The document contains 7 problems related to analyzing reciprocating air compressors. Problem 1 involves calculating the ideal volumetric efficiency and power input of a single-stage compressor. Problem 2 requires determining the power, volumetric efficiency, and time to deliver air for a single-acting compressor. Problem 3 involves calculating the actual volumetric efficiency, mass flow rate, speed, and power input of a single-stage compressor filling a receiver.

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THERMODYNAMICS - II
Numerical on Reciprocating Air Compressors

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1. A reciprocating air compressor with a bore of 15cm, a stroke of 20cm and
clearance of 5% runs at a speed of 300rev/min. The suction and delivery
pressure are 1 bar and 12 bar respectively. Calculate (i) ideal volumetric
efficiency and the power input assuming the index of compression and
expansion to be 1.3 (ii) Find also the theoretical maximum percentage
saving in work possible if the compression is carried out in two stages
with perfect intercooling instead of in single stage.

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2. A single acting air compressor has a cylinder of 15 cm bore and
the piston stroke is 25 cm. The crank speed is 600 rpm. Air is
taken from atmosphere of 1 bar and 27oC and is delivered at 11
bars. Assuming polytropic compression of the type pV1.25 = C, find
the power required to drive the compressor if its mechanical
efficiency is 80%. The compressor has a clearance of /20th of the
stroke volume. How long will it take to deliver 1 m3 of air at the
compressor delivery conditions? Also find the volumetric
efficiency of the compressor.

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Solution:

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3. The following data refers to a single stage air compressor: the
atmospheric conditions = 1 bar and 250C. The receiver pressure is
10 bar, cylinder diameter =12 cm, stroke to bore ratio = 1,
Clearance volume =1/25th of stroke volume. Index for both
compression and expansion is 1.25, Mechanical efficiency =80%. If
the receiver capacity is 600liters and it takes 8 minutes to fill the
receiver till its pressure is 10 bar starting from 1 bar. Determine (i)
Actual volumetric efficiency (ii) mass of air compressed per second
(iii) Speed of the compressor (iv) power input. Assume that receiver
temperature remains constant at 250 throughout the filling process.

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Solution:
(i) Actual volumetric efficiency

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(ii) Mass of air compressed per second

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(iii) Speed of the compressor

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(iv) Actual power input required.

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4. A multistage air compressor has suction pressure of 1 bar and
final discharge pressure of 40 bar. The maximum temperature of
air not to exceed 400K in any stage. The law of compression is
PV1.3 = C. Find the no of stages for minimum power input. Also
find the actual intermediate pressures and temperatures. What
will be the minimum power input in kW required to compress and
deliver 10kg/min of air and rate of heat rejection in each
intercooler? Assume ambient temperature as 270C and perfect
intercooling in between the stages.

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No of stages

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5. A two-cylinder, two-stage air compressor with perfect intercooling
takes in air at 1 bar and 270C. The law of compression in both
stages is with the index n=1.3. The compressed air is delivered at 9
bar. Calculate for unit mass flow rate of air the minimum work done
and heat rejected in the inter-cooler. Compare the value if the
compression is carried out in single stage with after-cooler.
Solution:

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6. In a single acting, two stage reciprocating air compressor 4.5kg of
air per minute compressed from 1.013 bar and 150C through a
pressure ratio of 9 to 1. Both stages have the same pressure ratio
and law of compression and expansion according to PV1.3 = C. If
the intercooling is complete, determine the indicated power and
the cylinder swept volumes required. Assume that the clearance
volume in both stages are 5% of their respective swept volumes
and the compressor runs at 300rpm.

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7. A single-stage double acting air compressor is required to deliver
14m3 of air per minute measured at 1.013 bar and 150C. The
delivery pressure is 7 bar and the compressor speed is 300 rpm.
Take clearance volume as 5% of swept volume with the
compression and expansion index as 1.3, calculate the swept
volume of the cylinder, the delivery temperature and indicated
power.

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