When a curved surface plate is immersed in a liquid, the liquid exerts pressure on all parts of the plate. This pressure acts perpendicular to the surface at every point. To analyze the total fluid force, it's often convenient to resolve it into horizontal and vertical components, as these components help simplify the calculation of the overall fluid pressure acting on the plate.

Fluid Force Components on a Curved Plate

For a submerged curved surface, the total fluid force can be broken down into two principal components, which are typically perpendicular to each other:

• Vertical Fluid Force: This component accounts for the weight of the liquid column that is directly above the curved surface.
• Horizontal Fluid Force: This component is determined by the hydrostatic pressure acting on the vertical projection of the curved surface.

Vertical Force Component (V)

The question states that the "Weight of liquid above the plate is V". This value 'V' directly represents the total vertical component of the fluid force acting on the curved plate. In fluid mechanics, the vertical force on a submerged curved surface is indeed equivalent to the weight of the liquid that is vertically above the surface, extending upwards to the free surface of the liquid. This vertical force acts downwards.

Horizontal Fluid Pressure (H)

The question also provides that the "Horizontal fluid pressure on the plate is H". This 'H' represents the total horizontal component of the fluid force acting on the curved plate. This horizontal force is typically calculated by considering the hydrostatic force that would act on the vertical projection of the curved surface onto a vertical plane. This horizontal force acts perpendicular to the vertical force.

Resultant Fluid Pressure on the Plate

Since the vertical fluid force (V) and the horizontal fluid pressure (H) are considered as perpendicular components of the total fluid pressure or force acting on the curved plate, their resultant can be determined using vector addition principles. When two forces or pressures act at a 90-degree angle to each other (orthogonally), their combined effect, known as the resultant, is calculated using the Pythagorean theorem.

Let \(R\) be the resultant fluid pressure acting on the plate.

Given the components:

• Vertical component of fluid pressure (weight of liquid above the plate) = \(V\)
• Horizontal component of fluid pressure = \(H\)

Because these two components are orthogonal, the resultant fluid pressure \(R\) is calculated as follows:

\[R = \sqrt{V^2 + H^2}\]

This formula accurately represents the magnitude of the total fluid pressure or force acting on the curved plate, taking into account both its vertical and horizontal components.