A small rocket motor is fired on a test stand

PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Waves, acoustics and compressible flow

Fluid Dynamics, Ch Euler's equation in Lamb's form and the four Bernoulli theorems

Problem

A small rocket motor is fired on a test stand. It burns stored propellant (there is no air intake) and ejects exhaust gas steadily through a nozzle of exit area

A_e = 0.03\,\mathrm{m^2}

at a mass flow rate

\dot m = 2.5\,\mathrm{kg\,s^{-1}}

and exit speed

U_e = 1800\,\mathrm{m\,s^{-1}}

, uniform across the exit plane. The exit-plane pressure is

p_e = 1.20\times10^5\,\mathrm{Pa}

and the surrounding atmospheric pressure is

p_a = 1.00\times10^5\,\mathrm{Pa}

. The unburnt propellant sits at rest in the motor and the gas flow inside is steady, so the momentum inside a fixed control surface round the motor stays constant even though its mass slowly falls. Using such a surface, which cuts across the exit plane (with no other flow crossing it, since the propellant is carried internally), find the force the test stand must supply to hold the motor in place.

Browse the problem library