Hydrostatic Force Overview

The term "hydrostatic force" refers to the total force exerted by a fluid at rest on a submerged or partially submerged surface. This force results from the pressure exerted by the fluid, which increases with depth. Understanding where this resultant force acts is crucial in fluid mechanics for designing structures like dams, gates, and submerged vessels.

Pressure Centre Definition

The point through which the resultant hydrostatic force acts on a submerged surface is precisely known as the Centre of Pressure.

• When a surface is submerged in a fluid, the fluid pressure varies with depth. The pressure is lowest at the shallowest part of the surface and increases linearly with depth.
• Because the pressure distribution is not uniform across the entire submerged area, the resultant force does not act at the geometric centroid of the area.
• Instead, the resultant force acts at a specific point called the Centre of Pressure, which is always located below the centroid of the submerged area for a horizontal or inclined plane surface.

Other Important Centres Explained

Let's examine the other options provided to differentiate them from the Centre of Pressure:

• Centre of gravity: This is the point where the entire weight of an object or body is considered to act. It is determined by the mass distribution of the body itself and is independent of any external fluid forces.
• Centre of buoyancy: This is the point through which the total buoyant force acts on a submerged or floating body. The buoyant force is the upward force exerted by a fluid that opposes the weight of an immersed object. The Centre of Buoyancy is located at the centroid of the volume of fluid displaced by the object. While both are related to fluid interaction, the Centre of Buoyancy deals with the force acting on the volume of displaced fluid, whereas the Centre of Pressure specifically deals with the resultant pressure force on a submerged surface.

Comparison of Centres

Pressure Centre Location

For a plane surface submerged in a fluid, the depth of the Centre of Pressure ($\text{h}_{\text{P}}$) from the free surface can be calculated using the formula:

$$\text{h}_{\text{P}} = \bar{\text{h}} + \frac{\text{I}_{\text{xx}}}{\bar{\text{h}}\text{A}}$$

Where:

• $\bar{\text{h}}$ represents the depth of the centroid of the submerged area from the free surface.
• $\text{I}_{\text{xx}}$ is the moment of inertia of the submerged area about an axis passing through its centroid and parallel to the free surface.
• $\text{A}$ is the area of the submerged surface.

This formula clearly indicates that the Centre of Pressure ($\text{h}_{\text{P}}$) is always deeper than the centroid ($\bar{\text{h}}$) of the submerged area, due to the increasing pressure with depth.

Conclusion on Hydrostatic Force

Therefore, based on the principles of fluid statics, the resultant hydrostatic force on a submerged surface always acts through the Centre of Pressure.