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A 4-m-long quarter-circlular heavy gate of radius 3 m is hinged about its upper edge A, as shown in the figure. The gate controls the flow of water over the ledge at B. Determine a) the hydrostatic force FR on the gate and b) the minimum weight of the gate required to keep the gate closed when the water level is at the upper edge of the gate, A. You may assume the gate has a zero thickness when calculating the moment. Given g = 9.8 m/s². Recall the hydrostatic forces and center of pressure are given by

A 4-m-long quarter-circlular heavy gate of radius 3 m is hinged about its upper edge A, as shown in the figure. The gate controls the flow of water over the ledge at B. Determine a) the hydrostatic force FR on the gate and b) the minimum weight of the gate required to keep the gate closed when the water level is at the upper edge of the gate, A. You may assume the gate has a zero thickness when calculating the moment. Given g = 9.8 m/s². Recall the hydrostatic forces and center of pressure are given by

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A 4-m-long quarter-circlular heavy gate of radius 3 m is hinged about its upper edge A, as shown in the figure. The gate controls the flow of water over the ledge at B. Determine a) the hydrostatic force FR on the gate and b) the minimum weight of the gate required to keep the gate closed when the water level is at the upper edge of the gate, A. You may assume the gate has a zero thickness when calculating the moment. Given g = 9.8 m/s². Recall the hydrostatic forces and center of pressure are given by uit JuIuLt unu uit ui cu n vi uR JuIIut unu 13 a u w FR = (Po+ pghc)A = PcA = PaveA | 3 m ab12 Yp = s ++ 2 (s + b/2 + PoMpg sin 0)]ab 4m B 62 2 12(s + b/2 + PoMeg sin 0)] The moment of a force F about A is equal to F times the distance from A to the line of action of F. Also, recall that the hydrostatic force passes thru the center of the circle. DI
Transcribed Image Text:A 4-m-long quarter-circlular heavy gate of radius 3 m is hinged about its upper edge A, as shown in the figure. The gate controls the flow of water over the ledge at B. Determine a) the hydrostatic force FR on the gate and b) the minimum weight of the gate required to keep the gate closed when the water level is at the upper edge of the gate, A. You may assume the gate has a zero thickness when calculating the moment. Given g = 9.8 m/s². Recall the hydrostatic forces and center of pressure are given by uit JuIuLt unu uit ui cu n vi uR JuIIut unu 13 a u w FR = (Po+ pghc)A = PcA = PaveA | 3 m ab12 Yp = s ++ 2 (s + b/2 + PoMpg sin 0)]ab 4m B 62 2 12(s + b/2 + PoMeg sin 0)] The moment of a force F about A is equal to F times the distance from A to the line of action of F. Also, recall that the hydrostatic force passes thru the center of the circle. DI
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