Suppose a tank is filled initially (at time t = 0) with 100 gallons of fresh clean water. Water containing 10 grams/gallon of chemical pollutants enters the tank at a rate of 2 gallons/day, and the mixture in the well-stirred tank leaves the tank at the rate of 1 gallon/day. (a) Find the amount of water W (t) as a function of time and deter- mine the time when that amount reaches 200 gallons. In order to do this, either set up a very easy ODE for W(t) or use your intuition about the problem. (b) Write down the differential equation that describes the total amount of pollutants P(t) in the tank and find the initial con- dition P(0) of this quantity at time t 0. Again, think in terms of rate in minus rate out. = (c) Find the total amount of pollutants in the tank at the time you determined in (a)
Suppose a tank is filled initially (at time t = 0) with 100 gallons of fresh clean water. Water containing 10 grams/gallon of chemical pollutants enters the tank at a rate of 2 gallons/day, and the mixture in the well-stirred tank leaves the tank at the rate of 1 gallon/day. (a) Find the amount of water W (t) as a function of time and deter- mine the time when that amount reaches 200 gallons. In order to do this, either set up a very easy ODE for W(t) or use your intuition about the problem. (b) Write down the differential equation that describes the total amount of pollutants P(t) in the tank and find the initial con- dition P(0) of this quantity at time t 0. Again, think in terms of rate in minus rate out. = (c) Find the total amount of pollutants in the tank at the time you determined in (a)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose a tank is filled initially (at time t
fresh clean water.
0) with 100 gallons of
Water containing 10 grams/gallon of chemical pollutants enters the
tank at a rate of 2 gallons/day, and the mixture in the well-stirred
tank leaves the tank at the rate of 1 gallon/day.
(a) Find the amount of water W(t) as a function of time and deter-
mine the time when that amount reaches 200 gallons. In order
to do this, either set up a very easy ODE for W (t) or use your
intuition about the problem.
(b) Write down the differential equation that describes the total
amount of pollutants P(t) in the tank and find the initial con-
dition P(0) of this quantity at time t = 0. Again, think in terms
of rate in minus rate out.
(c) Find the total amount of pollutants in the tank at the time you
determined in (a)
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