Shell balance

In fluid mechanics, it may be necessary to determine how a fluid velocity changes across the flow. This can be done with a shell balance.

A shell is a differential element of the flow. By looking at the momentum and forces on one small portion, it is possible to integrate over the flow to see the larger picture of the flow as a whole. The balance is determining what goes into and out of the shell. Momentum enters and leaves the shell through fluid entering and leaving the shell and through shear stress. In addition, there are pressure and gravity forces on the shell. The goal of a shell balance is to determine the velocity profile of the flow. The velocity profile is an equation to calculate the velocity based on a specific location in the flow. From this, it is possible to find a velocity for any point across the flow.