1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Shear Flow Against a Wall (Fluid Mechanics)

  1. May 10, 2013 #1
    1. The problem statement, all variables and given/known data

    Assume a shear flow against a wall, given by U= Uo (2y/ax - y^2/((ax)^2) where a is a constant. Derive the velocity component V (x; y) assuming incompressibility.

    2. Relevant equations
    Haven't been able to find any in my course notes.

    3. The attempt at a solution
    Some googling has taught me that shear flow is the flow induced by a shear stress force gradient. But I really need some sort of equation to solve this I think.
  2. jcsd
  3. May 12, 2013 #2
  4. May 12, 2013 #3
    Hi Isobel2. Welcome to Physics Forums.

    You need to make use of MaxManus' suggestion, and set the divergence of the velocity vector equal to zero:

    [tex]\frac{\partial V}{\partial y}=-\frac{\partial U}{\partial x} [/tex]

    But, before you start trying to do this by brute force, first define the following parameter:


    so that [tex]U = U_0(2\eta - \eta ^2)[/tex]

    Also note that [tex]\frac{\partial U}{\partial x}=\frac{\partial U}{\partial \eta}\frac{\partial \eta}{\partial x}=-\frac{\partial U}{\partial \eta}\frac{\eta}{x}[/tex]
    [tex]\frac{\partial V}{\partial y}=\frac{\partial V}{\partial \eta}\frac{\partial \eta}{\partial y}=\frac{\partial V}{\partial \eta}\frac{1}{ax}[/tex]

    Working with the parameter η in this way will make the "arithmetic" much simpler and less prone to error.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted