A centrifugal compressor operates with no prewhirl s run wit

A centrifugal compressor operates with no prewhirl s run with a rotor tip speed of 457 m/s. If V_u2 is 90% of U_2 and eta_u = 0.80, calculate the following for operation in standard sea level air (Assume sigma = phi = 1, T_01 = 280 degree C): Pressure ratio, Work input per kg of air (w), and The power required (P) for a flow of 29 kg/s.

Solution

solution:

U2=457 m/s

here whirl velocity at outlet is given by

Vu2=.9*U2=411.3 m/s

2)work done per kg of air wthout prewhirl

W=Vu2*U2=411.3*457=187964.1 j/kg

3)power requireed is

P=m\'*W=29*187964.1=5450958.9 w

4)workdone is

W=Cp*(T2-T1)

T1=280 c=553 K

we get

T2=467.02 C

5)isentropic efficiency is

ntt=T2\'-T1/T2-T1

T2\'=429.616 C=702.616 k

wherer pressure ratio is

Rp=(T2\'/T1)^1.4/.4

Rp=2.3119