Question

A converging-diverging nozzle has a throat area of 10 cm2 and an exit area of 28.96 cm2 . A normal shock stands in the exit when the back pressure is sea-level standard. If the upstream tank temperature is 400 K, estimate (a) the tank pressure and (b) the mass fl ow

Answer 1

The tank pressure is 5.08 kPa and the mass flow rate is 2.6 kg/s.

The given parameters:

• Throat area of the nozzle, $A^*$ = 10 cm² = 0.001 m²
• The exit area of the nozzle, A = 28.96 cm² = 0.002896 m²
• Air pressure at sea level = 101.325 kPa

The ratio of the areas of the converging-diverging nozzle is calculated as follows;

$= \frac{A}{A^*} \\\\= \frac{0.002896}{0.001} \\\\= 2.896$

From supersonic isentropic table, at $\frac{A}{A^*} = 2.896$, we can determine the following;

$M_e = 2.6 \ kg/s\\\\\frac{P_o}{P_e} = 19.954$

The tank pressure is calculated as follows;

$\frac{P_o}{P_e} = 19.954 \\\\P_e = \frac{P_o}{19.954} \\\\P_e = \frac{101.325 \ kPa}{19.954} \\\\P_e = 5.08 \ kPa$

Thus, the tank pressure is 5.08 kPa and the mass flow rate is 2.6 kg/s.

Learn  more about converging-diverging nozzle design here: brainly.com/question/13889483