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Chapter: Mechanical and Electrical - Thermal Engineering - Air Compressors

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Solved Problems: Air Compressors

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 PV1.35 = 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/m2

Pressure (P2) = 6bar = 600 KN/m2

PV1.35 = 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 d2 × 2.7

d2 = 0.3350

 

d = 0.57M

 

2.  A single stage single acting  reciprocating  air compressor is required  to  handle 30m3   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 =30m2

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/m2 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 27oc and leaves it at 4.7bar. The air enters the H.P. cylinder at 4.5bar and 27oc. 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× 105 N/m2

 

Temperature (T1) = 27oC = 27+273 = 300K Pressure (P2) = 4.7bar

 

Pressure (P3) = 4.5bar

 

Temperature (T3) = 27oC = 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× 103 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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