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rz_supra
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Homework Statement
A rocket operating with combustion chamber pressure and temperatures of 14MPa and 2500K respectively, has a throat diameter of 0.3m, and a nozzle area ratio of 50:1.
Find the thrust and specific impulse developed by the motor with back pressures of 1 bar (10^5 Pa) and zero.
At what back pressure would the nozzle be correctly expanded?
Assume the combustion products behave as a perfect gas, with a constant specific heat ratio (y) of 1.4, and a constant specific gas constant (R) of 300 J/kg/K
Homework Equations
throat P/chamber P = ((y+1)/2)^(y/(1-y)) (for M=1) M = Mach number
throat T/chamber T = y/(y+1) (for M=1)
mdot = [(area of throat * throat P)/sqrt(throat t)]*[sqrt(y/R)]*((y + 1)/2)*((y + 1)/2(1 - y))
area of throat = pi * throat radius * throat radius
The Attempt at a Solution
chamber P = 14MPa
chamber T = 2,500K
throat diameter = 0.3m; throat diameter = 0.15m
y = 1.4 (constant specific heat ratio)
R = 300 J/kg/K
Calculate mdot --> through conditions @ throat M=M*=1
throat P/chamber P = ((y+1)/2)^(y/(1-y))
throat P = 7.4MPa
throat T/chamber T = y/(y+1)
throat T = 2,083.3K
mdot = [(area of throat * throat P)/sqrt(throat t)]*[sqrt(y/R)]*((y + 1)/2)*((y + 1)/2(1 - y))
mdot = 782.47
area of throat = pi * throat radius * throat radius
area of throat = 0.0707
This is where I get stuck, I need to incorporate these back pressures of 10^5 Pa and 0 Pa somehow. I know that for a correctly expanded nozzle, pressure of exit = ambient pressure
Any help would be greatly appreciated!