Answer should be 14.66 degress and 0.484 gamma R^2 x W Please explain ### Problem DescriptionIf the gate is half filled by water (depth = R/2 as shown in the figure), determine the magnitude and direction of the resultant force.### Diagram Explanation- The diagram illustrates a quadrant-shaped gate submerged in water.- The quadrant is part of a circle with radius $ R $.- The water fills half the gate, thus the water depth is $ R/2 $.- Points in the diagram: - $ A $: Top left corner of the gate. - $ B $: Bottom right corner of the gate, adjacent to the boundary. - $ C $: Top right corner where the gate is hinged.- The curved edge $ AB $ of the quadrant is submerged in water.- The hinge is located at corner $ C $. ### Additional Considerations- The water exerts hydrostatic pressure on the gate.- The problem asks to find both the magnitude and the direction of the resultant force applied by the water on the gate.

Answered: If the gate is half filled by water…

If the gate is half filled by water (depth = R/2 as shown in the figure), determine the magnitude and direction of the resultant force R Hinge R/2

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Answer should be 14.66 degress and 0.484 gamma R^2 x W Please explain

### Problem Description

If the gate is half filled by water (depth = R/2 as shown in the figure), determine the magnitude and direction of the resultant force.

### Diagram Explanation

- The diagram illustrates a quadrant-shaped gate submerged in water.
- The quadrant is part of a circle with radius $ R $.
- The water fills half the gate, thus the water depth is $ R/2 $.
- Points in the diagram:
- $ A $: Top left corner of the gate.
- $ B $: Bottom right corner of the gate, adjacent to the boundary.
- $ C $: Top right corner where the gate is hinged.
- The curved edge $ AB $ of the quadrant is submerged in water.
- The hinge is located at corner $ C $.

### Additional Considerations

- The water exerts hydrostatic pressure on the gate.
- The problem asks to find both the magnitude and the direction of the resultant force applied by the water on the gate.

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