Oscillating Inflow Concentration
Not what you're looking for?
Oscillating Inflow Concentration
A tank initially contains 10 lb of salt dissolved in 200 gallons of water. Assume that a salt solution flows into the tank at a rate of 3 gal/min and the well-stirred mixture flows out at the same rate. Assume that the inflow concentration oscillates I n time, however, and is given by ci(t) = 0.2(1 + sin t) lb of salt per gallon. Thus, as time evolves, the concentration oscillates back and forth between 0 and 0.4 lb of salt per gallon.
(a) Make a conjecture, on the basis of physical reasoning, as to whether you expect the amount of salt in the tank to reach a constant equilibrium value as time increases. In other words, will lim Q(t) exist?
(b) Formulate the corresponding initial value problem.
(c) Solve the initial value problem.
(d) Plot Q(t) versus t. How does the amount of salt in the tank vary as time becomes increasingly large? Is this behavior consistent with your intuition?
Purchase this Solution
Solution Summary
The oscillating inflow for concentration is determined.
Solution Preview
See word file for answer.
Note: I leave the graphing portion of the answer to you and I ask that you include in your answer the calculation involving integration by parts.
Oscillating Inflow Concentration A tank initially contains 10 lb of salt dissolved in 200 gallons of water. Assume that a salt solution flows into the tank at a rate of 3 gal/min and the well-stirred mixture flows out at the same rate. Assume that the inflow concentration oscillates in time, ...
Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts