Critical pressure ratio for choked flow in a nozzle Let p 1 be the inlet (stagnation) pressure and p 2 the throat static pressure at choking. Express the critical pressure ratio (p 2 /p 1 ) in terms of the rati…

Concept/Approach For isentropic flow of a perfect gas, the sonic (choked) condition at the throat gives (p2/p1)crit = (2/(γ + 1))γ/(γ − 1). This is derived from the energy equation and isentropic relations at Mach = 1. Final Answer (2/(γ + 1))^(γ/(γ…

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Critical pressure ratio for choked flow in a nozzle Let p1 be the inlet (stagnation) pressure and p2 the throat static pressure at choking. Express the critical pressure ratio (p2/p1) in terms of the ratio of specific heats γ. Choose the correct expression.

Difficulty: Medium

(2/(γ + 1))^(γ/(γ − 1))
(γ + 1)/(γ − 1)
(2γ/(γ + 1))^(1/(γ − 1))
(γ − 1)/(γ + 1)

Correct Answer: (2/(γ + 1))^(γ/(γ − 1))

Explanation:

Concept/Approach

For isentropic flow of a perfect gas, the sonic (choked) condition at the throat gives (p₂/p₁)_crit = (2/(γ + 1))^{γ/(γ − 1)}.
This is derived from the energy equation and isentropic relations at Mach = 1.

Final Answer
(2/(γ + 1))^(γ/(γ − 1))

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