# Converging Diverging Nozzle problem

1. Apr 20, 2013

### nakas12

1. The problem statement, all variables and given/known data

Air flows through a symmetric converging-diverging nozzle where the cross-sectional area of the nozzle (in meters^2) varies accoding to the relationship:

A(x) = 1.0 - 0.8X +.80X^(2) ; where X is in meters and the nozzle is 1 meter long.

P2/P1 = .90 (there is subsonic inflow) A normal shock also occurs near the exit.

A) Determine the inflow and outflow mach numbers
B) The stagnation pressure ratio across the normal shock
C)The X location of the shock (in meter) from the inflow to the normal shock.

2. Relevant equations

I have been using the isentropic and normal shock tables to solve this problem which involve ratios of pressures, areas, and temperature.

3. The attempt at a solution

I assume Mach number at the throat will be 1
Mth (throat) = 1
L =1
Area of the throat: X=0.5
A(x) = 1.0-0.8(.5) + 0.8(.5^(2)) = 0.8
Throat area: 0.8 = A*

Area of the inlet = 1 = A1

A1/A* = 1.25
From this I find the Mach number at the inlet equal to .5533
M1 = .5533

I honestly need help with only finding the Mach numbers at the inlet and exit. I'm a little confused due to the equation for finding the area given. I could really really use some help. Thanks!