Suppose we have a tank that initially contains 10 litres of brine in which there is dissolved 1 kg of salt. Brine containing 0.5 kg of dissolved salt per litre is pumped into the tank at a rate of 6 litres/min. The solution is well stirred and pumped out at a slower rate of 3 litres/min.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Suppose we have a tank that initially contains 10 litres of brine in which there is dissolved
1 kg of salt. Brine containing 0.5 kg of dissolved salt per litre is pumped into the tank
at a rate of 6 litres/min. The solution is well stirred and pumped out at a slower rate
of 3 litres/min.
a) Write down the differential equation that could describe the amount of salt X(t) in
the tank.
b) How much salt is in the tank at any time t > 0? i.e. solve the IVP you have found
in part (a).

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