Let a spherical object move through a fluid in R3. For slow velocities, assume Stokes’ equations apply. Take the point of view that the object is stationary and the fluid streams by. The setup for the boundary value problem is as follows: given U = (U, 0, 0), U constant, find u and p such that Stokes’ equation holds in the region exterior to a sphere of radius R, u = 0 on the boundary of the sphere and u = U at infinity.
The solution to this problem (in spherical coordinates centered in the object) is called Stokes’ Flow:
where p0 is constant and n = r/r .
(a) Verify this solution.
(b) Show that the drag is 6πRνU and there is no lift.
If someone can help it would be great.
The Attempt at a Solution
a) [/B]I started using the stokes equations but couldn't get there.