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Homework Help: Fluid Mechanics newtons law of viscosity

  1. Jul 25, 2013 #1
    1. The problem statement, all variables and given/known data
    having problems differentiating

    2. Relevant equations
    Tw ( wall shear stress)= -U(viscosity)*du/dr
    been given u as 2V(1-(r/r)^2)

    3. The attempt at a solution
    i substituted u in and got

    d/dr (2V(1-(r/r)^2)
    i tried to multiply out the minus sign and 2V and got a very different answer i got -2V+2V (r/r)^2

    when the answer is supposed to be -4VR/R^2

    please help
  2. jcsd
  3. Jul 26, 2013 #2
    What do you mean here:

    been given u as
    2V(1-(r/r)^2) = 2V(1 - 1) = 0

  4. Jul 26, 2013 #3


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    Homework Helper

    Do you mean
    u = 2V\left(1 - \left(\frac{r}{r_0}\right)^2\right)
    where [itex]r_0[/itex] is the radius of what I assume to be a cylindrical pipe?

    The given answer is for [itex]du/dr[/itex]; to get [itex]T_w[/itex] you have to multiply that by [itex]-\mu[/itex].

    So far all you've done is multiply [itex]u[/itex] by -1. Try differentiating with respect to r first.
  5. Jul 26, 2013 #4
    r=R and its (r/R)^2
  6. Jul 26, 2013 #5
    okay now i have differentiated it with respect to r i get 2V2r/R^2) or -(4Vr/R^2) thanks again i was then required to use the wall shear stress to determine the frictional force but it is very straight forward from there
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