In a divergent nozzle, supersonic flow, which statement is true?

In a divergent nozzle, supersonic flow, which statement is true?

• A. Velocity decreases and pressure increases
• B. Velocity remains unchanged and pressure decreases
• C. Velocity decreases and pressure decreases
• D. Velocity increases and pressure decreases

Answer: (D)

In compressible flow, once the gas becomes sonic at the throat, a diverging (widening) section causes the flow to accelerate and the static pressure to drop. This happens because total enthalpy stays constant in isentropic flow, so any increase in kinetic energy (higher velocity) comes from a decrease in static pressure (and temperature). So in a divergent nozzle with supersonic flow, widening the area makes the flow speed up while the pressure falls, which is why the statement “velocity increases and pressure decreases” is true. The other possibilities describe subsonic behavior or no change in velocity, which don’t apply once the flow is supersonic in the diverging section.

In compressible flow, once the gas becomes sonic at the throat, a diverging (widening) section causes the flow to accelerate and the static pressure to drop. This happens because total enthalpy stays constant in isentropic flow, so any increase in kinetic energy (higher velocity) comes from a decrease in static pressure (and temperature). So in a divergent nozzle with supersonic flow, widening the area makes the flow speed up while the pressure falls, which is why the statement “velocity increases and pressure decreases” is true. The other possibilities describe subsonic behavior or no change in velocity, which don’t apply once the flow is supersonic in the diverging section.