Question

A two stage air compressor with perfect intercooling is compressing air from 1 bar to 4 bar The volumetric efficiency for the first and second stage compressors are 0.9 and 0.85. Intermediate pressure is based on least work requirement theory. If the stroke ratio of first and second stage compression is 1.2, the ratio of diameter of second to first stage compressor is

• A. 0.797
• B. 1.254
• C. 0.774
• D. 1.29

Answer 1

The correct option is A 0.797

For minimum work,
$P_2=\sqrt{P_1{P}_3}=2\text{bar}$
For perfect intercooling
${\eta }_{v1}{P}_1{D}_1^2{L}_1={\eta }_{v2}{P}_2{D}_2^2{L}_2$
$\frac{D_2}{D_1}=\sqrt{\frac{{\eta }_{v1}}{{\eta }_{v2}}\times \frac{P_1}{P_2}\times \frac{L_1}{L_2}}=\sqrt{\frac{0.9}{0.85}\times \frac{1}{2}\times 1.2}$
$\frac{D_2}{D_1}=0.797$