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!

Proof: Everywhere Tangent to Curve?

  1. May 6, 2008 #1
    Proof: Everywhere Tangent to Curve??

    If the function v depends on x and y, v(x,y) and we know there exists some function psi(x,y) such that
    vx = partial w.r.t (y) of psi
    vy= -(partial w.r.t (x) of psi)

    show that the curves psi(x,y) = constant, are everywhere tangent to v.
    Last edited: May 6, 2008
  2. jcsd
  3. May 6, 2008 #2
    Usually you are supposed to show effort to get there, but I think this is a case where either you get it or you don't.

    [tex]\nabla \psi[/tex] is normal to surfaces of constant [tex]\psi[/tex] and [tex]v\cdot \nabla \psi = 0[/tex]. Fill in the rest.
  4. May 6, 2008 #3
    Thanks a bunch! I'm a new poster and did not know about the effort rule...I had worked on it but did not post what I had worked on.

    I was trying to use the fact that if v = [tex]\nabla \times[/tex] [tex]\psi[/tex],

    then that would imply that [tex]\psi[/tex] is a stream function, which in cartesian co-ordinates would reduce to:

    Vx = [tex]\frac{\partial\psi}{\partial y}[/tex] and Vy = - [tex]\frac{\partial\psi}{\partial x}[/tex]

    which is basically what the problem had to begin with. Then, since I know that [tex]\psi[/tex] (x,y) is a stream function, doesn't it have to be tangent to v by virtue of the fact that its a streamline?
  5. May 6, 2008 #4
    Are you trying to curl a scalar field??
  6. May 7, 2008 #5
    oh right...i overlooked that part. thanks!
  7. May 9, 2008 #6
    so basically [tex] v. \nabla\psi = 0[/tex] which proves that [tex] v [/tex] and [tex]\nabla\psi[/tex] are perpendicular (since their dot product is 0) and so [tex]\psi[/tex] must be tangent to [tex] v [/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Proof: Everywhere Tangent to Curve?
  1. Tangent and Curves (Replies: 4)

  2. Tangent to the curve (Replies: 1)

  3. Tangent to a curve (Replies: 4)

  4. Tangents to the curves (Replies: 5)