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Preventing influx of salt.

Suppose the lake is in a hyper-saline situation with a near maximal head difference between the lake and the sea. Then any compensation releases would simply be absorbed by the lake without changing the direction of the sea to lake flow. In this case we can calculate the amount of salt prevented from entering the system by a release of volume tex2html_wrap_inline3407.

In this case we have Sea to Lake flow. Unfortunately we cannot assume we are operating beyond the effect of any transients, as the sudden release of water creates a transient, followed by another transient when the release ceases.

The full salt load equation from (60) is...
equation1467

Now there are three phases in this problem...

  1. Assume immediately prior to time t=0 the system is in steady state. ie. tex2html_wrap_inline3411
  2. At time t=0 water is released at rate tex2html_wrap_inline3415 until time tex2html_wrap_inline3417. During this phase the water level in the lake rises towards the new asymptotic level tex2html_wrap_inline3419.
  3. At time tex2html_wrap_inline3417 the flow rate returns to I, and the lake level drops towards the original level.

So at time t=0, V(0) = A(I/k+L), and tex2html_wrap_inline3427.

At time tex2html_wrap_inline3417,
equation1469

Now we can calculate the load at a time after the release has finished...
equation1471

We need the volume at time tex2html_wrap_inline3225 from equation (54)...
eqnarray1473

Substituting for the known values at time tex2html_wrap_inline3225...
eqnarray1475

Now we wish to know the full effect of the release, so for t large enough...
equation1477

Comparing this with what the load would have been without a release we have...
equation1479

Which is interesting in both its simplicity, and the total lack of effect of the transients.


John Carter
Tue Jun 17 09:50:07 SAT 1997