for
both the cylinders. The free air conditions are 1.01325 bar and 15°C and compressor
delivers 2.4 m3 of free air per minute. Neglecting the effect of clearance. Determine,
each of the below considering perfect and imperfect intercooling,
1) Intercooler pressure
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 3
2) Indicated power required for two stage and single stage compression to achieve
same delivery pressure, % saving in power with two stage compression and
what should be the ratio of diameter of cylinder for minimum work?
[Attention Note: clearly mention from above solution, why and which intercooling is
preferable?]
3. In a two stage single acting reciprocating compressor, intake pressure and temperature
are 1 bar and 20°C respectively. Air is taken into the compressor at the rate of 6 m3/min
and compressed to a final pressure of 9 bar. The law of compression in both the
cylinders is PV1.3 = C. If the intermediate pressure is ideal and intercooling is perfect and
the compressor runs at 600 rpm. Neglecting the clearance and determine,
1) Intermediate pressure
2) Volume of L.P. and H.P cylinder
3) Power required to drive the compressor if mechanical efficiency is 80%.
4) The rate of heat rejected in the intercooler
5) Rise in temperature of cooling water if the mass flow rate of water through the
intercooler is 8 kg/min. Take Cpa = 1 kJ/kg k for air and Cpw = 4.2 kJ/kg k for
water.
6) % saving of power by using three stage compressor and % excess power
required if compressor runs at single stage to achieve same delivery pressure.
[Attention Note: is it economical to achieve 9 bar delivery pressure in single stage?]
4. A single acting two stage RAC with complete intercooling delivers 10 kg/min of air at
16 bar at 400 rpm. The suction occurs at 1 bar and 15°C. The polytropic index is 1.25.
Calculate,
1) indicated power
2) FAD per minute
3) Heat rejected in intercooler
4) Swept volume and clearance volume of L.P cylinder if the clearance ratios for
L.P and H.P cylinders are 0.04 and 0.06 respectively.
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 4
5. A multistage single acting reciprocating air compressor has perfect intercooling. The
pressure and temperature at the end of suction stroke in L.P cylinder is 1 bar, 15°C
respectively. If 8.4 m3/min of FAD at 60 bar when the work done is minimum. Calculate,
1) Number of stages if pressure ratio per stage is not to exceed 4
2) Exact stage pressure ratio
3) Intermediate pressures
4) Ratio of cylinder volume
5) Total indicated power and % excess power required by using single stage
compression to achieve same delivery pressure. Take n = 1.3. Neglecting
clearance.
6. The diameter of reciprocating air compressor cylinder is 140 mm and stroke length of
the piston is 180 mm and the clearance volume is 77 cm3. The pressure and
temperature at the end of suction and at beginning of compression is 0.97 bar and 13°C.
The delivery pressure is constant at 4 bar. Taking the law of compression and
expansion as PV1.3 = constant. Calculate,
(1) The heat rejected during the compression
(2) B.P of the compressor if mechanical efficiency 80%
(3) Volumetric efficiency referred to suction and ambient conditions
(4) Isothermal efficiency, adiabatic efficiency, overall isothermal efficiency
(5) % of air delivered with reference to air compressed, mass of air compressed,
mass of air delivered
[Attention Notes: 1. Illustrate that clearance volume play a vital role in reciprocating air
compressor. 2. How volumetric efficiency referred to suction and ambient conditions
distinguished from each other?]
7. A single stage double acting reciprocating air compressor is required to deal with 17
m3 of air per minute measured at 1.01325 bar and 15°C. The pressure and temperature
at the end of suction is 0.966 bar and 32°C, the delivery pressure being 6.3 bar, the
speed is 550 rpm. Assuming a clearance volume is 5% of the stroke volume, law of
compression and expansion is PV1.32 = constant. Calculate,
(1) The necessary swept volume
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 5
(2) Volumetric efficiency referred to suction and ambient condition
(3) Cylinder dimension if stroke to bore ratio 1.5
(4) I.P of the compressor
[Attention Note: up to which extent clearance can be minimized? What are the constrains
for optimum clearance?]
8. A single acting, two stage reciprocating air compressor has to deals with 3 m3/min of
air under atmospheric conditions 1 bar, 25°C at 220 rpm and delivers it at 80 bar,
assuming perfect intercooling between stages. Find out,
(1) Minimum power to drive the compressor
(2) Diameter of L.P and H.P cylinder and common stroke length
(3) % saving in minimum power if compression is assumed as three stage
Take piston speed is 154 m/min, mechanical efficiency of compressor is 80%,
volumetric efficiency is 85% same for each stage, law of compression in both the
cylinders is PV1.3 = C.
Practice Examples
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.
[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?]
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 6
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
3. 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.
