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Problem 3 We wish to represent flow through the sketched constriction in an otherwise straight, parallel wall, two-dimensional channel of height Y. Flow through the channel is inviscid, incompressible and uniform far upstream with velocity V One way to study this problem is to introduce a concentrated vortex (vortex point) at a height Y above the lower wall. n) Write a formula for the streami function ψ of the flow: the formula must be written in Cartesian is constant at the coordinate system with point A (see the figure) as the orig Check that lower wall. b) Find the strength Γ needed for a given constriction height l. c) Find the velocities at points A and B. Which one is higher? d) Is the flow irrotational everywhere? Why? Problem 3 We wish to represent flow through the sketched constriction in an otherwise straight, parallel wall, two-dimensional channel of height Y. Flow through the channel is inviscid, incompressible and uniform far upstream with velocity V One way to study this problem is to introduce a concentrated vortex (vortex point) at a height Y above the lower wall. n) Write a formula for the streami function ψ of the flow: the formula must be written in Cartesian is constant at the coordinate system with point A (see the figure) as the orig Check that lower wall. b) Find the strength Γ needed for a given constriction height l. c) Find the velocities at points A and B. Which one is higher? d) Is the flow irrotational everywhere? Why?
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