Explanation Given: The volume of water leaving the tank per second is V = c A h 2 g h , The radius of the hole at the base is 2 in and the acceleration due to gravity is 32 ft / s 2 . Procedure used: The expression for volume of water in the tank: V = A w h The expression for Torricelli's equation: d V d t = − c A h 2 g h Here, the contraction factor is c the height of the water is h and the area of the hole is A h . Calculation: Write the expression for volume of water in the tank. V = A w h (1) Differentiate equation (1) with respect to time. V = A w h d V d t = A w d h d t (2) Substitute − c A h 2 g h for d V d t in equation (2)

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 1.3, Problem 13E

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The differential equation for the height h of water at the time t for the cubical tank.

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Chapter 1.3, Problem 12E

Chapter 1.3, Problem 14E

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The differential equation for the height h of water at the time t for the cubical tank.

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