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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

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!