Velocity field around a sphere

Due to the symmetry of a moving sphere of radius R, the velocity v of the fluid only depends on the distance variable r (the origin of the coordinate system is taken at the center of the sphere) and on the velocity of the sphere U, and so does the vector A. The only axial vector that can be obtained with rand U is the vectorial product 

The quantity g(r)n also can be written in the form of V/(r). Then g(r) is the derivative of/(r) with respect to r and curl A in eq 1.43 can be expressed more simply with help of the relation 

After some algebra in spherical coordinates, integration of this equation and taking into account the fact that w = 0 at large distance leads to 

Substituting this expression into eq 1.46 and using the no-slip condition on the sphere leads to the components of v 

55 (and r R) show that v.k 0, meaning that the fluid is everywhere moved in the direction of U. 

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