Understanding Fluid Pressure and Hydrostatics

Pressure and Fluids

What is Pressure?

Sometimes the effect of force also depends on the size of the surface on which it operates. The pressure takes into account two variables: the strength and the surface. Pressure occurs when a force acts on a unit area.

Pressure is defined as the force acting on a unit area (p = F / S). The SI unit is the newton per square meter (N/m²), which is called the pascal and whose symbol is Pa (1 Pa = 1N / 1 m²). Pressure is a scalar because it acts with an equal numerical value in all directions.

What are Fluids?

The term fluid includes both liquids and gases, and their properties are:

1. They do not have their own shape.
2. They take the form of the container that contains them.

This is because the particles that make up the fluids have freedom of movement and therefore can change position.

Fluid Statics

The part of physics that studies the properties of fluids is called fluid statics. When it comes to fluids, particularly water, it is called hydrostatics. If the fluid being studied is a gas, it is called aerostatics. The force exerted by a liquid in equilibrium on any surface is always perpendicular to this, and the orientation determines the direction (dH₂O = 1000 kg/m³).

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a liquid under its own weight.

Properties of Hydrostatic Pressure:

1. The pressure inside a liquid acts in all directions.
2. The pressure is higher the greater the depth.
3. The pressure is greater the higher the density of the liquid.
4. The pressure does not depend on the shape or width of the container.

The hydrostatic pressure at some depth under the free surface of a liquid at rest is the product of the density of the liquid by the acceleration of gravity and the depth of the point considered (p = d · g · h).

Hydrostatic Paradox

Hydrostatic Paradox: When several containers of various shapes and capacities, open at the top and connected by their base (communicating vessels), are filled with a particular fluid, it reaches the same height in all of them.

Fundamental Principle of Hydrostatics

Fundamental Principle of Hydrostatics: "The difference in pressure between any two points of a homogeneous liquid in equilibrium is equal to the product of the density of the fluid, the acceleration of gravity, and the height difference" [Pa-Pb = d · g · (Ha-Hb)].

Superimposed Miscible Liquids

Superimposed Miscible Liquids: Liquid heights are inversely proportional to their respective densities, given that the pressures at points of the same horizontal are equal (Da · Ha = Db · Hb).