# Rocket Engine Thrust Formula Help

#### mleesk

hello,

does anyone know how to derive the ROCKET ENGINE THRUST formula:

T = P/R AV + (P-B)A

i know you need to use F=ma and Momentum flow rate equations to get the first place. but what do you do after that?

Any help would be greatly appreciated.

Thanks,
Michael

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#### FredGarvin

Explain your variables. I see you are accounting for pressure difference across the nozzle in the second term, but I want to make sure of the variables in the first term.

#### jaap de vries

The thrust is the sum of the momentum change (mass flow) * (exit velocity) if the nozzle is over or under expanded than you will get extra thrust from the exit area times the pressure difference (Exit Plane Pressure - Ambient Pressure) * (Exit Area)

$$\dot{m} V+({V}_{exit} -{V}_{amb}){A}_{exit}$$

The mass flow is density times velocity times area, by perfect gas law

$$\rho = \frac{P}{RT}$$

$$\frac{P}{RT}V^{2}+({V}_{exit} -{V}_{amb}){A}_{exit}$$

so it looks like there is a T missing and the velocity should be squared. CHECK YOUR UNITS!!

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