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I have the following problem with respect to fluid mechanics:

A source of strengthQis in a 3D space and subjected to a parallel flowUalong the x-axis. The position of the source is at (xq,yq,zq). This will lead to the following velocity potential in cartesian and cylindrical coordinates

figure 1

With the velocity in the x-direction determined to be

figure 2

To calculate the surfacerho(x)which separates the fluid (coming from the source) from the fluid, (coming from the parallel flow), one can use the law of volume conservation (because of constant density). In that body which is described by that surface, the flow through any plane x=constant should equal toQ

figure 3

I know this is the correct way to calculate the separation surface, but from this point I can not go further: how do I solve the integral? Or can I use some trick?

Btw: sorry for the clumsy format, but I canâ€™t LateX

Thanks!

Steven

If this is the wrong sub-forum, please let me know

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# Homework Help: Fluid mechanics: Separation surface of a source in a parallel flow (3D)

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