Program Explanation Given information: The vertical tank contains 9 ft water initially. The radius of the tank is 3 ft and the radius of the bottom hole is 1 in . 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 2 ) 2 a = π 144 The horizontal cross sectional area of the tank A ( y ) = A can be calculated as, A = π ( 3 ) 2 A = 9 π Now substitute 32 for g , π 144 for a and 9 π for A in equation (1) as, 9 π d y d t = − π 144 2 ⋅ 32 y 9 π d y d t = − π 144 8 y d y d t = − 1 162 y Now use the method of separation of the variable in above differential equation. d y y = − d t 162 Now integrate both sides

5th Edition

ISBN: 9780135904206

Author: Edwards

Publisher: PEARSON

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Chapter 1.4, Problem 55P

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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 54P

Chapter 1.4, Problem 56P

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Chapter 1 Solutions

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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