3) Two tanks are connected in series, one flowing into the other (see picture).

Question

3) Two tanks are connected in series, one flowing into the other (see picture). The first tank initially contains 100l of pure water . A salt solution is pumped into the tank at 5 l/min with a concentration of Co 9/l. Let the concentration of salt in tank 1 be C1. The salt solution in tank 1 is pumped into tank 2 at 5l/min. Tank 2 intially contains 200 l of water and 1000 g of salt. Let the concentration of salt in tank 2 be C2. Liquid leaves tank 2 at 5l/min. set up two differential equations to describe the concentration of salt in each of two tanks at time t, and determine the initial conditions. Extra credit - Assuming Co is constant find C1 and C2 as a function of time.

Explanation / Answer

For tank 1,

rate of change of salt mass in tank=rate of salt coming in-rate of salt going out

dm1/dt=5C0 g/min -5C1 g/min

Dividing by volume of tank,

dC1/dt=0.05C0-0.05C1

Initial condition is C1(0)=0 (since it is pure water initially).

Doing the same balance for the second tank,

dm2/dt=5C1-5C2

Dividing by volume of tank 2,

dC2/dt=0.025C1-0.025C2

Initial condition is C2(0)=1000/200=5g/L

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