Find the thrust from the engine

[jdawg]

Homework Statement

A static thrust stand is to be designed for testing a jet engine. The inlet conditions for the test are an inlet area of 1 {m²}, inlet velocity of 250 {m/s}, and gage static pressure of -22.5 {kPa}. The expected conditions at the 0.3 {m²} outlet are an exhaust gas velocity of 444 {m/s}, gage static pressure of 0 {kPa} and temperature of 268 {K}. Find the thrust the engine produces. Assume constant mass flow rate through the engine (i.e. mass of fuel in negligible) and that the gauge pressure is atmospheric pressure

Homework Equations

The Attempt at a Solution

First I calculated the total pressure entering and exiting the turbine:
(ρv²/2)+P+ρgh=P_total

The first term being dynamic pressure, the second being static pressure, and the third being hydrostatic pressure. I assumed hydrostatic pressure was negligible since I was given no information about the height.

P_total,1=15.78 kPa
P_total,2=120.75 kPa

Then I used F=P₂A₂
And found the force to be 402.5 kN

Does what I did make sense? I'm not really sure if this is the proper way to find the force of the thrust.

 

[haruspex]

Bernoulli's equation is based on conservation of energy. I would guess the engine is adding quite a bit.
What is the mass flow rate?
What is the rate of change of momentum of the air flowing through?