An example of a non-useful control volume would be the left half of the tank---how would one calculate the flux from left to right across the center of the tank?

From Hemond and Fechner, 1994.

In this derivation, we have assumed that each particle settles independently---that is, we have assumed ``discrete settling.'' In systems of very high particle concentration, this assumption is sometimes not valid, as you will find when you study flocculation in CE352.

The pressure force is really a gravitational force also, because it results from the weight of material above the subsurface water.