Show that curves of constant ψ(x,y) are streamlines

[bakra904]

Fluid Dynamics Question about streamlines...help!?

If the velocity field, v, of a fluid 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 streamlines of the flow. (a streamline is a curve which is everywhere tangent to v)

 

[DavidWhitbeck]

See other thread. Man that's so annoying when someone posts the same question twice!