Explanation Given information: The vertical cross section of a tank containing the milk 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 milk is 64.5 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. The centre point of the semicircle is ( 0 , 1 2 ) and its radius is 1 2 . Therefore the equation for the curve is x 2 + ( y − 1 2 ) 2 = ( 1 2 ) 2 . ⇒ x = 1 4 − ( y − 1 2 ) 2 The thin slab has thickness Δ h and length L. Then, we have L = 2 x = 2 1 4 − ( y − 1 2 ) 2 The area of the slab is Δ A = L Δ h = 2 1 4 − ( y − 1 2 ) 2 Δ h The distance from the surface of the water to the x-axis is 1 m

7th Edition

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 21PS

To determine

To find:The fluid force against the end of the vertical plate.

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Chapter 6.5, Problem 20PS

Chapter 6.5, Problem 22PS

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Chapter 6 Solutions

Calculus

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The fluid force against the end of the vertical plate.

Solution Summary: The author calculates the fluid force against the end of a vertical plate. The horizontal axis lies at the bottom of the tank and the positive vertical axes points up.

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Chapter 6 Solutions