Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fluid Flow: Principal Rates of Deformation/Principal Axes

  1. Mar 19, 2007 #1
    Hi all,

    I've been stumped on this problem for over a month. Any guidance would alleviate my overwhelming frustration. Here is the original problem statement:

    Find the principal rates of deformation and principal axes for the flow given by: u = (x,y) and v = 0, satisfying the continuity equation (density = rho = constant)
    [tex] \frac{\partial u_i}{\partial x_i} = 0[/tex]​

    Attached to this post is my attempt to work out the solution. I'm not sure how to proceed on, so your help would be greatly appreciated. Thanks!

    Attached Files:

    Last edited: Mar 19, 2007
  2. jcsd
  3. Mar 19, 2007 #2
    I guess that continuity should be du_i/dx_i=0 instead of div(u_3)=0.

    Anyhew, your solution seems correct up till and including the principal directions (with the note that u=u(y) only, i.e. 2-D shear flow). When I calculate the principal values and directions in the old fashion way (as eigenvalues/eigenvectors of the strain rate tensor), I get the same directions, but principal values are +/- du/dy.

    Cheers //Rope
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook