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Shear Stress for Fluids

  1. Feb 26, 2009 #1
    1. The problem statement, all variables and given/known data
    I have an empirically-derived equation for the shear stress of a fluid on a surface, given by the equation below.

    I am supposed to take the derivative of density with respect to distance, and I must use this equation to find an expression for density.

    Delta = Boundary layer thickness.
    Nu = Kinematic Viscosity
    u = Velocity
    Rho = Density

    2. Relevant equations

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    3. The attempt at a solution

    I know the definition of shear stress for fluids (The second equation above). I've tried to equate it to the empirical formula, knowing that dynamic viscosity, mu, is just density*kinematic viscosity.

    The density variables cancel though.

    I can't have a tau term in the density expression, so I can't just algebraically manipulate the first equation to equal density.
     
  2. jcsd
  3. Feb 26, 2009 #2

    Delphi51

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    Homework Helper

    I don't know anything about this topic, but it appears you have
    sheer stress = a(b/u)^4 = c*du/dy and want to find the formula relating u and y.
    I'm using a, b, c to save wear and tear on the keyboard.
    If so, you can write it as a/c*b^.25*dy = u^.25*du
    Integration yields a/c*b^.25*y = u^1.25 + D
     
  4. Feb 26, 2009 #3
    Thanks, but that's not what I'm looking for.

    I need to take the derivative of density with respect to y, and I need to use the shear stress to take the derivative. So I need to find a relationship between density and stress.

    I've tried using the Newtonian definition suggested by Stokes. I tried using Reynolds Number to relate density and velocity, so that I can use the velocity relation to find an expression of density in terms of shear stress, but no luck.
     
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