Answer to Question #189053 in Thermal Power Engineering for curious

Question

1. The throat area a convergent–divergent jet nozzle is 0.0125 m² and the nozzle entry conditions for the flow are 2.0 MPa and 1500 k respectively. Assuming stagnation conditions at the entry, estimate the flow rate through the nozzle. The ratio of specific heats may be assumed as 1.37. The nozzle exit area = 0.1m², inlet pressure and temperature are 2.5 MPa and 1100 k respectively. Exit pressure is 113745 Pa. The ratio of specific heats may be assumed as 1.4.

Answer 1

Convergent -Divergent nozzle

$\frac{A_2}{A^*}= \frac{0.1}{0.0125}=8$

From the isentropic flow tables we have $\gamma =1.37; M=2.89$

In this case divergent section of the nozzle acts as a nozzle

From the gas table

$\frac{P_2}{P_O}=0.032; \frac{T_2}{T_0}=0.39 \implies P_2 =0.032*2=0.064 MPa; T_2=0.39*1500=585K$

Speed of sound, $c_2=\sqrt{\gamma RT_2}=\sqrt{1.37*287*585}=479.6m/s$

$\frac{v_2}{c_2}=M_2 \implies v_2=479.6*2.89=1386.04=m/s$

$\rho_2=\frac{P_2}{RT_2}=\frac{0.064}{287*585}=0.381 kg/m^3$

Mass flow rate

$\dot{m}=\rho_2A_2v_2=\rho_1A_1v_1=\rho_tA_tv_t=0.381*0.1*1386.04=52.81kg/s$