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Where does this equation come from?

  1. Aug 24, 2011 #1
    Hi,

    In a text book I found an equation for the volumetric flow rate of air through a channel (tube). I can't find from where the equation is coming, someone an idea?

    The equation which I mean is: Q = - pi*d^4/(128*viscosity)* dp/dx

    I know that Q = A*v = pi*d^2/4 *v

    Also from the simplified equation of motion 'v' can be calculated as:

    dp/dx = viscosity * ddv/ddy (dd = second derivative)

    from this equation v = ?? if I fill v in, in Q = pi*d^2/4 *v will this give Q = - pi*d^4/(128*viscosity)* dp/dx ??
     
  2. jcsd
  3. Aug 24, 2011 #2

    lightgrav

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    Homework Helper

    Work is being done by the Pressure gradient, to friction with the walls, due to the viscosity. ... your Q is mass density times v dot dA, integrated over the tube's cross-section Area. the velocity goes to zero at the tube surface, and is maximum in its center.
     
  4. Aug 24, 2011 #3
    the density comes from massXvolume

    and the mass comes from 1/2mv^2=Ek



    i hope this helped a little bit
     
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