# Tough Integration Problem involving flow from a tank

1. Oct 17, 2004

### alonzo

Please help!!! This problem is really complex and i have no idea where to start (or finish for that matter!!!!!)
A holding tank of 7000 litres is full of water which has been contaminated by a pollutant. The tank contains 0.01 percent contaminant by volume. Water with a contaminant concentration of 0.001 percent now flows from a river into the tank at a rate of 5 litres per minute. Since the tank is full, there is an overflow of water into a nearby lake.

1) What is the concentration of contaminant in the tank after 5 hours?

2) The farmer who owns the tank claims that the contents of the tank is under the legislated upper concentration limitation of 0.002 percent for the contaminant. If the inflow has been running for 4 hours, is the farmer's claim correct?

3) What is the volume of contaminant that has overflowed into the nearby lake after four hours?

Thanks 4 ur help!

2. Oct 17, 2004

### Tide

Define the concentration of the water in the tank as amount of contaminant divided the volume (contaminant plus water).

If R is the rate (liters per minute) at which contaminated water of concentration $C_{in}[/tex] enters the tank then the concentration of water in the tank is $$C = C_{0}e^{-Rt/V} + \left(1 - e^{-R t / V} \right) C_{in}$$ where [itex]C_0$ is the initial concentration of the contaminant in the tank and V is the volume of the tank.

This assumes that the contaminant becomes uniformly distributed throughout the tank immediately after it enters the tank. This may or may not be a good assumption in your particular case since you haven't identified what the contaminant is.

That should get you started!

Last edited: Oct 17, 2004