Question

the viscousity force f going against the movement of a spere

Answer 1

This depends somewhat on the fluid, and on the velocity of the body to determine the type of flow over the surface.

However, for many applications (air or water for example)

The 'drag force' is given by

\[F _{d}=C _{d}\frac{ 1 }{ 2 } \rho AV ^{2}\]

Where Cd is drag coefficient, rho is density of fluid ,V is velocity, and A is area of body (typically cross section in direction of travel)

For a sphere Cd is typically around 0.5 - 1

Answer 2

I think you mean resistive force
\[F= C _{1}r v + C _{2}r ^{2} v ^{2}.\]
C1 viscous term.
C2 pressure term.
r radius of the ball
v velocity of the sphere.
And I think your question means to use the viscous term and ignore pressure term.

Answer 3

Yes - I agree I have given the wrong equations above. My apologies.

Viscosity can be measured with a 'falling ball viscometer' which is based on the viscous resistance to a spherical ball falling through the fluid.

I don't know the theory of these.

http://en.wikipedia.org/wiki/Viscometer