4. 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.
5. 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
4) Volumetric efficiency
5) Cylinder size if stroke to bore ratio 1.3.
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 7
7. A two stage single acting reciprocating air compressor is required to delivers air at 70
bar from a induction pressure of 1 bar at a rate of 2.4 m3/min measured at 1.01325 bar
and 15°C. The compression is carried out in two stages with an ideal intermediate
pressure and complete intercooling. The clearance volume is 3% of swept volume in
each cylinder. The index of compression and expansion is 1.25 for both the cylinder.
The temperature at the end of induction stroke in each cylinder is 32°C. The mechanical
efficiency is 85%. Take speed of compressor 750 rpm. Determine,
(1) Indicated power
(2) Saving in power over single stage compression between the same pressures
(3) Swept volume of each cylinder
(4) The required power output of the drive motor.
[Attention Note: how to get better mechanical efficiency? Discussed the factors involved.]
8. A three stage, reciprocating compressor has L.P cylinder of 300 mm bore and 200 mm
stroke, clearance volume of L.P cylinder is 5% of swept volume, intake pressure and
temperature are 1 bar, 17°C respectively, the final delivery pressure is 27 bar,
intermediate pressures are ideal and intercooling is perfect, the compression and
expansion index can be taken as 1.3 throughout. Determine,
(1) Intermediate pressures
(2) Effective swept volume of L.P cylinder
(3) The temperature and volume of air delivered per stroke at 27 bar
(4) Work done per kg of air
[Attention Note: which one is true? Clearance volume will be decrease, remains constant
or increase stage by stage in RAC]
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1
ASSIGNMENT – 7 ROTARY COMPRESSORS
Theory
1. Explain Root blower with the neat sketch and derive expression for the Roots
efficiency.
2. Explain vane type compressor with neat sketch and P-V diagram.
3. Describe the working of a screw compressor and list its applications.
4. With neat sketch explain construction and working of Scroll compressor. State the
advantages of scroll compressor.
5. Compare Screw compressor and Scroll compressor.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1
ASSIGNMENT – 8 CENTRIFUGAL COMPRESSORS
Theory
1. Describe principle construction and working of centrifugal compressor with pressure
and velocity diagram.
2. Explain inlet and outlet velocity triangles and work done equation for the centrifugal
compressor.
3. With the help of velocity triangles and head-capacity curves, discuss salient features of
radial, backward and forward curved vanes in a centrifugal compressor and state
function of volute casing.
OR
Explain the effect of blade shape of impellers on performance of Centrifugal compressor.
Also classify the blades based on curvature.
4. Define following terms.
a) Isentropic efficiency
b) Slip factor
c) Power input factor
d) Pressure (loading) coefficient
e) Pre-whirl
5. What is pre-whirl? Sketch the velocity diagrams with and without pre whirl for a
centrifugal compressor.
6. Define degree of reaction (R) for a centrifugal compressor stage and prove that;
2 22
2
1 cos
2 1 cot
ecR
where ϕ is flow coefficient
7. Explain the phenomenon of surging, choking and stalling in centrifugal compressor.
8. Give comparison between Centrifugal compressor and Reciprocating compressor.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2
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.
2. Following data relates to the Centrifugal compressor.
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.
3. Following data refers to the Centrifugal compressor.
Speed = 16000 RPM
Isentropic efficiency = 0.82
Inducing temperature of air = 17⁰C
Impeller mean eye diameter = 200 mm
Work done by impeller = 175 kJ/kg
Absolute velocity at inlet = 120 m/s
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 3
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.
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, 30⁰C
Isentropic efficiency = 0.8
Slip factor = 0.94
Absolute velocity at inlet = 150 m/s
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.
5. 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 26⁰ 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.
6. 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
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 4
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.
7. Following data relates to the centrifugal compressor.
Volume flow rate = 10 m3/s
Speed = 6000 RPM
Pressure ratio = 4
Isentropic efficiency = 0.83
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.
8. Following operating conditions are relates to the centrifugal compressor.
Mass flow rate = 8 kg/s
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 temperature at inlet = 1.013 bar, 288 K
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 5
If the air leaving the guide vanes has a velocity of 90 m/s at 75⁰ 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.
Practice Examples
1. A centrifugal compressor has inlet guide vanes fitted at the eye such that free vortex
flow is achieved at entry to the blade. At the tip radius of the eye the inlet relative Mach
number is not to exceed 0.75 and an impeller total to total efficiency is 0.9 is required.
The air leaves the tip of the inlet guide vanes with a velocity of 90 m/s, the impeller tip
diameter is 0.45 m, and the outlet diameter is 0.76 m. The radial component of velocity
at exit from the impeller is 50 m/s and the impeller rotates at 12000 rpm. If a slip factor
is 0.9 is assumed. Find: (1) the guide vane angle at the tip and, (2) the static pressure at
impeller outlet.
