Question

Problem 3 We wish to represent flow through the sketched constriction in an otherwise straight, parallel- wall two diniensional channel of henght y Flow through the channel is mvistid, intorn ressible and uniform far upstream with velocity VOne way to study this problem is to introduce a concentrated vortex (vortex point) at a height Y above the lower wall la a) Write a formula for the stream function of the flow; the formula must be written in Cartesian coordinate system with point A (sce the figure) as the origin. Check that is constant at the lower wall. b) Find the strength I needed for a given constriction height H c) Find the velocities at points A and B. Which one is higher? d) Is the flow irrotational everywhere? Why?

Answer 1

Given data:L Chonnel 04 hefô h ty-flow . In Viscid , İn@mWunble and 一(wo.dtmenSJonal hetsht MCEn

NLn unction nd ^he Srnth neded a iven a Jivev)

ohere V2 o fncl one iher he a end b ave he a and 2-7

lpnce the above eauadion becony 84 y-y