Question

Following results are obtained from a test on an air compressor. Compressor delivery stagnation pressure is 2.97 bar and compressor delivery stagnation temperature is 427 K. Ambient condition is 0.99 bar and 288 K. The isotropic efficiency of compressor is (Take $\gamma =1.4$ for air)

• A. $80\%$
• B. $76.40\%$
• C. $70.3\%$
• D. $85\%$

Answer 1

The correct option is B $76.40\%$

$\frac{T_{2s}}{T_1}={\left(\frac{P_2}{P_1}\right)}^{\frac{\gamma -1}{\gamma }}={\left(\frac{2.97}{0.99}\right)}^{\frac{0.4}{1.4}}$
and $T_1=288\text{K}$
$T_{2s}=1.37\times 288=394.2\text{K}$
$\Rightarrow {\eta }_c=\frac{T_{2s-T_1}}{T_2-T_1}=\frac{394.2-288}{427-288}$
${\eta }_c=76.40\%$