2. Following operating conditions are relates to the centrifugal compressor.
Mass flow rate = 15 kg/sec
Speed = 12000 RPM
Overall static pressure ratio = 4:1
Isentropic efficiency = 80%
Slip factor = 0.9
Flow coefficient at impeller exit = 0.3
Hub diameter of eye = 15 cm
Velocity of air at inlet = 140 m/s
Velocity of air at exit from impeller= 140 m/s
Stagnation temperature at inlet = 300 K
Stagnation pressure at inlet = 1 bar
Determine (1) impeller diameters, (2) width of impeller at exit, (3) power required to
drive the compressor assume equal pressure ratio in the impeller and diffuser.
3. A centrifugal compressor has 17 radial vanes of tip diameter 165 mm and rotates at
46000 rpm and the air mass flow rate is 0.6 kg/s with no whirl at inlet. Calculate the. At
the inlet to the impeller the mean diameter of the eye is 63.5 mm while the annulus
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 6
height at the eye is 25 mm. the static pressure and temperature at the impeller inlet are
0.93 bar and 293 K respectively. Determine: theoretical power required to run the
compressor. (1) The blade angle at the mean diameter at impeller inlet, (2) the
stagnation temperature at impeller exit and (3) the stagnation pressure impeller exit if
the total to total efficiency of the impeller is 90%.
4. A two stage centrifugal compressor having intercooler has two impellers of same tip
diameter and both of them are running at same speed. The first stage has a pressure
ratio of 3.5:1 and the isentropic efficiency is 0.8 while the pressure coefficient is 0.75.
The intercooler removes 80% of the temperature rise occurring in the first stage. If the
coefficient for the second stage are same as those for the first stage. Calculate: (1) the
delivery conditions of air and (2) work done by each stage per kg of air. Assume that
initial conditions are 0.95 bar and 17⁰C.
5. 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.
6. 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 15⁰C 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.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 7
7. 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 22⁰C 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.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1
ASSIGNMENT – 9 AXIAL FLOW COMPRESSORS
Theory
1. With a suitable sketch explain the working principle of an axial flow compressor.
Draw the stage velocity triangles and derive an equation for work input.
2. Derive an expression for pressure ratio per stage of an axial flow compressor in
terms of isentropic efficiency, work done, blade velocity, blade angles and inlet
temperature.
3. Sketch symmetrical, unsymmetrical aerofoil and compressor cascade. Define and
show the important angles, chord, pitch.
4. For 50% degree reaction of axial flow compressor prove that α1 = β2 and α2 = β1,
notations carry usual meaning.
5. State applications of an axial flow compressor. Give comparison between an axial
flow compressor and centrifugal compressor.
6. Define following terms with reference to axial flow compressor:
a) Flow coefficient
b) Blade loading coefficient
c) Work done factor
d) Radial equilibrium
7. Explain the phenomenon of surging and stalling in an axial flow air compressor.
8. Explain various losses associated in a stage of axial flow compressor.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2
Examples
1. 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 = 15⁰
Angle of absolute air velocity at rotor inlet = 45⁰
Work done factor = 0.86
Inlet stagnation pressure = 1 bar
Inlet stagnation temperature = 27⁰
Determine the total pressure ratio of the first stage and overall static pressure ratio.
2. First stage of an axial flow compressor delivers 20 kg/s of air at 9000 rpm. Stage
temperature rise is 200C. Men blade velocity is 180 m/s and axial velocity 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.
3. 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 = 45⁰ and 10⁰
Work done factor = 0.86
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
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 3
(ii) Number of stages required
(iii) Inlet Mach number relative to rotor at the mean blade height of the first stage.
4. A multi stage axial flow compressor absorbs 2211 kW when delivering 10 kg/s of air
from stagnation conditions 1 bar and 15C⁰. 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.
5. The following data refers to an axial flow compressor.
Pressure of air at inlet of an axial flow compressor = 768 mm of Hg
Temperature of air at inlet of an axial flow compressor = 41C⁰
Diameter at mean blade section = 500 mm
Peripheral velocity = 100 m/s
Mass flow rate through the stage = 25 kg/s
Work done factor = 0.95
Mechanical efficiency = 92%
Stage efficiency = 88%
If air angles are β1 = 51⁰, α1 = α3 =7⁰and the air is turned through 42⁰ 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
6. 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 30⁰relativ 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%.
