Hello thereddevilsIn a small time , the sphere moves a distance .We now assume that a volume of fluid proportional to the surface area of the sphere multiplied by the distance has its velocity changed from zero to the velocity, , of the sphere, due to impact with the sphere's surface. Since the SA of the sphere is proportional to the square of its radius, the mass of fluid affected in time is therefore equal to

where is the density of the fluid, and is a constant.

Its change in momentum is therefore

Therefore, using Newton's Second and Third Laws, the force that this mass of fluid exerts on the sphere is equal to the rate of change of its momentum; i.e.

As . So the force on the sphere is therefore

Grandad