# Hydrostatic Force

By Deepak Yadav|Updated : October 4th, 2022

Before getting into the specifics of hydrostatic force, let's first understand hydrostatic pressure. the pressure that fluid in equilibrium with gravity exerts at any given time. As the weight of the fluid increases when a downward force is applied, hydrostatic pressure is proportional to the depth measured from the surface.

In a closed container, the fluid pressure may be influenced by forces, acceleration, or gravity. Take a coating of water from the bottle's top into consideration. The water layer pressing against the bottle's sides creates pressure. The pressure put on the bottom by the top layer increases as we descend from the top of the bottle to the bottom. More pressure at the container's bottom is a result of this phenomenon. Let's learn about concepts related to hydrostatic force through examples and definitions.

## What is Hydrostatic Force?

Fundamental concepts in fluid mechanics include calculating the hydrostatic force and the location of the center of pressure. A location on the submerged surface where the hydrostatic pressure acts is known as the center of pressure.

### Definition of Hydrostatic Force

The resultant force created by a liquid's pressure loading acting on submerged surfaces is known as hydrostatic force.

When a surface is immersed in a fluid, the fluid's forces act on the surface. These forces must be determined for designing storage tanks, ships, dams, and other hydraulic structures. Since there are no shearing stresses in place for fluids at rest, we know that the force must be perpendicular to the surface. If the fluid is incompressible, the pressure changes linearly with depth.

## Hydrostatic Force Formula

Hydrostatic forces result from a liquid's pressure loading acting on submerged surfaces. The total hydrostatic force for a horizontal plane surface submerged in liquid, a plane surface inside of a gas chamber, or any other plane surface subject to the influence of uniform hydrostatic pressure is given by:

F = pA

where A is the area and p is the uniform pressure.

## Applications of Hydrostatic Force

There are various applications of hydrostatic force. This force provides various advantages because of its property. The structural design of water-control structures like dams, floodwalls, and gates is heavily influenced by the position and strength of the water pressure force pressing on those structures.

Many hydraulic equipment components must be designed following the principles of hydrostatic force and its course of action.

The hydrostatic force exerted on the vertical surface of the quadrant when it is submerged by adding water to the tank can be calculated by taking into account the following:

• The hydrostatic force at any point on the curved surfaces is normal to the surface and resolves at the pivot point since it is positioned at the origin of the radii. Because the hydrostatic forces travel through the pivot, they have no net influence on the upper and lower curved surfaces and produce no torque that may change the assembly's equilibrium.
• The forces on the quadrant's sides are horizontal and balance one another out (equal and opposite)
• The balance weight balances the hydrostatic force on the vertical submerged face. Therefore, the value of the balance weight and the depth of the water can be used to compute the resulting hydrostatic force on the face.
• The system is in equilibrium if the moments produced by the hydrostatic force and added weight (mg) about the pivot points are equal, that is:

mg×L = F×y

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• We know that matter exerts pressure in all of its states. Gases and liquids press against a container's walls equally. The normal force exerted by a liquid per unit area of the surface in contact is referred to as hydrostatic pressure or liquid pressure.

• In general, the area of a surface multiplied by the unit pressure at its center of gravity yields the total hydrostatic pressure on any planar surface. F=pcgA. pcg denotes the pressure at the center of gravity.

• The pressure that a fluid exerts at a specific place within itself when it is in balance with gravity is known as hydrostatic pressure. Due to the growing weight of the fluid pushing down from above, hydrostatic pressure rises according to the depth measured from the surface.

• A fluid that is not moving is referred to as hydrostatic. So, hydrostatic pressure refers to the pressure "within" a non-moving fluid, as opposed to the pressure exerted by, for example, water from a fire hose.

• Differences in hydrostatic pressure—the pressure a static fluid exerts—cause the buoyant force. The buoyant force applied to an object that is partially or entirely submerged in a fluid is equal to the weight of the fluid that is displaced by the object, according to the Archimedes principle.

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