Consider a source of flow in \(3 \mathrm{D}\) of strength \(S\) (dimensions \(L^{3} / T\) ), Then the flow is axisymmetric and independent of the \(\theta\)-direction in the spherical coordinate system. Show by a mass balance that

\[S=4 \pi r^{2} v_{r}\]

and hence derive Eq. (15.41) for the potential due to a unit source in 3D.

Transcribed Image Text:

1 K(x,) = (15.41) 4rex