In the context of hydrostatics, the resultant hydrostatic force acting on a submerged plane surface passes through which of the following points?
The centre of pressure of the submerged surface.
Understanding the Resultant Hydrostatic Force on Submerged Surfaces
In fluid mechanics, specifically within the study of hydrostatics, we often consider the forces exerted by a static (non-moving) fluid on objects submerged within it. When a plane surface is submerged in a fluid, the pressure varies with depth. This pressure exerts a force on every small element of the surface.
The resultant hydrostatic force is the single, equivalent force that represents the combined effect of all these distributed pressure forces acting on the submerged plane surface. It's essentially the net force due to the fluid pressure.
Calculating the Magnitude of the Resultant Force
The magnitude of the resultant hydrostatic force ($F$) acting on a submerged plane surface is calculated using the following formula:
\( F = P_c \times A \)
Where:
- \( P_c \) is the gauge pressure at the centroid of the submerged surface.
- \( A \) is the total area of the submerged surface.
This formula tells us the total strength of the force, but it doesn't tell us *where* on the surface this force acts.
Identifying the Point of Application: The Centre of Pressure
The point where the resultant hydrostatic force acts is known as the centre of pressure (CP).
The resultant hydrostatic force on a submerged plane surface acts through the centre of pressure of that surface. This point is crucial for understanding moments and stability.
For a submerged plane surface:
- If the surface is horizontal, the centre of pressure coincides with the centroid.
- If the surface is inclined or vertical, the centre of pressure is located at a point deeper than the centroid. This is because the pressure increases with depth, so the forces acting on the lower parts of the surface have a greater magnitude, shifting the overall point of action downwards.
Analysis of Other Options
Let's examine why the other options are not the correct point of application for the resultant hydrostatic force:
| Option | Reasoning |
|---|---|
| Centroid of the submerged surface | The pressure at the centroid is used to calculate the magnitude of the resultant force ($F = P_c \times A$), but the force itself generally acts at a different point (the centre of pressure), except for horizontal surfaces. |
| Centre of gravity (CG) of the fluid displaced | The CG of the displaced fluid is relevant for determining the buoyant force (Archimedes' Principle), not the resultant hydrostatic force acting directly on the submerged surface. |
| Metacentre of the body | The metacentre is a concept used in analyzing the stability of floating or submerged bodies. It relates to the initial restoring moment when the body is slightly tilted, not the direct point of application of the hydrostatic force on a plane surface. |
Therefore, the resultant hydrostatic force acting on a submerged plane surface acts through the centre of pressure.
Important Questions from Hydrostatic Force
The centre of pressure of a plane submerged surface
The depth of the center of pressure on a vertical rectangular gate (4 m wide and 3 m high) with water up to top surface is
If a planar surface is immersed in a liquid, the resultant liquid pressure acts at a point called ___________.
The resultant of all normal pressure acts
Which is the law that states that the intensity of pressure at a point in a fluid at rest is the same in all directions?
