A liquid forms a free vortex around a drain as shown in Figure 5.74. If the depth of liquid at a distance, r0, from the drain is h0, determine an expression for the depth, h, of the liquid as a...

A liquid forms a free vortex around a drain as shown in Figure 5.74. If the depth of liquid at a distance, r0, from the drain is h0, determine an expression for the depth, h, of the liquid as a function of the distance, r, from the drain. Your final result should be in terms of the strength Γ of the vortex. Assume steady flow.