Choked flow facts — identify the wrong statement Which of the following statements about compressible flow in a steam/gas nozzle is wrong?
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AAt the critical pressure ratio, the velocity at the throat equals the local speed of sound
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BFlow in the convergent portion of a C–D nozzle is subsonic (before choking)
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CFlow in the divergent portion of a properly expanded C–D nozzle is supersonic
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DTo exceed sonic velocity by expanding below the critical pressure, a divergent portion is not necessary
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E—
Answer
Correct Answer: To exceed sonic velocity by expanding below the critical pressure, a divergent portion is not necessary
Explanation
Introduction / Context:Understanding choking and the role of nozzle geometry is central to turbine, rocket, and ejector design. Several statements are listed; only one contradicts fundamental gas-dynamics principles.
Given Data / Assumptions:
- Steady, adiabatic, single-phase compressible flow.
- Converging–diverging nozzle with a well-defined throat.
- Isentropic flow used for ideal reasoning.
Concept / Approach:Choking occurs when Mach = 1 at the throat; the corresponding downstream (back) pressure equals the critical pressure. Upstream of the throat in a convergent passage, the flow is subsonic. To achieve supersonic speeds, the flow must pass through a diverging section after reaching Mach 1 at the throat; a mere convergent nozzle cannot produce supersonic flow from subsonic inlet conditions.
Step-by-Step Solution:Evaluate A: correct — critical condition sets throat velocity to sonic.Evaluate B: correct — subsonic accelerates in convergence up to Mach 1 at the throat.Evaluate C: correct — beyond the throat, a diverging section accelerates flow to supersonic if back pressure is low enough.Evaluate D: wrong — a divergent section is required to go beyond sonic; without it, a purely convergent nozzle cannot deliver supersonic outlet flow from subsonic inlet.
Verification / Alternative check:Standard area–Mach relations mandate that for M > 1, area must increase; experimental data confirm that supersonic velocities occur only in diverging ducts past a sonic throat, not in a purely converging nozzle.
Why Other Options Are Wrong:They are consistent with textbook compressible-flow theory and observed nozzle behavior.
Common Pitfalls:Confusing throttling valves (constant area) with nozzles; mixing up “critical pressure” with “critical point” in thermodynamics.
Final Answer:To exceed sonic velocity by expanding below the critical pressure, a divergent portion is not necessary