Critical pressure ratio for nozzles – proper expression Choose the correct expression for the critical pressure ratio in a steam nozzle, given inlet pressure p1 and throat (critical) pressure p2.

Introduction / Context:The critical pressure ratio characterizes the onset of choking in compressible nozzle flow. It compares the throat static pressure at sonic conditions to the inlet (stagnation/total or chamber) pressure and determines whether further reduction in back pressure will increase mass flow.

Given Data / Assumptions:

• p1 is the inlet (upstream) total pressure used for the ratio.
• p2 is the static pressure at the throat when Mach = 1.
• Ideal isentropic assumption for the critical condition.

Concept / Approach:By convention, the critical pressure ratio is defined as the ratio of throat pressure to inlet pressure, i.e., p2/p1. For a given working fluid, this ratio has a specific value that triggers choked flow. For perfect gases it depends on the specific heat ratio; for steam, steam-table relations or empirical coefficients are used.

Step-by-Step Solution:Identify the two pressures: p1 (inlet), p2 (throat at sonic conditions).Form the ratio as throat over inlet → p2/p1.This ratio is less than 1 and marks the limit beyond which mass flow becomes insensitive to back pressure.

Verification / Alternative check:Performance curves display a plateau in mass flow once p_back/p1 falls below p2/p1. For air with γ = 1.4, the ideal ratio is around 0.528; steam values differ but the definition remains p2/p1.

Why Other Options Are Wrong:

• p1/p2 is the reciprocal of the standard definition.
• p1 p2 and p1 + p2 have incorrect dimensions or meaning.
• p1 − p2 indicates a pressure drop, not a ratio.

Common Pitfalls:Mixing up back pressure with critical throat pressure; the critical ratio specifically uses throat quantities at Mach 1.

Final Answer:p2/p1