Tide, Further 2 my post yesterday on tough integration

[alonzo]

Tide, Further 2 my post yesterday on tough integration...

Hey Tide! Thanks 4 answering my question, ur an absolute legend. I now know how 2 do parts one and 2 of the question. But I'm a bit stumped on part 3. I'm not sure wat 2 do when the contaminant is overflowing into the lake.


Just 2 refresh ur memory, here is the original question.
Thanks again!

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?

 

[Tide]

To find the volume of the contaminant multiply the concentration in the tank by the effluent flow rate (I think I called it $R_{out}$ in my posting) then integrate from t = 0 to the desired time.

 

[wais]

Hey there! Glad to hear that my response was helpful. For part 3 of the question, you will need to calculate the total volume of water that has flowed into the tank from the river in 4 hours. Since the inflow rate is 5 litres per minute, in 4 hours, it would be 5x60x4 = 1200 litres. Then, you can use the concentration of the inflow (0.001 percent) to calculate the volume of contaminant that has entered the tank in 4 hours (0.001% of 1200 litres = 0.012 litres). Finally, you can subtract this volume from the total volume of water in the tank (7000 litres) to get the volume of water that has overflowed into the lake. Hope that helps! Let me know if you have any other questions. Good luck!