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Problem with units

  1. Jan 8, 2016 #1
    1. The problem statement, all variables and given/known data
    The velocity profile between two plates separated by a distance, h=2 {m}, has a flow distribution given by:

    1%257D%257B2%255Cmu%257D%255Cfrac%257Bdp%257D%257Bdx%257D%255Cleft%2528y%255E2-hy%255Cright%2529.png

    The dynamic viscosity of the fluid is given as 1.5E-1 {Pa s}. The upper wall is moving at velocity u0 of 7 {m/s}. The pressure gradient dp/dx is -0.015 {Pa/m}. Find the shear stress at y=0.8 {m}.

    Input your answer to in {N/m2} or {Pa} to four decimal places.

    2. Relevant equations


    3. The attempt at a solution
    I feel like this problem should be just plug and chug, but my units aren't working out to be in Pa.
    u(0.8m)=(7m/s)(0.8m/2m)+(1/(2*(1.5E-1)Pa*s))(-0.015Pa/m)((0.8m)2-1.6m2)
    I keep getting 2.85 m/s
     
  2. jcsd
  3. Jan 8, 2016 #2

    SteamKing

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    Remember u(y) is the velocity profile of the fluid, not the shear stress, so units of m/s are consistent.

    What is the formula for shear stress in a fluid?

    https://en.wikipedia.org/wiki/Shear_stress
     
  4. Jan 8, 2016 #3
    Ohh ok! I guess I should've read the question a little more closely. Did you end up with 0.5344 Pa?
     
  5. Jan 8, 2016 #4

    SteamKing

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    I didn't solve the problem. I merely noted that you had confused the formula for the velocity profile with the formula for shear stress.
     
  6. Jan 8, 2016 #5
    Oh ok, do you think that the value I got is reasonable?
     
  7. Jan 8, 2016 #6

    SteamKing

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    I have no idea without solving the problem myself.

    Since you have apparently done the work, why don't you post it?
     
  8. Jan 8, 2016 #7
    τ(y)=μ(u/y)
    τ(y)=(1.5E-1 Pa*s)((2.85 m/s)/(0.8m))=0.5344 Pa
     
  9. Jan 8, 2016 #8

    SteamKing

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    This doesn't seem to be the formula for shear stress in a fluid. What happened to the ∂u/∂y, which is not the same as u/y ?
    Need to use the correct formula here.
     
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