Nozzle flow — definition of critical pressure For a converging or converging–diverging nozzle handling steam or gas, the discharge (mass flow rate) reaches a maximum at a particular exit/back pressure. This special back pressure is called the “critical pressure.” Is this statement correct?

Introduction / Context:
Nozzle sizing in turbines and ejectors relies on the concept of choked flow. As the back pressure is reduced, mass flow initially increases but eventually becomes insensitive to further reductions because the throat reaches sonic conditions. The back pressure at which this transition occurs is associated with a critical pressure ratio.

Given Data / Assumptions:

• Steady, adiabatic flow; negligible shaft work.
• Single-phase gas/steam; throat well-defined.
• Isentropic analysis for the ideal critical condition.

Concept / Approach:
For isentropic flow of a perfect gas, choking occurs when the Mach number at the throat equals 1. The mass flow rate per unit area then depends only on upstream stagnation conditions. The corresponding downstream pressure equals the critical pressure p* such that p*/p0 = function of specific heat ratio. Below this back pressure, the mass flow does not increase—discharge is maximized.

Step-by-Step Solution:
Reduce back pressure from near-stagnation: mass flow rises as the pressure differential grows.At the critical pressure ratio, throat Mach = 1; ṁ reaches a maximum.Further reduction of exit pressure affects only the supersonic part (if a diffuser exists) or creates expansion waves but leaves ṁ unchanged for a fixed upstream state.

Verification / Alternative check:
Converging nozzles choke at the throat; converging–diverging nozzles can expand to supersonic speeds past the throat but the mass flow remains set by the choked throat when upstream conditions are fixed.

Why Other Options Are Wrong:
“Disagree” would deny well-established choking behavior used in every gas-dynamics textbook and design code.

Common Pitfalls:
Confusing “critical pressure” (a specific back pressure ratio) with “critical point” of a substance in phase equilibrium thermodynamics.

Final Answer:
Agree