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Source (sink) flow

Potential function for 2D source of strength m at r = 0:

It satisfies (check Laplace's equation in polar coordinate in the keyword search utility), except at (so must exclude r = 0 from flow)

1.
Question: Derive the equations for the velocity field for the 2D source.

(a)
Hint: expression for the gradient in polar coordinates (use the keyword utility: coordinate system - velocity vector)

2.
Question: Evaluate the outward volume flux.

(a)
Hint: Consider a contour which contains the 2D source.

(b)
Hint: Use Gauss theorem to deform the contour into a small circle of radius around the source.

(c)
Hint: Evaluate the flux in the direction normal to the circle (radial velocity) and integrate along the circle.

If sink. Source with strength located at :

3D source - Spherical coordinates

A spherically symmetric solution: (verify except at )

Define 3D source of strength located at :

1.
Question: Evaluate the net outward volume flux.

Keyword Search

Next: Solution: Equations for the Up: 3.7 - Simple Potential Previous: Uniform Stream