Let the density of the fluid be 
and the density of the sphere be 
and let the viscosity of the fluid be 
. Let the terminal velocity of the sphere in the fluid be v.As the sphere falls through the fluid there are three forces acting on it, i) the force of gravity
, ii) the buoyant force due to the fluid 
and iii) the viscous force due to fluid on the sphere is given by 
. Since the body is moving at terminal velocity and there is no acceleration, all these forces must cancel out. Hence, we have,
The Reynold's number for a sphere moving in fluid is given by,
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