Definition and derivation of hydraulic force on plane surface Free surface- Centroid, c Location of resultant force (center of pressure, CP) FIGURE 2.12 Notation for hydrostatic force on an inclined plane surface of arbitrary shape.
Definition and derivation of hydraulic force on plane surface Free surface- Centroid, c Location of resultant force (center of pressure, CP) FIGURE 2.12 Notation for hydrostatic force on an inclined plane surface of arbitrary shape.
Chapter2: Loads On Structures
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d08af96-d033-4b75-9fc7-24c5a2c93954%2F9296e73f-08aa-4ca3-ae7c-2857edb67911%2F3r51n17_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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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