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 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

Question: 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

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.

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