Questions: Isentropic Nozzle Flow and Choked Conditions

Question 1

A converging-diverging rocket nozzle is operating with a choked throat (M = 1). The back pressure downstream is then reduced further. What happens to the mass flow rate through the nozzle?

• A. Mass flow rate increases because the larger pressure difference across the nozzle drives more flow
• B. Mass flow rate stays the same — the throat is at M = 1 and has reached its maximum mass flow for the given stagnation conditions
• C. Mass flow rate decreases because the lower back pressure disrupts the supersonic expansion region
• D. The throat unchokes and transitions back to subsonic, increasing mass flow

Answer: (B)

Once the throat is choked (M = 1), the mass flow rate is determined entirely by the inlet stagnation conditions (pressure, temperature) and throat area — not by back pressure. At the sonic condition, acoustic disturbances (pressure signals) traveling upstream are exactly cancelled by the flow velocity, so no information about back pressure changes can reach the throat. Reducing back pressure further changes the exit flow structure (shock positions, expansion fans) but cannot increase the mass flow above the choked value.

Question 2

A rocket nozzle is designed to operate at high altitude where ambient pressure is near zero. At sea-level launch, the ambient pressure is much higher. Assuming the combustion chamber conditions are identical, how does sea-level operation affect mass flow through the nozzle?

• A. Mass flow decreases at sea level because the higher ambient pressure partially opposes the flow
• B. Mass flow is unchanged — if the nozzle is choked, only upstream stagnation conditions and throat area determine mass flow
• C. Mass flow increases at sea level because the higher pressure differential drives more propellant through
• D. Mass flow is unchanged only if the exit pressure exactly equals ambient pressure

Answer: (B)

A choked nozzle is isolated from downstream conditions by the sonic throat. Mass flow is set by stagnation pressure, stagnation temperature, throat area, and gas properties — all of which are controlled by the combustion chamber, not the atmosphere. At sea level versus high altitude, the ambient pressure difference affects the exit flow structure (causing overexpansion and oblique shocks), nozzle efficiency, and thrust magnitude, but not the mass flow rate. This is why rocket performance analysis focuses on the combustion chamber and throat, not on ambient conditions.

Question 3

In supersonic flow through a diverging nozzle, increasing the cross-sectional area accelerates the flow to higher Mach numbers.

• T. True
• F. False

Answer: True

This counterintuitive result follows from the area-Mach relation for compressible flow. In subsonic flow, a diverging duct decelerates the flow (as in an incompressible venturi). But once flow passes through a sonic throat, the situation reverses: in supersonic flow, density drops faster than area increases, so the continuity equation (mass conservation) requires velocity to increase with area. A diverging section after a sonic throat is the only way to continue accelerating gas beyond M = 1 — which is why converging-diverging nozzles are required for supersonic jets and rockets.

Question 4

A converging-primarily nozzle can produce supersonic exit flow if the pressure ratio across it is made large enough.

• T. True
• F. False

Answer: False

A converging nozzle can only accelerate flow up to M = 1 at its exit (the throat). This is the maximum — no matter how large the pressure ratio, the exit cannot exceed sonic conditions in a converging nozzle. To continue accelerating beyond M = 1, a diverging section must follow the throat. Without a diverging section, sonic conditions at the exit represent the choked limit and the flow never becomes supersonic. This is why all supersonic applications (jet engines with supersonic inlets, rocket nozzles) use converging-diverging geometry.

Question 5

Why can pressure disturbances from downstream of a choked nozzle throat not travel upstream to increase mass flow?

Model answer: Pressure disturbances (sound waves) propagate at the local speed of sound relative to the medium. At the choked throat, the flow velocity equals the speed of sound. A disturbance trying to travel upstream against this flow would need to move faster than the local flow speed — but pressure waves travel at exactly the speed of sound in the fluid, so they are perfectly cancelled by the opposing flow velocity. The net upstream propagation speed is zero. Any disturbance originating downstream is swept away by the flow and cannot cross the throat. This acoustic isolation means the mass flow through the throat is determined entirely by upstream stagnation conditions and throat area, decoupled from whatever pressure environment exists downstream.

This is fundamentally an information-propagation argument: in a fluid, all mechanical information travels at the speed of sound. At M = 1, the flow exactly cancels this propagation upstream. This is why choked-flow orifices are used as metering devices in industry — the upstream conditions set the flow rate precisely, independent of downstream pressure fluctuations.