Program Explanation Given information: The cylindrical tank contains V 0 gallons of water in T minutes. Proof: 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. In the given problem A ( y ) = A is constant for every height. The radius of the cross-section of the cone is proportional to the height y . Now use the method of separation of the variable to solve the equation (1). A d y d t = − k y d y d t = − k y y − 1 2 d y = − k d t Now integrate both sides. ∫ y − 1 2 d y = ∫ − k d t y 1 2 1 2 = − k t + c 2 y 1 2 = − k t + c Therefore, the resultant equation is as follows, 2 y 1 2 = − k t + c ........ ........ (2) The initial condition is y ( 0 ) = h . Now substitute 0 for t and h for y in equation (2) to obtain the value of C . 2 h 1 2 = − k ( 0 ) + c c = 2 h It is given that the cylindrical tank contains V 0 gallons of water in T minutes

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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Question

Chapter 1.4, Problem 57P

Program Plan Intro

Program Description: Purpose of the problem is to prove that V=V0[1−tT]2 after t≤T by Toricelli’s law.

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Chapter 1.4, Problem 56P

Chapter 1.4, Problem 58P

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Chapter 1 Solutions

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

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Prob. 10P Ch. 1.3 - Prob. 11P Ch. 1.3 - Prob. 12P Ch. 1.3 - Prob. 13P Ch. 1.3 - Prob. 14P Ch. 1.3 - Prob. 15P Ch. 1.3 - Prob. 16P Ch. 1.3 - Prob. 17P Ch. 1.3 - Prob. 18P Ch. 1.3 - Prob. 19P Ch. 1.3 - Prob. 20P Ch. 1.3 - Prob. 21P Ch. 1.3 - Prob. 22P Ch. 1.3 - Prob. 23P Ch. 1.3 - Prob. 24P Ch. 1.3 - Prob. 25P Ch. 1.3 - Prob. 26P Ch. 1.3 - Prob. 27P Ch. 1.3 - Prob. 28P Ch. 1.3 - Verify that if c is a constant, then the function...Ch. 1.3 - Prob. 30P Ch. 1.3 - Prob. 31P Ch. 1.3 - Prob. 32P Ch. 1.3 - Prob. 33P Ch. 1.3 - (a) Use the direction field of Problem 5 to...Ch. 1.3 - Prob. 35P Ch. 1.4 - Prob. 1P Ch. 1.4 - Prob. 2P Ch. 1.4 - Prob. 3P Ch. 1.4 - Prob. 4P Ch. 1.4 - Prob. 5P Ch. 1.4 - Prob. 6P Ch. 1.4 - Prob. 7P Ch. 1.4 - Prob. 8P Ch. 1.4 - Prob. 9P Ch. 1.4 - Prob. 10P Ch. 1.4 - Prob. 11P Ch. 1.4 - Prob. 12P Ch. 1.4 - Prob. 13P Ch. 1.4 - Prob. 14P Ch. 1.4 - Prob. 15P Ch. 1.4 - Prob. 16P Ch. 1.4 - Prob. 17P Ch. 1.4 - Prob. 18P Ch. 1.4 - Prob. 19P Ch. 1.4 - Prob. 20P Ch. 1.4 - Prob. 21P Ch. 1.4 - 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Knowledge Booster

Program Description: Purpose of the problem is to prove that V = V 0 [ 1 − t T ] 2 after t ≤ T by Toricelli’s law.

Solution Summary: The author explains how Toricelli's law is used to prove that V=V_0left[1-tTright]2 after T minutes.

Program Description: Purpose of the problem is to prove that V=V0[1−tT]2 after t≤T by Toricelli’s law.

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Chapter 1 Solutions