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In a given rocket engine, a mass flow of propellants equal to 87.6 lbm/s is pumped into the combustion chamber, where the stagnation temperature after combustion is 6000°R. The combustion products have mixture values R = 2400 ft·lb/(slug·°R) and γ = 1.21. If the throat area is 0.5 ft2 , calculate the stagnation pressure in the combustion chamber in lb/ft2 . Hint: use your knowledge about choked flow.

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Answer:

15 atm

Explanation:

Solution

Given that:

The first step is to convert mass flow rate unit

m = 87.6 lbm/s = 2.72  slug/sec

Now,

We express the mass flow rate, which is

m = p₀ A* /√T₀√y/R ( 2/ y+1)^(y+1) (y-1)

so,

2.72 = p₀ ^(0.5)/√6000√1.21/2400 (2/2.21)^10.52

Thus,

p₀ =  31736 lb/ft^2

Then,

We convert the pressure in terms of atmosphere

p₀ = 31736/ 2116 = 15 atm

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