Explanation Given information: A tank has a shape of a parabola y = x 2 , revolved around the y-axis. Water leaks from a hole of area B = 0.0005 m 2 at the bottom of the tank. Let y ( t ) be the water level at time t. Formula used: g = 9.8 m / s 2 By Torricelli law: v = 2 g h , where g is the gravity, and h is the vertical distance between the liquid surface and the centre of the opening. Calculation: Let v ( t ) denotes the velocity of water flowing through the hole when the tank is filled to height y, A ( y ) = π y be the area of the horizontal cross section of the trough at height y. Then y ( t ) satisfies the differential equation d y d y = B ⋅ v ( t ) A ( t ) . We have g = 9.8 m / s 2 . By Torricelli law, v = − 2 g y v = − 2. ( 9.8 ) y = − 19.6 y The area of the hole is B = 0.0005 m 2 . Then the differential equation for y becomes d y d t = B . v ( t ) A ( t ) = − 0.0005 19.6 y π y = − 0

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 10.1, Problem 48E

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To find:The time taken for the tank to empty if it is initially filled to height y0=1m.

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Chapter 10.1, Problem 47E

Chapter 10.1, Problem 49E

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ACHIEVE STANDALONE ACCESS F/ CALC 4E

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The time taken for the tank to empty if it is initially filled to height y 0 = 1 m .

Solution Summary: The author calculates the time taken for the tank to empty if it is initially filled to height y_0=1m.

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Chapter 10 Solutions