Differential Equations with Boundary-Value Problems
9th Edition
ISBN: 9781337632515
Author: Dennis G. Zill
Publisher: Cengage Learning US
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Textbook Question
Chapter 3.1, Problem 28E
In Example 5 the size of the tank containing the salt mixture was not given. Suppose, as in the discussion following Example 5, that the rate at which brine is pumped into the tank is 3 gal/min but that the well-stirred solution is pumped out at a rate of 2 gal/min. It stands to reason that since brine is accumulating in the tank at the rate of 1 gal/min, any finite tank must eventually overflow. Now suppose that the tank has an open top and has a total capacity of 400 gallons.
- (a) When will the tank overflow?
- (b) What will be the number of pounds of salt in the tank at the instant it overflows?
- (c) Assume that although the tank is overflowing, brine solution continues to be pumped in at a rate of 3 gal/min and the well-stirred solution continues to be pumped out at a rate of 2 gal/min. Devise a method for determining the number of pounds of salt in the tank at t =150 minutes.
- (d) Determine the number of pounds of salt in the tank as t → ∞ Does your answer agree with your intuition?
- (e) Use a graphing utility to plot the graph of A(t) on the interval [0, 500).
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Chapter 3 Solutions
Differential Equations with Boundary-Value Problems
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