Given this information, how would you calculate the maximum height required to open the gate. (no numbers, just concept. formula and a clear explanintion **Definition and Derivation of Hydraulic Force on Plane Surface****Figure 2.12**: Surface of arbitrary shape.This image illustrates the concept of hydrostatic force on an inclined plane. It includes a plane surface submerged in a fluid where various forces and dimensions are marked:- A free surface at the top of the fluid, with the water line and atmospheric boundary.- The fluid exerts a differential force, \(dF\), on a small area, \(dA\), of the plane surface, with the total resultant force \(F_R\) acting perpendicularly.- \(h\) is the depth from the free surface to the centroid of the submerged surface.- The angle \(\theta\) represents the inclination of the surface relative to the horizontal.- The centroid \(c\) is marked, denoting the geometric center of the submerged area.- The center of pressure (CP), where the resultant force acts, is identified near the centroid.- Coordinates \(x_R\), \(y_R\), \(x_c\), and \(y_c\) define locations along the plane surface.**Notation for Hydrostatic Force on an Inclined Plane**The diagram aids in visualizing how the distribution of hydrostatic pressure leads to a resultant force on an inclined surface, critical for engineering applications like dam and tank wall design.

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Answered: Definition and derivation of hydraulic…

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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Given this information, how would you calculate the maximum height required to open the gate. (no numbers, just concept. formula and a clear explanintion

**Definition and Derivation of Hydraulic Force on Plane Surface**

**Figure 2.12**: Surface of arbitrary shape.

This image illustrates the concept of hydrostatic force on an inclined plane. It includes a plane surface submerged in a fluid where various forces and dimensions are marked:

- A free surface at the top of the fluid, with the water line and atmospheric boundary.
- The fluid exerts a differential force, \(dF\), on a small area, \(dA\), of the plane surface, with the total resultant force \(F_R\) acting perpendicularly.
- \(h\) is the depth from the free surface to the centroid of the submerged surface.
- The angle \(\theta\) represents the inclination of the surface relative to the horizontal.
- The centroid \(c\) is marked, denoting the geometric center of the submerged area.
- The center of pressure (CP), where the resultant force acts, is identified near the centroid.
- Coordinates \(x_R\), \(y_R\), \(x_c\), and \(y_c\) define locations along the plane surface.

**Notation for Hydrostatic Force on an Inclined Plane**

The diagram aids in visualizing how the distribution of hydrostatic pressure leads to a resultant force on an inclined surface, critical for engineering applications like dam and tank wall design.

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