Explanation Given information: The vertical end of a trough is an equilateral triangle, 3 ft on a side. The trough is filled with a fluid of weight density δ = 40 l b / f t 3 . Formula used: Suppose a flat surface is submerged vertically in a fluid of weight density δ and that the submerged portion of the plate extends from h = a to h = b on the vertical axis. Then the total force exerted by the fluid is given by of area A is submerged horizontally at a depth h in a fluid, the weight of the fluid exert a force called fluid force which is given by F = ∫ a b δ h L ( h ) d h Calculation: The weight density of fluid is δ = 40 l b / f t 3 . Consider the coordinate system in which the horizontal axis lies at the bottom of trough and the positive vertical axis points up. cos π 6 = x 3 ⇒ x = 3 3 2 f t The thin slab has thickness Δ h and length L. By similar triangles, we have L 3 3 2 − h = 3 3 3 2 L = 2 3 ( 3 3 2 − h ) L = ( 2 − h 2 3 ) The area of the slab is Δ A = L Δ h = ( 2 − h 2 3 ) Δ h . The distance from the surface of the water to the x-axis is 3 3 2

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 6, Problem 67SP

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To find:The force on the end of the trough.

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Chapter 6, Problem 66SP

Chapter 6, Problem 68SP

Chapter 6 Solutions

Calculus

Ch. 6.1 - Prob. 1PS Ch. 6.1 - Prob. 2PS Ch. 6.1 - Prob. 3PS Ch. 6.1 - Prob. 4PS Ch. 6.1 - Prob. 5PS Ch. 6.1 - Prob. 6PS Ch. 6.1 - Prob. 7PS Ch. 6.1 - Prob. 8PS Ch. 6.1 - Prob. 9PS Ch. 6.1 - Prob. 10PS

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The force on the end of the trough.

Solution Summary: The author explains how the force on the end of a trough is 135 lb.

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Chapter 6 Solutions