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.

Question

Engineering

Meredith Pierce

24 January, 21:51

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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Answers (1)

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Aaron Ingram · Answer 1

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