Vortex flow (a) Show that the complex potential w (iT 2) in z describes the flow in a vortex Verify that the tangential velocity is given by v T 2 and that v r 0 This type of flow is sometimes called a free vortex (b) Compare the functional dependence of v on r in (a) with that which arose in Examp...

dw dz Vortex flow a By using Eq 4312 we find that Vx 1 Z xiy 4040 y ir in ...

Vortex flow (a) Show that the complex potential w = (iT/2) in z describes the flow in

Question:

Vortex flow

(a) Show that the complex potential w = (iT/2π) in z describes the flow in a vortex. Verify that the tangential velocity is given by v_θ = T/2ππ and that v_r = 0. This type of flow is sometimes called a free vortex.

(b) Compare the functional dependence of v_θ on r in (a) with that which arose in Example 3.6-4 the latter kind of flow is sometimes called a forced vortex. Actual vortices, such as those that occur in a stirred tank, have a behavior intermediate between these two idealizations.