= (a) Show that F(z) = (c/21)ln(z) gives a flow directed radially outward, as shown in Figure 1, so that F models a poin

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A Show That F Z C 21 Ln Z Gives A Flow Directed Radially Outward As Shown In Figure 1 So That F Models A Poin 1 (151.02 KiB) Viewed 80 times

= (a) Show that F(z) = (c/21)ln(z) gives a flow directed radially outward, as shown in Figure 1, so that F models a point source at z = 0 (that is, a source line x = 0, y = 0 in space) at which fluid is produced, if the strength or discharge of the source, c, is constant, positive, and real. Also show that, if c is constant, negative, and real, that the flow is directed radially inward, so that F models a sink at z = 0, a point at which fluid disappears. Note z=0 is the singular point of F(z) [10 points). Figure 1 Figure 2 = (b) Show that F(z) = (-Ki/21)n(z) gives a flow circulating counterclockwise around z=0, as shown in Figure 2, where z = 0 is a vortex, when K is both real and positive. Note that each time we travel around the vortex, the potential increases by K [10 points). =