A stream function in a two-dimensional flow is A = 2xy.

Question

Show that the flow is irrotaional(potential kind).

Let q=(u,v) be the velocity
of the two-dimensional flow.

Then w know, u = delta(A)/delta(y) and v =-[delta(A)/delta(x)] , where delta denote partial derivative.

We've been thought that the necessary and sufficient condition for a potential kind of flow is curl q= 0.

So here, I get curl q=0, which implies tgisflowis of potential kind(irrotaional)

So for this question, my professor has used an alternative appoach. Can anyone verify whether my method is an acceptable answer for this problem?

Thank you!

Answer 1

∇×A=0 is the way I'd do it.

Answer 2

So grad * A implies irrotational condition of the fluid flow??

Answer 3

grad * A = 0 implies irrotaional condition of the flow