Ideal gas helium flows through the inlet of an isentropic nozzle with a velocity of 25 m/s, and the exit flow is at 100 kPa, 300 K, and has a velocity of 250 m/s. a. Determine the inlet temperature. b. Determine the inlet pressure. c. Determine the area ratio between inlet and exit

a. The inlet temperature is approximately 305.232 K

b. The inlet pressure is approximately 452.0108 kPa

c. The area ratio between the inlet and exit is approximately 2.2509

Explanation:

a. From the energy equation related to the question, we have;

Where;

= The specific heat capacity for helium = 5.913 kJ/(kg·K)

= The inlet temperature

= The exit temperature = 300 K

= The inlet velocity = 25 m/s

= The exit velocity = 250 m/s

Therefore, we have;

The inlet temperature = ≈ 305.232 K

b. From the following equation for the critical pressure, for helium, we have;

Where;

= The critical pressure = 2.26 atm for helim

= The inlet pressure

n = The polytropic constant

We have;

The inlet pressure, ≈ 4.641 atm ≈ 452.0108 kPa

c. The inlet to exit pressure ratio is given as follows;

Therefore, we have;

The area ratio between the inlet and exit, ≈ 2.2509.