Sonic Condition at the Nozzle Throat – Compare with Speed of Sound In steady, isentropic nozzle flow of a compressible fluid, the flow becomes choked at the minimum area. At this choked condition, the fluid velocity at the throat equals, is less than, or is greater than the local speed of sound?

Introduction / Context:
Choking in compressible flow marks the transition to a sonic condition that caps the mass flow rate for given upstream stagnation conditions. This principle is central to nozzle design, gas safety valves, and rocket propulsion. The question asks what the throat velocity equals at the onset of choking.

Given Data / Assumptions:

• One-dimensional, steady, isentropic flow in a converging (or converging–diverging) nozzle.
• Well-defined upstream stagnation (total) pressure and temperature.
• Throat is the minimum cross-sectional area.

Concept / Approach:

At the critical (choked) condition, the Mach number at the throat is M* = 1. By definition, Mach number M = V/a, where V is the local flow speed and a is the local speed of sound. Therefore, M* = 1 implies V_throat = a_throat. Downstream of the throat in a diverging section, the flow can accelerate to supersonic speeds (M > 1) if the back pressure permits; upstream of the throat in a purely converging nozzle, the flow remains subsonic (M < 1).

Step-by-Step Solution:

Verification / Alternative check:

Area–Mach relations show that the minimum-area location corresponds to M = 1 for isentropic flow. Experimental Schlieren images and pitot-static measurements confirm sonic condition at the throat when choked.

Why Other Options Are Wrong:

'Less than' describes subsonic pre-throat regions; 'more than' describes supersonic, which occurs only downstream in a diverging section after choking is established. 'Indeterminate' is incorrect because the sonic condition follows from isentropic nozzle theory; 'zero due to vena contracta' confuses internal flow contraction with compressible nozzle throat behavior.

Common Pitfalls:

Mixing local speed of sound with upstream value; forgetting that sonic condition is local (depends on local temperature). Also, conflating choking with shock formation—shocks may occur downstream but are not required at the throat.

Final Answer:

equal to