1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Converting surface integral to line

  1. Jan 15, 2014 #1
    1. The problem statement, all variables and given/known data
    I have the following integral
    \int_{ABC}{\mathbf{v}\cdot \nabla f_id\sigma}
    where $d\sigma$ is an area element, $\mathbf v$ is a velocity vector and [itex]f_i[/itex] some function. The integral is performed across a triangle ABC and it is assumed that f is linear.

    In my book this integral becomes
    \mathbf v\cdot \int_{AB}{f_id\mathbf l} + I_s,
    where [itex]I_s[/itex] is the flux across [itex]BC[/itex] and [itex]AC[/itex]. Can someone explain to me how this integral is solved?
  2. jcsd
  3. Jan 15, 2014 #2


    User Avatar
    Science Advisor

    Use "Stoke's theorem" that you should remember from Calculus:
    [tex]\oint_C \vec{f}\cdot d\vec{r}= \int_\sigma\int \nabla\times\vec{f}dS[/tex]
    where C is the boundary of surface [itex]\sigma[/itex].
  4. Jan 15, 2014 #3
    Hi HallsofIvy

    Thanks, I remember that. But the RHS is in terms of a rotation operatir, not the gradient as I have.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted