forces on submerged surfaces

Forces on Submerged Surfaces in a static fluid is also an important section. It deals with Horizontal, vertical and curved surfaces submerged under fluid and the various forces applied on these section. Some easy, which other tricky questions are expected from this section.

Hydrostatic forces

• When a fluid is in contact with a surface is exerts a normal force on the surface which is termed as the hydrostatic force.

 Examples:

 A plate exposed to a liquid, such as a gate valve in a dam, the wall of a liquid storage tank, or the hull of a ship at rest, is subjected to fluid pressure distributed over its surface.

• On a plane surface, the hydrostatic forces form a system of parallel forces, and we often need to determine the magnitude of the force.
• The point of action of total hydrostatic force on the submerged surface is called the Centre of Pressure (CP).

Hydrostatic forces on inclined plane submerged surface in a liquid

Consider a plane surface of arbitrary shape immersed in a liquid in such a way that the plane of the surface makes an angle θ with the free surface of the liquid as shown in figure.

The force is given by 

Hence force is independent of the angle of inclination (θ). Thus, force for Horizontal and vertical submerged bodies will also be given by same expression. 

Centre of Pressure (h*)

It is defined as the point where whole of hydrostatic force is assumed to acting.

Plane vertical surface (θ = 90°)

Thus, Centre of pressure for the vertical submerged surface is given by

Plane horizontal surface (θ = 0°)

 

 

Hydrostatic forces on curved surfaces

AC = curved surface

F_Y = vertical component of F_R

F_X = Horizontal component of F_R

F_R = Resultant force on curved surface.

Horizontal component of force on curved surface

The horizontal component of force on a curved surface is equal to hydrostatic force on the vertical projection area.

Horizontal force 

Where,

A = Projected Area

 = depth of centroid of an area.

This force will act at center of pressure of the corresponding area.

Vertical component of force on curved surface

• The vertical component of force on a curved surface is equal to weight of the fluid contained by the curved surface up to the free surface of the liquid.

              Vertical force (F_Y) = weight of the fluid above the curved surface up to the free surface

 

 Resultant Force and direction:

• Resultant Force,

• The angle from the horizontal at which this force will act:

 

• It will act at the centre of gravity of the volume of liquid contained in portion extended above the curved surface up to the free surface of the liquid.

 

 

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