HW27solution - A R T m o o 2 1 1 1 2 1 1 2 1 1 Collect...

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AAE 334 Fall 2011, Homework 27 SOLUTIONS Due Monday, November 21 at the beginning of class. Derive an expression for the mass flow through a choked throat of a converging-diverging nozzle based on: - knowledge of upstream stagnation condition conditions o p and o T , - throat area of A , - gas properties for air as an ideal gas, - steady quasi-one-dimensional flow, and - an isentropic process from upstream stagnation conditions to the throat. Because the throat is choked, the mass flow at the throat can be written as a product of sonic conditions: A u m The air speed at sonic conditions is the speed of sound, thus, RT a u . Substitute: A RT m . Now relate sonic density and sonic temperature back to isentropic stagnation conditions,
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Unformatted text preview: A R T m o o 2 1 1 1 2 1 1 2 1 1 Collect constants together, R A T m o o 2 1 1 1 2 1 1 Use Ideal Gas law to change density: R A T RT p m o o o 2 1 1 1 2 1 Simplify temperature, continue to group the constants, R A T p m o o 1 2 1 1 2 and simplify, 1 1 1 2 R T p A m o o...
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This note was uploaded on 02/21/2012 for the course AAE 334 taught by Professor Collicott during the Fall '09 term at Purdue University.

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