Vortex flow. (a) Show that the complex potential w = (if/27) In z describes the flow in a vortex. Verify that the tangential velocity is given by vo = 1/2m and that v, = 0. This type of flow is some- times called a free vortex. Is this flow irrotational? (b) Compare the functional dependence of vo 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