This preview shows page 1. Sign up to view the full content.
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 convergingdiverging
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 quasionedimensional 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,
This is the end of the preview. Sign up
to
access the rest of the document.
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...
View
Full
Document
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.
 Fall '09
 COLLICOTT

Click to edit the document details