Explanation Given information: The vertical cross section of a tank containing the seawater is given by 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 water is 62.4 l b / f t 3 Consider the coordinate system in which the horizontal axis lies at the bottom of tank and the positive vertical axis points up. cos π 4 = x 2 ⇒ x = 2 1 2 = 2 f t The thin slab has thickness Δ h and length L. The x and y- intercepts are ( 1 , 0 ) a n d ( 0 , 2 ) respectively. Therefore, the equation for the line representing the hypotenuse must be y = − 2 x + 2 ⇒ x = 2 − y 2 Then L = 2 x = 2 ( 2 − y 2 )

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ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 6.5, Problem 22PS

To determine

To find:The integral for the fluid force against the vertical plate.

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Chapter 6.5, Problem 21PS

Chapter 6.5, Problem 23PS

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Chapter 6 Solutions

Calculus

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The integral for the fluid force against the vertical plate.

Solution Summary: The author explains how the integral for the fluid force against the vertical plate is (62.4)sqrt2displaystyle

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Chapter 6 Solutions