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Lake Pollution Solutions
In this part of the module, we will look at solutions for the differential equation
that gives a mathematical model for the concentration of contamination
in a lake. The volume V of water in the lake is assumed to be
constant. The contaminant is carried into the lake by an incoming flow
of water at a rate Q (volume per time unit) and with a concentration
(mass per unit of volume). There is a corresponding
outflow at rate Q from the lake, and this outflow has the same
concentration C of contaminant as the lake (as is the case for a
well-mixed lake). C and
will depend on time, in
general. We allow for a chemical reaction, with rate constant k, in
which the contaminant in the lake decay into other substances that
are of no concern. For more details on the assumptions behind this
equation and the derivation of the terms, please go
back to the previous screen and
choose one of the explanatory options.
Here are some scenarios for what happens in the lake, together with the choices you should make in the following screens in order to simulate each one. Choose "No Reaction [k(t)=0]" if the decay reaction is negligible, and choose "First Order Constant Reaction [k(t)=k, for k constant]" if you would like to have the option of choosing a rate constant in your simulations.