I want to calculate the exhaust velocity of a rocket. This is the formula that I found at http://en.wikipedia.org/wiki/Rocket_engine_nozzles which is:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

V_e = \sqrt{{\frac{T*R}{M}}*{\frac{2*k}{k-1}}*[1-(P_e/P)^(^k^-^2^)^/^k] }

[/tex]

V_{e}= Exhaust velocity at nozzle exit, m/s

T = absolute temperature of inlet gas, K

R = Universal gas law constant = 8314.5 J/(kmol·K)

M = the gas molecular mass, kg/kmol (also known as the molecular weight)

k = c_{p}/ c_{v}= isentropic expansion factor

c_{p}= specific heat of the gas at constant pressure

c_{v}= specific heat of the gas at constant volume

P_{e}= absolute pressure of exhaust gas at nozzle exit, Pa

P = absolute pressure of inlet gas, Pa

I'll use 1 of the Space Shuttle Main Engine for this equation. The statistics for the SSME are:

- Thrust at Lift Off = 1.8 MN
- Chamber pressure = 18.9399 MPa
- Nozzle Area ratio = 77
- Exhaust Velocity = 3,560 m/s
- Chamber Temperature = 3,573.15 Kelvin
- SSME consume 3,917 liters per second of fuel
- Exit Pressure = 7.2326 kilopascals

For the molecular mass, do I have to find the mass of it in moles for Oxygen and Hydrogen seperately or when they mix together to form H_{2}O? I would like an explanation on what is c_{p}/ c_{v}to further understand the equation.

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# Rocket Engine Exhaust Velocity

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