A supersonic nozzle is also a convergent–divergent duct, which is fed by a large reservoir at the inlet to the nozzle. In the re

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A supersonic nozzle is also a convergent–divergent duct, which is fed by a large reservoir at the inlet to the nozzle. In the re

servoir of the nozzle, the pressure and temperature are 10 atm and 300 K, respectively. At the nozzle exit, the pressure is 1 atm. Calculate the temperature and density of the flow at the exit. Assume that the flow is isentropic and (of course) compressible.

Physics

1 answer:

Softa [3K] · Answer 1 · 2026-02-22T18:54:27+03:00

Answer:

155.38424 K

2.2721 kg/m³

Explanation:

$P_1$ = Reservoir pressure = 10 atm

$T_1$ = Reservoir temperature = 300 K

$P_2$ = Exit pressure = 1 atm

$T_2$ = Exit temperature

$R_s$ = Specific gas constant = 287 J/kgK

$\gamma$ = Specific heat ratio = 1.4 for air

Assuming isentropic flow

$\frac{T_2}{T_1}=\frac{P_2}{P_1}^{\frac{\gamma-1}{\gamma}}\\\Rightarrow T_2=T_1\times \frac{P_2}{P_1}^{\frac{\gamma-1}{\gamma}}\\\Rightarrow T_2=00\times \left(\frac{1}{10}\right)^{\frac{1.4-1}{1.4}}\\\Rightarrow T_2=155.38424\ K$

Flow temperature at exit is 155.38424 K

Density at exit can be derived using the ideal gas equation

$\rho_2=\frac{P_2}{R_sT_2}\\\Rightarrow \rho=\frac{1\times 101325}{287\times 155.38424}\\\Rightarrow \rho=2.2721\ kg/m^3$

Flow density at exit measures 2.2721 kg/m³