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.

- Solution: Equations for the velocity field for the 2D source.
- Solution: Net outward volume flux for 2D sorce.
- Solution: Net outward flux for a 3D source.