Explanation Given: the curve y = x 4 and the line y = 16 . Calculation: Consider that ends of the container have a shape of the region R . And it is bound by y = x 4 and x = y 4 , which makes the region R one end of the container. Consider the typical horizontal strip on the end of the container is located at y feet above the x-axis, which means it is h = 16 − y feet below the surface of the water. The strip is Δ y feet wide and L = 2 x feet long. Write L as a function of y : y = x 4 That implies; x = y 4 That implies; L ( y ) = 2 x = 2 × y 4 Therefore; Δ A = L Δ Y = 2 × y 4 Δ y And the total fluid force exerted by the water on one end of container may be modeled by the integral: F = ∫ 0 16 δ × h × L ( y ) d y Where, δ = 62.4 l b . f t − 3 h = ( 16 − y ) L ( y ) d y = area of the strip And, F = ∫ 0 16 62

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6, Problem 44SP

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To find: the fluid force exerted by the water on one end of the container.

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Chapter 6, Problem 43SP

Chapter 6, Problem 45SP

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Chapter 6 Solutions

Calculus

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the fluid force exerted by the water on one end of the container.

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Chapter 6 Solutions