Mechanical and Electrical - Thermal Engineering - Air Compressors

**SOLVED
PROBLEMS**

1. A single
stage double acting air compressor of 150KW power takes air in at 16 bar &
delivers at 6 bar. The compression follows the law PV^{1.35} = C. the
compressor runs at 160rpm with average piston speed of 150 m/min. Determine the
size of the cylinder.

**Given
data**

Power (P) = 150KW

Piston speed (2lN) = 150m /min

Speed (N)
= 160rpm 160/6 0 = 2.7rps

Pressure
(P1) = 1bar = 100 KN/m^{2}

Pressure (P2)
= 6bar = 600 KN/m^{2}

PV^{1.35}
= C, n = 1.35

Hence it
is a polytropic pr ocess.

**To find**

Size of
the cylinder (d) ?

**Solution**

It is
given that,

*2lN *= 2.5m/s

150 = 2 ×
82.899 d^{2} × 2.7

d^{2}
= 0.3350

**d = 0.57M**

2. A single stage single acting reciprocating
air compressor is required to handle 30m^{3} of

free air
per hour measured at 1 bar . the delivery pressure is 6.5 bar and the s peed is
450 r.p.m

allowing
volumetric efficienc y of 75%;an isothermal
efficiency of 76%
and mechanical

efficiency of 80%
Find the indicated mean effective pressure and the po wer required the

compressor

**Given
data**

Volume V1 =30m^{2}

Pressure P1=1 bar
,

P2=6.5
bar Speed N=450
r.p.m

Volumetric
efficiency ηv=75%

Isothermal
efficiency ηi=76%

Mechanical
efficiency ηm=80%

**To find**

The
indicated mean eff ective pressure

The power
required to drive the compressor

**Solution**

Indicted
Mean Effectiv e Pressure

We know
that isothermal work done

Therefore the power required to drive the compressor = =2.56KW

**Result**

Indicated mean effective pressure pm=184.5KN/m^{2} The
power required to drive the compressor =2.56KW

3. A two stages, single acting
air compressor compresses air to 20bar. The air enters the L.P cylinder at 1bar
and 27^{o}c and leaves it at 4.7bar. The air enters the H.P. cylinder
at 4.5bar and 27^{o}c. the size of the L.P cylind er is 400mm diameter
and 500mm stroke. The clearance volume In both cylinder is 4% of the respective
stroke volume. The compressor runs at 200rpm, taking index of compression and
ex pansion in the two cylinders as 1.3, estimate 1. The indicated power
required to run the comp ressor; and 2. The heat rejected in the intercooler
per minute.

**Given data**

Pressure
(P4)= 20bar

Pressure
(P1) = 1bar = 1× 10^{5} N/m^{2}

Temperature (T1) = 27^{o}C = 27+273 = 300K Pressure
(P2) = 4.7bar

Pressure
(P3) = 4.5bar

Temperature (T3) = 27^{o}C = 27+273 = 300K Diameter
(D1) = 400mm 0.4m Stroke (L1) = 5 00mm = 0.5m

K = 0.04

N =
200rpm ; n = 1.3

**To find**

Indicated
power required to run the compressor

**Solution**

We know the sw ept volume of the L.P cylinder

= 2043.5×
10^{3} J/min = 2034.5 KJ/min

Total indicated work done by the compressor,

W = WL + WH = 2123.3 + 2034 .5 = 4157.8 KJ/min

Indicated power required to run the compressor

= 4157.8 /
60

= 69.3KW

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