(adsbygoogle = window.adsbygoogle || []).push({}); 1. Suppose that three tanks in series, connected by pipes of the same size are filled with water that is moved through the system with pumps at the rate of 5 gal/min. The first tank is 1000 gal. The second tank is 750 gal. And the third tank is 500 gal. The contents of each tank is vigorously stirred. The in-feed to Tank 1 is a constant flow of water in the same sized pipe from an external source at the same flow rate and the outflow from Tank 3 flows into a lake at the same flow rate. [Dye is added to the inflow at a constant rate for exactly one minute per hour over a long period of time (weeks, months,whatever)]

What is the concentration of the dye RELATIVE to its input concentration as a function of time over a 10-hour period after the "long-time" has passed.

Do you have to make further assumptions to solve the problem?

How do you deal with the "relative" concentration?

2. Okay so obviously this is a conservation of mass problem, so flow in - flow out = 0

3. I have drawn an accurate picture, and I have set up what I believe to be the correct system of equations:

x_{1}' = (Q_{s}A - Q_{12}x_{1})*1/V_{1}

x_{2}' = (Q_{12}x_{1}- Q_{23}x_{2})*1/V_{2}

x_{3}' = (Q_{23}x_{2}- Q_{3L}x_{3})*1/V_{3}

Where:

x_{1}= Concentration in Tank 1, so on for x_{2}and x_{3}

A = Entrance rate of substance with units kg*t/v

Q_{1}= rate at which the substance is transported by water flow (same throughout)

V_{1}= Volume of tank 1, so on for V_{2}, V_{3}.

Whatever you guys know what this stuff means these are straight forward normally but this one is throwing me off bad. I don't know if my system is right or what to solve I've been working on it and the rest of a huge problem set for too long.

It is due tomorrow morning. Please help.

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# Homework Help: Conservation of mass/flow through tanks

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