The blades are radial at the impeller outlet and flow velocity of 60 m/s may be assumed throughout constant. The outer radius of the impeller is twice the inner one and slip factor is 0.9. calculate; i) Final temperature of air, ii) Power input to compressor, iii) Impeller diameter at inlet and outlet and iv) Width of impeller at inlet.

Given:

$N = 12000\hspace{0.05cm}rpm,\hspace{0.25cm}P_1 = 1\hspace{0.05cm}bar,\hspace{0.25cm}T_1 = 27^\circ = 300\hspace{0.05cm}K,\hspace{0.25cm}V = 600\hspace{0.05cm}m^3/min\\ \frac{P_2}{P_1} = 4,\hspace{0.25cm}\eta_{iso} = 0.85,\hspace{0.25cm}V_f = V_{f1} = V_{f2} =60\hspace{0.05cm}m/s,\hspace{0.25cm} R_2 = 2R_1,\hspace{0.25cm}\phi_s =0.9$

To Find:

$T_2, \textit{Power}, D_1,D_2,B_1$

Solution:

$\hspace{5cm}1 - 2^1 : \textit{Isentropic Compression}\\ \frac{T_2^{'}}{T_1} = (\frac{P_2}{P_1})^\frac{r -1}{r}\\ T_2^{'}= 300\hspace{0.05cm} (4)^\frac{1.4 - 1}{1.4}\\ T_2^{'} = 445.798\hspace{0.05cm}K\\ …