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Math · Advanced Math
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3. Two tanks of different volumes are horizontally connected by a pipe. Tank A is a 100-litre tank with lid initially full of water containing salt at a concentration of 0.5g/litre. Tank B is a 120-litre tank without lid, initially full of pure water. Starting at time 0, water containing salt at concentration of Se g/litre is pumped into tank A from an outside source at 4litre/hr. Water is piped out from this tank into tank B at 4litre/hr. Water evaporates from the tank B at litre/hr. Water is also pumped out of tank B and then down a drain at a rate of 3litre/hr (a) Use the information given in the paragraph to draw a diagram explaining the mixing problem. 3 marks) Construct a system of differential equation describing the rate of change of amount of salt in tanks A and B (b) (4 marks) (c) Using Laplace transform, find the amount of salt in each tanks as a function of time. (11 marks) d) What is the concentration of the salt in tank A after a long time? (2 marks)
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