Lake to sea flow.

Assume that for the period of calculation the flow is from lake to sea only then..

Dividing through by S/dt and integrating...

Substituting in V(t) and evaluating the integral and simplifying...

Where K is a constant of integration. Now we need to find K in terms of the amount of salt in the system at time t=0.

Therefore K is...

Thus finally we have...

Load for lake to sea flow.

This comprises physically speaking of three parts...

1. The initial load in the system.
2. The load moved by any change in volume of the system.
3. And an exponential decay. In this case the effect of the initial salt load fades exponentially.

We see again that the load depends very weakly on the estuary constant k. The major effect here is the term which basically says the load of salt decreases exponentially at a decay rate equal to the in flow divided by the lake volume. Thus again we can say, in this model, ``Potter's channel'' would have very little effect.