Consider steady potential flow around a sphere of radius R. The velocity far from the sphere is…

/in /by

Consider steady potential flow around a sphere of radius R. The velocity far from the sphere is given by v=Uez.a)Write the governing equation and the boundary conditions in terms of the potential.b)Give reasons why the velocity potential can be postulated to be of the form f(r,?)=f(r)cos?.

c)Using the trial expression for the velocity potential in part (b), find the solution for the f(r) and also the potential using Laplace’s equation.

d)Find the solution for the pressure distribution in the fluid, definingpe)Calculate the net force on the sphere resulting from the pressure. Doesd’Alembert’s paradox result? (Hint: it is easiest to answer this question by dotting the pressure force withe2, which gives the resultant force in the direction of flow)

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