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Homework Help: Converging Diverging Nozzle problem

  1. Apr 20, 2013 #1
    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!
  2. jcsd
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