Explanation Given information: A quadrant spherical shell is submerged in a liquid which has a specific weight of γ h > R To find an analytical expression, the resultant hydrostatic force has to be found. Therefore, the below equation is used to find the resultant force. F R = F x 2 + F y 2 + F z 2 1 2 The both horizontal components F x and F y are equal. The center of gravity of quarter circle panels is 4 R 3 π above the bottom. The vertical force component is equal to the weight above the spherical shell. It can be represented as below, F z = W c y l i n d e r − W s p h e r e s h e l l Calculation: To find horizontal force, According to the above-mentioned explanation, F x = F y = γ A h 1 = γ π 4 R 2 h − 4 R 3 π To find vertical force in z direction, According to the above mentioned explanation, F z = W c y l i n d e r − W s p h e r e s h e l l = γ π 4 R 2 h − γ 1 8 4 3 π R 3 = γ π 4 R 2 h − 2 3 R To get an analytical expression, substitute the above values in below equation which gives the resultant force

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 2, Problem 2.93P

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An analytic expression for the resultant hydrostatic force on the shell and its line of action.

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Chapter 2, Problem 2.92P

Chapter 2, Problem 2.94P

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