Upstream of the throat of an isentropic converging-diverging nozzle at the inlet V1 = 150 m/s, p1
= 100 kPa, and T1 = 20 ?C. If the discharge flow is supersonic and the throat area is 0.1 m2,
determine the mass flow rate in kg/s for the flow of ideal gas air.
Solution
Local sound speed a = sqrt (kRT)
= sqrt (1.4*287*(20+273))
= 343.11 m/s
Mach no, Ma1 = V/a
= 150 / 343.11
= 0.437
Stagnation pressure P0 = P1*(1 + 0.2*Ma1 ^2)^3.5
= 100*(1 + 0.2*0.437^2)^3.5
= 114.03 kPa
Stagnation temperature T0 = T1 + V1 ^2 / (2*Cp)
= (20+273) + 150^2 / (2*1005)
= 304.2 K
Mass flow m = 0.6847*P0*A / sqrt(R*T0)
= 0.6847*114.03*10^3*0.1 / sqrt(287*304.2)
= 26.424 kg/s