Pressure

• Pressure (the symbol: P) is the force per unit area applied in a direction perpendicular to the surface of an object.

Pressure is an effect which occurs when a force is applied on a surface. Pressure is the amount of force acting on a unit area. The symbol of pressure is P.

Formula

    Mathematically:

where:

P is the pressure,

F is the normal force,

A is the area.

Pressure is a scalar quantity. It relates the vector surface element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:

The minus sign comes from the fact that the force is considered towards the surface element, while the normal vector points outwards.

The SI unit for pressure is the pascal (Pa), equal to one newton per square meter (N/m² or kg·m⁻¹·s⁻²). 

This special name for the unit was added in 1971; before that, pressure in SI was expressed simply as N/m²

• Although pressure itself is a scalar, we can define a pressure force to be equal to the pressure (force/area) times the surface area in a direction perpendicular to the surface. The pressure force is a vector quantity.
• Pressure forces have some unique qualities as compared to gravitational or mechanical forces. In the figure shown above on the right, we have a red gas that is confined in a box. 
• A mechanical force is applied to the top of the box. The pressure force within the box opposes the applied force according to Newton's third law of motion. The scalar pressure equals the external force divided by the area of the top of the box. Inside the gas, the pressure acts in all directions. So the pressure pushes on the bottom of the box and on the sides. 
• This is different from simple solid mechanics. If the red gas were a solid, there would be no forces applied to the sides of the box; the applied force would be simply transmitted to the bottom. But in a gas, because the molecules are free to move about and collide with one another, a force applied in the vertical direction causes forces in the horizontal direction.

• Fluid pressure

Fluid pressure is the pressure at some point within a fluid, such as water or air.

Fluid pressure occurs in one of two situations:

1. an open condition, such as the ocean, a swimming pool, or the atmosphere; or
2. a closed condition, such as a water line or a gas line.

• Pressure in open conditions usually can be approximated as the pressure in "static" or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only negligible changes in the pressure. Such conditions conform with principles of fluid statics. 
• The pressure at any given point of a non-moving (static) fluid is called the hydrostatic pressure.

Closed bodies of fluid are either "static," when the fluid is not moving, or "dynamic," when the fluid can move as in either a pipe or by compressing an air gap in a closed container. The pressure in closed conditions conforms with the principles of fluid dynamics.

Liquid pressure or pressure at depth

Used with liquid columns of constant density or at a depth within a substance (ex. pressure at 20km depth in the earth).

P = gdh

Where:

P is Pressure

g is gravity at the surface of overlaying material

d is density of liquid or overlaying material

h is height of liquid or depth within material