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## Q. 6.P.7

Air, at 1500 kN/m² and 370 K, flows through an orifice of 30 mm² to atmospheric pressure.
If the coefficient of discharge is 0.65, the critical pressure ratio 0.527, and the ratio of the specific heats is 1.4, calculate the mass flowrate.

## Verified Solution

If the critical pressure ratio $w_c$ is 0.527 (from Problem 6.6), sonic velocity will occur until the pressure falls to $(101.3 / 0.527)=192.2 kN / m ^2$. For pressures above this value, the mass flowrate is given by:

$G=C_D A_0 \sqrt{\left(k P_1 / v_1\right)[2 /(k+1)]^{(k+1) /(k-1)}}$            (equation 6.29)

If $k=1.4, G=C_D A_0 \sqrt{\left(1.4 P_1 / v_1\right)(2 / 2.4)^{2.4 / 0.4}}=C_D A_0 \sqrt{\left(0.468 P_1 / v_1\right)}$

$P_1=1,500,000 N / m ^2$

and:       $v_1=(22.4 / 29)(370 / 273)(101.3 / 1500)=0.0707 m ^3 / kg$

Substituting gives: $G=\left(0.65 \times 30 \times 10^{-6}\right) \sqrt{(0.486 \times 1,500,000 / 0.0707)}=\underline{\underline{0.061 kg / s }}$