1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Flow Field Continuity

  1. Sep 6, 2010 #1
    1. The problem statement, all variables and given/known data

    A flow field is described by

    |V| = f(r) ;

    x^2 + y^2 = c (streamlines)

    What form must f(r) have if continuity is to be satisfied? Explain your results.

    2. Relevant equations

    equation of continuity: div V = d(ur)/dr + (ur)/r = 0

    where (ur) is the radial velocity

    3. The attempt at a solution

    I manipulated the continuity equation to be...
    -d(ur)/(ur) = dr/r
    Then I integrated both sides and got...
    1/(ur) = r
    Now I'm not sure what to do next or if i'm even on the right path. Can someone that understands this problem give me a hint?
     
  2. jcsd
  3. Sep 7, 2010 #2

    hunt_mat

    User Avatar
    Homework Helper

    What you have implicitly assumed is that as the modulus of te velocity vector field is independent on the angle then that means that the individual components are, which is not the case. So you have to take:
    [tex]
    \mathbf{V}=u_{r}(r,\theta )\hat{\mathbf{r}}+u_{\theta}(r,\theta )\hat{\mathbf{\theta}}
    [/tex]
    With the property that:
    [tex]
    \sqrt{u_{r}^{2}+u_{\theta}^{2}}=f(r)
    [/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Flow Field Continuity
Loading...