Program Explanation Given information: The height of the cylindrical tank is 5 ft . The radius of the tank is 3 ft and the radius of the bottom hole is 1 in . The tank contains half of the liquid initially. Calculation: The given problem is of draining 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 = − a 2 g y ........ (1) Here, A ( y ) is the horizontal cross sectional area of the tank and a is the area of the hole and the value of g = 32 ft/s 2 . In the given problem A ( y ) = A is constant for every height. The area of the hole a can be calculated as, a = π ( 1 12 ) 2 a = π 144 Therefore, the equation can be written as, A ( y ) d y d t = − a 2 g y A ( y ) d y d t = − π 18 18 Assume z denotes the distance from the center of the cylinder down to the fluid surface. Therefore, the horizontal cross sectional area of the tank A ( y ) = A can be calculated as, A = 10 ( 9 − z 2 ) 1 2 The value of y = 3.2

5th Edition

ISBN: 9780135962176

Author: Edwards

Publisher: PEARSON CO

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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 60P

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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 59P

Chapter 1.4, Problem 61P

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Chapter 1 Solutions

EP DIFFERENTIAL EQUATIONS+..-MYLAB ACCE

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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. The horizontal cross sectional area of the tank is constant for every height.

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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