The following are the model for Dynamics of 3 tanks in series Tanks 1 dC_1/dt =

Question

The following are the model for Dynamics of 3 tanks in series Tanks 1 dC_1/dt = 1/tau (C_0 - C_1) Tank 2 dC_2/dt = 1/tau(C_1 - C_2) Tank 3 dC_3/dt = 1/tau (C_2 - C_3) Where C_1, C_2 and C_3 are the concentration in tank1, tank2, and tank 3, respectively. C_0 = 0.1, time constant tau=10 minute. Get the concentration profile of tanks for time span 0 to 50 minute by solving above system of ODE using solver ode45. Analytical solution of tank 1 concentration is C_1 = C_0 (1 - e^-t/tau) Plot tank 1 concentration (Analytical & numerical) to compare the results.

Explanation / Answer

Let us assume that the Tank1, Tank 2 and Tank3 as A1,A2 and A3 respectively. Then the solution of the problem will be as follows:

Equations A1-A3 are solved for pulse input of tracer, andthen eq A1 becomes

C1/C0=e-t/t1   and let this be A4.

The A4 value is substituted into eq A2, and the solution canbe written as:

C2/C0 = 1/t2(1/t2 - 1/t1) (e-t/t1-e-t/t2) as A5

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