Paper 1, Section II, A
Consider inviscid, incompressible fluid flow confined to the plane. The fluid has density , and gravity can be neglected. Using the conservation of volume flux, determine the velocity potential of a point source of strength , in terms of the distance from the source.
Two point sources each of strength are located at and . Find the velocity potential of the flow.
Show that the flow in the region is equivalent to the flow due to a source at and a fixed boundary at
Find the pressure on the boundary and hence determine the force on the boundary.
[Hint: you may find the substitution useful for the calculation of the pressure.]
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