Short Answer:

The center of pressure is the point on an immersed surface at which the total pressure force acts. It is the exact location where the resultant pressure acts on a surface that is submerged in a fluid.

In simple words, the center of pressure is the point through which the total pressure force due to a fluid passes. It is generally located below the centroid of the surface because pressure increases with depth. The concept of center of pressure is very important in hydraulic engineering, dam design, and fluid mechanics.

Detailed Explanation :

Center of Pressure

The center of pressure is a key concept in fluid statics, which deals with fluids at rest. When a surface (like a plate, gate, or wall) is immersed in a fluid, the fluid exerts pressure on every point of that surface. The intensity of pressure increases with depth due to the weight of the fluid.

Because pressure is not uniform over the entire surface — being higher at greater depths — the total force due to pressure acts at a particular point. This specific point where the resultant pressure force acts is known as the center of pressure.

It is important to understand that the center of pressure is not the same as the centroid of the surface. The centroid is the geometric center, while the center of pressure is the point where the total pressure force can be assumed to act for practical analysis.

Concept of Pressure Distribution

When a plane surface is immersed in a static fluid, the pressure increases linearly with depth.

• At the surface level (top of the plane), the pressure is minimum.
• At the bottom (deeper level), the pressure is maximum.

The total pressure acting on the surface is the sum of all the small pressure forces acting on tiny elements of the surface. These numerous small forces combine to form a single resultant force, and the point of action of this resultant is the center of pressure.

Because of the linear variation of pressure with depth, the center of pressure is always located below the centroid of the submerged area.

Mathematical Expression for Center of Pressure

Let us consider a plane surface of area  submerged vertically or inclined in a liquid.

• Let  be the depth of the centroid of the surface below the free surface of the liquid.
• Let  be the moment of inertia of the surface area about the horizontal axis passing through the centroid.

Then, the depth of the center of pressure (hₚ) below the free surface is given by:

Where,
= Depth of center of pressure below the free surface
= Depth of centroid of the area below the free surface
= Moment of inertia of the area about its centroidal axis
= Area of the surface

This formula shows that the center of pressure depends on the shape of the surface and its orientation in the fluid.

Explanation of the Formula

• The first term  represents the average depth of the surface (centroid).
• The second term  represents the additional distance below the centroid due to non-uniform pressure distribution.

As the moment of inertia () and area () are always positive, the value of  is always greater than . Hence, the center of pressure always lies below the centroid for vertically or inclined submerged surfaces.

Center of Pressure for Different Surfaces

1. For a Vertical Plane Surface:
   The pressure increases linearly with depth, so the center of pressure is located below the centroid.
2. For a Horizontal Plane Surface:
   The pressure on all points is the same, so the center of pressure and centroid coincide.
3. For an Inclined Plane Surface:
   The center of pressure lies below the centroid along the line of symmetry.

Practical Applications of Center of Pressure

The concept of the center of pressure is very important in the design and analysis of many engineering systems where fluids exert forces on surfaces. Some of the major applications include:

1. Dams and Reservoir Walls:
   The pressure of water acts on the dam wall. Engineers must calculate the exact location of the center of pressure to ensure the dam’s stability and prevent it from overturning.
2. Gates and Valves:
   In hydraulic structures, the gates used to control the flow of water experience pressure forces. The position of the center of pressure helps determine the hinge point and design strength.
3. Submerged Plates:
   The analysis of plates or panels under water or oil helps in designing underwater equipment and storage tanks.
4. Ship and Submarine Design:
   Knowledge of the center of pressure helps maintain balance and stability when a vessel moves or turns underwater.
5. Aircraft and Wind Tunnel Testing:
   In aerodynamics, the center of pressure helps in studying lift and drag forces on airplane wings or airfoils.

Difference Between Centroid and Center of Pressure

• The centroid is the geometric center of the area.
• The center of pressure is the point where the total pressure force acts.
• The center of pressure is always below the centroid for a submerged vertical surface because of the increasing pressure with depth.

Importance of Center of Pressure

Understanding the center of pressure is essential in fluid mechanics because it helps engineers:

• Predict how pressure forces act on structures.
• Design surfaces that can withstand fluid forces safely.
• Calculate moments and stability of submerged surfaces.
• Avoid failure due to uneven pressure distribution.

It ensures that structures such as tanks, dams, and ships remain safe and balanced under the influence of hydrostatic forces.

Conclusion

The center of pressure is the point on an immersed surface where the resultant pressure force acts. It represents the average location of fluid pressure on the surface. Because pressure increases with depth, the center of pressure always lies below the centroid of the surface. This concept is essential in fluid mechanics and has great importance in designing hydraulic structures, gates, tanks, and underwater systems. Correctly locating the center of pressure ensures safety, stability, and efficiency in engineering applications.