Flow in a Closed Channel

The flow inside the closed channel of width given by , is given by

Thus, the differential equations for the streamlines are

We immediately notice that we can eliminate the variable from these equations. Indeed, dividing the second by the first, we see that

This results in a separable differential equation for ; separating the variables, we find

which has the solution

where is a constant of integration.

We can plot the resulting family of streamlines and equipotential curves.