Consider a compressor with operates with a pressure ratio of 15 and an adiabatic efficiency of 0.88. the incoming total temperature is 320 k and the incoming total pressure is 135 kpa. the compressor operates with 9 stages, all of which have the same pressure ratio and stage efficiency:

a. determine the pressure ratio per stage
b. determine the stage efficiency
c. determine the polytropic efficiency

a. 1.3510 b. 88.02% c. 80.14%

Explanation:

Pressure Ratio= 15

Adiabatic Efficiency (ηad)= 0.88

Incoming Temperature= 320K

Incoming Pressure= 135KPa

Compressor with 9 stages with P10/P1= 15

a. (P2/P1) x (P3/P2) x  (P4/P3) x  (P5/P4) x  (P6/P5) x  (P7/P6) x  (P8/P7) x  (P9/P8) x  (P10/P9) = 15

same Pressure Ratio (Rp)

(Rp)^9 = 15

Rp= (15)^(1/9) = 1.3510

c. (1/ηpc) = [{ln((P2/P1)^((k-1)/k)) - 1)/ηad + 1}/{ln((P2/P1)^((k-1)/k))}]

where k= 1.4

((P2/P1)^((k-1)/k))= (1.3510)^(0.4/1.4) = 1.08975

(1/ηpc) = [ln{((1.08475-1)/0.88) + 1}]/[ln((P2/P1)^((k-1)/k))]

(1/ηpc) = 0.0970648/0.077794

ηpc= 0.8014 = 80.14%

b. T₂/T₁ = (P2/P1)^((k-1)/k) = 1.08975

T₂= 348.704 K

ηad = T₂ - T₁/ Ti₂ - T₁

0.88= 348.704 - 320/ Ti₂ - 320

Ti₂= 352.613 K

Efficiency of stage η = {(Rp)^((r-1)/r)) - 1}/{(Ti₂/T1) - 1}

η= (1.3510)^((0.4/1.4)) - 1/((352.613/320) - 1)

η= 0.0897/0.1019= 0.8802

ηstage= 88.02 %

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