7. The following data refers to an axial flow compressor.
Stage stagnation temperature rise = 22 K
Mass flow of air = 25 kg/s
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 4
Rotational speed = 150 rev/s
Axial velocity through the stage = 157 m/s
Mean blade speed = 200 m/s
Work done factor = 0.95
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
Practice Examples
1. The following data refers to a test on an axial flow compressor. Atmospheric
temperature and pressure at inlet are 18°C and 1 bar. Total head temperature in
delivery pipe is 165°C. Total head pressure in delivery pipe is 3.5 bar. Static
pressure in delivery pipe is 3 bar. Calculate (a) total head isentropic efficiency, (b)
polytropic efficiency, and (c) air Velocity in delivery pipe.
Answers: 85.2 %. 87.5%, 194.75 m/s
2. The first stage of an axial flow compressor is designed for free vortex condition,
with no inlet guide vanes. The rotational speed is 9000 rpm, and stagnation
temperature rise is 20° C. The hub-tip ratio is 0.6, the work done factor is 0.94 and
isentropic efficiency of the stage is 0.90. Assuming an inlet velocity of 150 m/s and
ambient conditions of 1 bar and 300 K, compute (a) the tip radius and
corresponding rotor angles, if the Mach number relative to the tip is limited to 0:92,
(b) mass flow entering the stage (c) stage stagnation pressure ratio and power
required and (d) the rotor air angle at the root section.
Answers: 0.292 m, 27.19 kg/s, 1.226, β1= 47.71°, 546.7 KW, β2 = 13.23°
3. Air at 1.0132 bar and 288 K enters an axial flow compressor stage with an axial
velocity 150 m/s. There are no inlet guide vanes. The rotor stage has a tip diameter
of 60 cm and a hub diameter of 50 cm and rotates at 100 rps. The air enters the
rotor and leaves the stator in the axial direction with no change in velocity or radius.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 5
The air is turned through 30° as it passes through rotor. Assuming the constant
specific heats and that the air enters and leaves the blades at the blades angles,
(i) construct the velocity diagram at mean dia. for the stage, (ii) mass flow rate, (iii)
power required, and (iv) degree of reaction
4. An axial flow compressor stage has the following data,
Temperature and pressure at inlet = 27°C and 1.0 bar
Degree of reaction = 0.5
Mean blade ring diameter = 36 cm
Rotational speed = 18000 rpm
Blade height at entry = 6 cm
Air angles at rotor at stator exit = 25°
Axial velocity of flow = 180 m/s
Work done factor = 0.88
Stage efficiency = 85 %
Mechanical efficiency = 96.7 %
Determine: (a) Air angles at the rotor and stator entry, (b) Mass flow rate of air, (c)
Power required to drive the compressor, (d) The loading coefficient, (e) Pressure
ratio developed by the stage and (f) Mach number at the rotor entry.
5. The following data refers to an axial flow air compressor having number of similar
stages with equal work done per stage and uniform velocity of flow throughout.
Overall stagnation pressure ratio = 3.5
Stagnation inlet temperature = 60°C
Relative air angle at rotor inlet = 130°
Relative air angle at rotor outlet = 100°
Blade velocity = 185 m/s
Degree of reaction = 0.5
Overall stagnation isentropic efficiency = 87%
The data refer to mean blade height and the measurement of angles is done in the
same sense from the blade velocity direction. Calculate (a) Stagnation (Total head)
outlet temperature and (b) Number of stages.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 6
6. An axial compressor has a mean diameter of 60 cm and runs at 15,000 rpm. If the
actual temperature rise and pressure ratio developed are 30°C and 1.3 respectively,
determine (a) power required to drive the compressor while delivering 57 kg/s of
air, assuming mechanical efficiency 86% and initial temperature of 35°C (b) the
stage efficiency and (c) the degree of reaction if the temperature at the rotor exit is
55°C.
FLUID POWER ENGINEERING (2151903)
B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1
ASSIGNMENT 10 MISCELLANEOUS HYDRAULIC MACHINES
Theory
1. Write working principle of hydraulic press. With neat sketch explain construction
and working of hydraulic press. Derive equation for ‘leverage of press’ and state uses
of hydraulic press.
2. With neat sketch explain construction and working of Hydraulic accumulator.
3. Explain working of Differential hydraulic accumulator with neat sketch.
4. Draw a neat sketch and explain the operation of Hydraulic intensifier.
5. With neat sketch explain operation of Hydraulic crane.
6. Write short notes on Hydraulic jack with neat sketch.
7. With neat sketch explain construction and working of Hydraulic lift.
8. Write a short on Hydraulic ram and derive its efficiency.
9. Explain with neat sketch operation and principal of Fluid coupling.
10. Write a short on Fluid torque converter. Write down comparison between Fluid
coupling and Fluid torque converter.
11. Write short note on Hydraulic jack.
12. Explain with neat sketch the working of air lift pump.