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Homework Help: Fluid Dynamics for a nozzle

  1. Feb 10, 2012 #1
    1. The problem statement, all variables and given/known data
    Open ended problem really, nothing is given except that I need a thrust of 30 lbf. Similar to dyson fan which entrains and induces air, increasing airflow 15 times. Working around this concept, I'm trying to design a nozzle so I can calculate the ratio of inlet and exit areas. So far I know that for the most efficient nozzle, the exit pressure must equal atmospheric. This is all for subsonic flow.

    2. Relevant equations
    Wasn't exactly sure where to start, so I took Bernoulli's equation (ignoring gz term), substituted the conservation of mass terms, and plugged that into a thrust equation.

    3. The attempt at a solution
    Bernoulli's: Vi^2/2 + Pi/rho = Ve^2 + Patm/rho
    COM: Ai*Vi = Ae*Ve
    Thrust: F= mdot*Ve + (Pe-Patm)Ae, Pe=Patm

    Throw that all together,

    F = rho *(Ae^2/Ai)*Vi *sqrt(Vi^2 + 2(Pi - Patm)/rho))

    Here I have 4 unknowns if I have a constraint that F must equal 30lbf. I could set Ae^2/Ai as a ratio and take it down to 3 unknowns, but that doesn't help much. Any thoughts on how I could nail this down so I have one input and output?
  2. jcsd
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