A convergent nozzle fed from a constant pressure, constant temperature reservoir, is discharging air to atmosphere at 1 bar (absolute) with choked flow at the exit (marked as \(Q\)). Flow through the nozzle can be assumed to be isentropic. If the exit area of the nozzle is increased while all the reservoir parameters and ambient conditions remain the same, then at steady state
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For choked flow, when the nozzle exit area increases and the reservoir conditions remain constant, the Mach number at the exit may change, but the nozzle may un-choke.
Step 1: Understanding choked flow.
In choked flow conditions, the mass flow rate reaches its maximum value, and the flow speed at the exit reaches the speed of sound (Mach 1). This condition is achieved when the nozzle is at its smallest possible cross-section, called the choked exit. For a convergent nozzle, this happens at the throat (exit) when the flow is sonic. Step 2: Effect of increasing the exit area.
When the exit area is increased, the flow no longer remains choked, and it will become subsonic. However, for the nozzle to remain choked, the pressure in the reservoir must be sufficiently high to support the supersonic flow condition. Thus, the nozzle will remain choked if the parameters are kept constant, but the exit area increase implies the Mach number at the nozzle exit increases as well, leading to a decrease in Mach number at section P. Step 3: Final analysis.
- (A) the nozzle will remain choked: Incorrect, the nozzle will un-choke after the area increases.
- (C) the Mach number at section P will increase: Correct, as the flow adjusts to the new area, the Mach number will increase at section P.
