Question #189053
  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.
1
Expert's answer
2021-05-07T08:11:59-0400

Convergent -Divergent nozzle

A2A=0.10.0125=8\frac{A_2}{A^*}= \frac{0.1}{0.0125}=8

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

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

From the gas table

P2PO=0.032;T2T0=0.39    P2=0.0322=0.064MPa;T2=0.391500=585K\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, c2=γRT2=1.37287585=479.6m/sc_2=\sqrt{\gamma RT_2}=\sqrt{1.37*287*585}=479.6m/s

v2c2=M2    v2=479.62.89=1386.04=m/s\frac{v_2}{c_2}=M_2 \implies v_2=479.6*2.89=1386.04=m/s

ρ2=P2RT2=0.064287585=0.381kg/m3\rho_2=\frac{P_2}{RT_2}=\frac{0.064}{287*585}=0.381 kg/m^3

Mass flow rate

m˙=ρ2A2v2=ρ1A1v1=ρtAtvt=0.3810.11386.04=52.81kg/s\dot{m}=\rho_2A_2v_2=\rho_1A_1v_1=\rho_tA_tv_t=0.381*0.1*1386.04=52.81kg/s


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