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# Mathematical modeling using linear first order equations

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Two tanks each hold 3 liters of salt water and are connected by two pipes (see figure below) the salt water in each tank is kept well stirred. Pure water flows into tank A at a rate of 5 liters per minute and the salt mixture exits tank B at the same rate.
Salt water flows from tank A to tank B at the rate of 9 liters per minute and flows from tank B to tank A at the rate of 4 liters per minute. If tank A initially contains 1 Kg of salt and tank B contains no salt, find the quantities of salt in tank A and tank B respectively, at any time t &#8805; 0.

See attached file for full problem description with symbols and diagram.

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#### Solution Preview

Please see the attached file.

Let CA and CB be the concentration of salt in tank A and B (kg of salt/L)
Initial Volume of tank VA = VB = 3 (liters)
Perform material balance for each tank:
Rate of change of material = Rate of mass in - Rate of mass out
Tank A:
Tank B:
Equipped with the two differential ...

#### Solution Summary

The solution provides very detailed theory for developing governing equations of continuous flow stirred tank reactors. It then provides explanations and calculations for the final answer in a 3-page Word document.

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