Program Explanation Given information: The tank contains 12 ft water initially at 12 noon and then after one hour the water is dropped to 6 ft . Calculation: The given problem is of training tank. The Toricelli’s law is used for a draining tank. The Toricelli’s law can be represented as, A ( y ) d y d t = − k y ........ (1) Here, A ( y ) is the horizontal cross sectional area of the cone and k is constant. The cross sections of the tank are circles. The height is y 0 ft and the radius is x 0 ≥ 0 such that y 0 = x 0 4 3 . Therefore, the radius of the tank can be calculated as, y 0 3 4 = x 0 Therefore, the value of A ( y ) = A can be calculated as, A ( y 0 ) = π x 0 2 = π y 0 3 2 Now define the function as, A ( y ) = π y 3 2 Now substitute π y 3 2 for A ( y ) in equation (1) as, π y 3 2 d y d t = − k y ........(2) Now use the method of separation of the variable to solve the equation (1). π y 3 2 d y d t = − k y π y 3 2 y d y d t = − k π y d y = − k d t Now integrate both sides. π ∫ y d y = ∫ − k d t π y 2 2 = − k t + c y 2 = − 2 π k t + c Therefore, the resultant equation is as follows, π 2 y 2 = − k t + c

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 1.4, Problem 58P

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Program Description: Purpose of the problem is to find the time when the tank goes to empty.

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Chapter 1.4, Problem 57P

Chapter 1.4, Problem 59P

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Chapter 1 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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Program Description: Purpose of the problem is to find the time when the tank goes to empty.

Solution Summary: The author explains how the Toricelli's law is used for a draining tank.

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Program Description: Purpose of the problem is to find the time when the tank goes to empty.

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Chapter 1 Solutions