So I have this 1000 gallon tank with 500 gallons in it. In the water there is 50 lb of particulate matter.
At time = 0, pure water is added at 20gal/min and mixed solution is drained at 10gal/min.
I need to find out how much particulate matter is in the tank when it reaches overflowing.
Since water is flowing in at 20 and going out at 10, that's a net fill rate of 10. So since I have 500 gallons to fill, that should take me 50 mins.
Since the water is pure, my rate in looks like this:
20 gal/min * 0lbs/gal = 0 lbs/gal
Rate out:
10gal/min * ylbs/500gal = ylbs/50mins
Therefore:
dy/dt = 0 - y/50
dy/dt + y/50 = 0.
p(t) = 1/50, P(t) = t/50, q(t) = 0, u(t) = e^(t/50)
After doing the differential equation, I get 18.4 lbs.
However, the book says the answer should be 25 lbs.
Is my setup correct?
I end up with y(t) = 50e^(-t/50)
At time = 0, pure water is added at 20gal/min and mixed solution is drained at 10gal/min.
I need to find out how much particulate matter is in the tank when it reaches overflowing.
Since water is flowing in at 20 and going out at 10, that's a net fill rate of 10. So since I have 500 gallons to fill, that should take me 50 mins.
Since the water is pure, my rate in looks like this:
20 gal/min * 0lbs/gal = 0 lbs/gal
Rate out:
10gal/min * ylbs/500gal = ylbs/50mins
Therefore:
dy/dt = 0 - y/50
dy/dt + y/50 = 0.
p(t) = 1/50, P(t) = t/50, q(t) = 0, u(t) = e^(t/50)
After doing the differential equation, I get 18.4 lbs.
However, the book says the answer should be 25 lbs.
Is my setup correct?
I end up with y(t) = 50e^(-t/50)