Question

Air at a temperature of 350 K enters a centrifugal compressor running at 16000 rpm, The impeller diameter is 0.6 m and isentropic efficincy of compressor is 0.88. Assume that absolute velocities at inlet and outlet are equal. If the slip factor and work factor are 0.9 and 1.05 respectively; pressure ratio developed is

• A. 7.14
• B. 6.13
• C. 5.15
• D. 6.65

Answer 1

The correct option is C 5.15

$\text{Impeller diameter,}{D}_2=0.6m$

$N=16000rpm$

$u_2=\frac{\pi D_{2}N}{60}=\frac{\pi \times 0.6\times 16000}{60}=502.654m/s$

$\text{Slip factor},{\varphi }_s=0.9$

$\text{Work factor},{\varphi }_w=1.05$

$\text{Inlet factor},T_1=350K$

As we know, compressor work ,

${\omega }_c=c_p(T_2-T_1)={\varphi }_s{\varphi }_w{u}_2^2$

$\Rightarrow 1.005\times 1000(T_2-350)=0.9\times 1.05\times {502.654}^2$

$T_2=587.577K$

${\eta }_c=0.88=\frac{T_{2s}-T_1}{T_2-T_1}=\frac{T_{2s}-350}{587.577-350}$

$\Rightarrow T_{2s}=559.068K$

$\frac{T_{2s}}{T_1}=r_p^{\gamma -1}/\gamma$

$\frac{559.068}{350}=(r_p{)}^{1.4-1/1.4}$

$\text{Pressure ratio,}{r}_p=5.15$