Question

2. Water flows over a flat surface at 8 m/s, as shown in figure. A pump draws off water through a narrow slit at a volume rate of 0.2 m2/s per meter length of the slit. Assume that the fluid is incompressible and inviscid and can be represented by the combination of a uniform flow and a sink. a) Based on method of superposition, propose a general expression for stream function ψ velocity potential ф, and velocity components of v, and vo ii. for flow field in figure. Given that r is the radius from the centre of slit, Uis the upstream velocity θ is the angle measured from x axes, and m in the strength of sink. Find the location of point A which is the stagnation point on the wall. (Note that a source strength of 04 m2/s must be used to obtain 0.2 m?/s through slit which is only one half of a "full" sink.) b) c) Determine the minimum distance H from the flat surface so that the water does not get sucked into the slit.

Answer 1

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