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: 8220100802454

Author: Calvis

Publisher: PEARSON

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Heuristic System

The term heuristic is derived from the Greek word heurisko, which means “I find, discover”. Heuristics can be mental shortcuts or approaches designed from previous experiences. The main aim of the heuristic approach is to find a good enough solution to s…

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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

Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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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