An axisymmetric stagnation flow results from directing a circular stream perpendicular to a planar surface, which deflects

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An axisymmetric stagnation flow results from directing a circular stream perpendicular to a planar surface, which deflects the fluid outward radially. Suppose that the surface is at z = 0, and the approaching flow is in the –z direction.

(a) Show that the velocity field

where C is any positive constant and vθ = 0, is irrotational.

(b) Determine

(c) Confirm that this velocity and pressure satisfy the full Navier–Stokes equation.

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