Question

A centrifugal compressor delivers 10kg/s of air with a total head pressure ratio of 4 : 1. The speed of the compressor is 10000 rpm, inlet temperature is ${12}^{0}C$, slip factor is 0.85, power input factor = 1.07 and 85% isentropic efficiency.The overall diameter of the impeller is _______cm.

• A. 81

Answer 1

The correct option is A 81
81 (80 -82)

$\frac{T_{2s}}{T_1}={\left({\tau }_p\right)}^{\gamma -1/\gamma }={\left(4\right)}^{0.4/1.4}$

$T_{2s}=423.5K$

$T_2=T_1=\frac{T_2-T_1}{{\eta }_c}=\frac{425.5-285}{0.85}$

$T_2-T_1=162.95K$
Work Done
$\sigma \mu u_2^2=c_p(T_2-T_1)$

$x_2=\sqrt{\frac{c_p(T_2-T_1)}{\sigma \mu }}=\sqrt{\frac{1005\times 162.95}{0.55\times 1.07}}$

$u_2=424.33m/s=\frac{\pi D_{2}N}{60}$

$D_2=\frac{424.33\times 60}{n\times 10000}=0.810m$

$D_2=81.0cm$