A rocket engine burns propellant to give chamber conditions ,

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Fluids & Continuum Physics · Momentum, energy and conservation laws

Signal Speeds in Fluids, Ch Flow through nozzles: area change, choking and thrust

Problem

A rocket engine burns propellant to give chamber conditions

T_0 = 3400\,\mathrm{K}

p_0 = 8.00\,\mathrm{MPa}

, with combustion-gas properties

\gamma = 1.22

and molar mass

24\,\mathrm{g\,mol^{-1}}

(so

R = 346.4\,\mathrm{J\,kg^{-1}\,K^{-1}}

). The throat area is

A^* = 0.0150\,\mathrm{m^2}

. The flow through the diverging section is isentropic and quasi-one-dimensional. Take sea-level ambient pressure as

p_{\rm a} = 1.00\times10^5\,\mathrm{Pa}

and

g_0 = 9.80665\,\mathrm{m\,s^{-2}}

. ((a)) A first-stage version of the engine carries a bell whose area ratio

A_{\rm e}/A^*

is chosen so the exit pressure equals sea-level ambient pressure. Find that area ratio, the exit Mach number, the thrust, and the specific impulse at sea level. ((b)) An upper-stage version of the same engine (same chamber and throat) instead carries a bell of area ratio

50.0

, sized for vacuum operation. Find its exit Mach number, exit pressure, thrust in vacuum, and specific impulse in vacuum. ((c)) If the upper-stage bell were test-fired at sea level instead, find the thrust it would deliver if the internal flow stayed exactly as computed in part (b), using the sea-level back pressure only in the pressure term of the thrust equation, and say why the real thrust would differ from this value.

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