Explanation Given: A hole of area B = 0.002 m 2 and cylindrical tank’s height is 3 m . A base of area 10 m 2 . Calculation: Suppose a cylinder of height y and area of cross-section A . It is given that a hole has an area of B = 0.002 m 2 and the tank has across-sectional area of A = 10 m 2 . According to Toricelli’s Law, the velocity of the water flowing through a hole is: v = − 2 g y , where g = 9.8 m s 2 . So, the differential equation for the height of the water in the tank is: d y d t = B v ( y ) A ( y ) , where A ( y ) is the cross-sectional area of the tank at height y . Now, d y d t = B v ( y ) A ( y ) = B ( − 2 g y ) A = 0.002 ( − 2 ( 9.8 ) y ) 10 = − 0.0002 19.6 y So, the separation of variables and then integrating: y − 1 2 d y = − 0.0002 19.6 d t 2 y 1 2 = − 0.0002 19.6 t + C y ( t ) = ( C − 0.0002 19.6 t ) 2 The tank is originally full at t = 0 , so the initial condition y ( 0 ) = 10 , 10 = C ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 10.1, Problem 45E

To determine

We need to determine how long does it take

a. For half of the water to leak out

b. For the tank to empty.

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Chapter 10.1, Problem 44E

Chapter 10.1, Problem 46E

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We need to determine how long does it take a. For half of the water to leak out b. For the tank to empty.

Solution Summary: The author calculates how long it takes for half of the water to leak out and for the tank to empty.