Helium expands in a nozzle from 220 psia, 740 R, and negligible velocity to 15 psia. Calculate the throat and exit areas for a mass flow rate of 0.2 Ibm's, assuming the nozzle is isentropic. Why must this nozzle be converging-diverging?
The throat and exit areas of the nozzle for given mass flow rates and also why the nozzle must be of converging-diverging type.
Answer to Problem 126EP
The throat area of the nozzle is
The exit area of the nozzle is
The exit Mach number comes out to be greater than the 1, hence the nozzle must be of converging-diverging type.
Explanation of Solution
Given:
Stagnation Temperature
Stagnation Pressure
Exit pressure at nozzle is
Mass flow rate
Assuming flow is isentropic.
Calculation:
Properties of helium,
R is gas constant,
Mach number is given by
The flow is imagined to be isentropic, so the stagnation temperature and stagnation pressure remain sameoverall the nozzle.
Throat temperature is given by
Throat pressure is given by
Exit area of throat is given by
Throat density is given by
Inlet velocity is given by
Substitute
Therefore, throat area is given by
Pressure at the exit of nozzle is given as
Pressure at nozzle exit is given by
Temperature at nozzle exit is given by
Area of exit at nozzle is given by
Density at exit of nozzle is given by
Velocity at exit of nozzle is given by
Substitute,
Conclusion:
Thus, the throat area of the nozzle is
The exit area of the nozzle is
The exit Mach number comes out to be greater than the 1, hence the nozzle must be of converging-diverging type.
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Fluid Mechanics: Fundamentals and Applications
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