# Buoyancy in muddy water

Consider the buoyancy force in water with very small but macroscopic particles in it. Such particles (suspension) will very slowly drift downwards and will eventually settle on the bottom. If one did not know that the particles are present there then for calculating the buoyancy force, $F = \rho V g$, one would just use the average density of water with suspended particles in it, which is larger than the density of pure water. Would this be a correct calculation?

Suppose we do an experiment with a cylindrical vessel filled with water and a fully submerged float in it, attached to the bottom with a cord, and then we drop some amount of very fine powder into the water. The powder will form a cloud that will slowly drift downward. What would be the observable effect (if any) on the tension in the cord, once the cloud of particles fully covers the float? Assume that the cloud transverse size is large enough to fully cover the cross-section of the vessel.

-
add comment

## 1 Answer

I would think the tension force will increase, as the average liquid density has increased. Note, for example, that the water pressure on the bottom will increase more than it would be if the same volume of water is added. The particles move downwards with a constant speed, so their full weight acts on the water (until they are on the bottom).

-
But the particles will bombard the upper side of the float, so there is a downward force from that, correct? Maybe that is the dominant effect and the tension force will decrease? –  Maxim Umansky Jul 12 '13 at 5:06
I don't think there is any 'bombarding' going on. For that to happen you need inertia which, for these slowly settling particles, will be completely absent due to dominant viscous effects. –  Michiel Jul 12 '13 at 6:03
add comment