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I am stuck on a homework question, all because I dozed off in class.

I understand what a stream function is but I don't know how to apply it to calculate the flow in pretty much anything.

Here's the problem I am stuck on. I choose to not give out the question in it's entirety.

An incompressible stream function is given by $\psi (x,y)$ .Use the stream function to find the volume flow passing through the rectangular surface whose corners are defined by (x,y,z)=(2L,0,0),(2L,0,b),(0,L,b) and (0,L,0).

My Doubt Where do I apply the stream function, at the corners of the rectangular surface or the midpoints? Or am I going in the wrong direction?

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How do you obtain a flow rate from a velocity function? How do you obtain a velocity function from a stream function? –  Bernhard May 29 '13 at 14:59
    
@Bernhard Velocity times unit area should give out the volume rate, but one has to find the gradient of the stream function to find the velocity components of the field right? –  nerorevenge May 29 '13 at 15:10
    
True, what if the velocity is not constant along the area? –  Bernhard May 30 '13 at 5:42
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1 Answer 1

The Curl of the stream function will give the velocity field of the fluid. Integrate this velocity field over the given area to get the volume flow rate required.

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