= 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)
= 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)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please help solve this problem
Transcribed Image Text:=
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)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 21 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
