Let F( 1r) denote the complex potemi al function for the

Chapter 0, Problem 11.22

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Let F( 1r) denote the complex potemi al function for the flow of an uid over a step in the bed of a deep stream represented by the shaded region of the u plane in fig. 29. Appendix 2. where the fluid velocity \I approaches a real constant \10 ;1" lrrl tends to infinity in that region. The transformation that maps the upper half of the::: plane onto the region is noted in Exercise 3. Csc the chain rule clF dF cl: clu cl: clwand. in terms of the points:: = x \Vhose images arc the points along the bed of the stream.show thatWI= IVi1I \/ 1 __ \. - 'I . I x +I~ote that the speed increases from I Vo I along A' B' unti I IV I = x al B '. then diminishesto zero al C'. and increases toward I Vol from C' to D': note. t