## Table of contents

**Pressure** is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. This definition can be stated for the generic point of any stressed surface (not necessarily flat but without angular points):

- considering a surface element small enough to be considered flat (as it can be confused with the corresponding element of the tangent plane locally to the surface);
- considering the ratio between the stress component according to the normal to the element and the area of the latter and defining then the pressure in the given point as the limit of this ratio when the area of the element.

When describing a container of gas, the term pressure (or absolute pressure) refers to the average force per unit area that the gas exerts on the surface of the container.

In fluid mechanics, on a microscopic scale, the pressure exerted by a fluid on a surface with which it is in contact is caused by the collisions of particles (atoms or molecules) of the fluid itself against the surface with which it comes into contact. As a consequence of an impact, the component normal to the surface of the momentum of a particle is reversed. The surface exerts on the particle an impulsive force, and for Newton’s third law the particle exerts an equal and opposite force, perpendicular to the surface (red arrows). So the resultant of the reaction forces exerted by the many particles of the fluid, generates the pressure on the surface.

Entering into the details of the interactions, or better of the stresses, on material objects, we can see that fluids are only affected by pressure (Pascal’s law), while solids are more generally affected by tension.

## Absolute and relative pressure

Pressure can be measured either absolutely or relatively, depending on whether a reference pressure is taken into account or not. **Absolute or real pressure**: is the pressure measured assuming as reference the ideal or absolute vacuum (this measurement is independent from weather and altitude). Absolute pressure is zero-referenced against a perfect vacuum, using an absolute scale, so it is equal to gauge pressure plus atmospheric pressure.

**Relative pressure**: is the pressure measured assuming as reference another pressure (for example the terrestrial atmospheric pressure) present in the measuring environment and at that moment.

## Negative pressure

Although pressure is, generally, positive in value, there are several situations in which negative pressures may be encountered, such as:

- in the case of relative (gauge) pressures; for example, an absolute pressure of 50 kPa can be described as a relative pressure of -51 kPa (i.e., 51 kPa below an atmospheric pressure of 101 kPa);
- negative absolute pressures are actually stresses, and both solids and liquids can be put under negative absolute pressure by putting them under tension. Microscopically, molecules in solids and liquids have “attractive” (attracting) interactions that exceed thermal kinetic energy, so some internal tension can be sustained. Thermodynamically, however, a material under negative pressure is in a metastable state, and is particularly fragile in the case of liquids where the negative pressure state is similar to superheating, which consequently is easily susceptible to cavitation phenomena;
- the Casimir effect can create a small attractive force due to interactions under vacuum conditions; this force is sometimes called “vacuum pressure” (not to be confused with the negative relative pressure of a vacuum);
- for non-isotropic stresses in rigid bodies, depending on how the orientation of a surface is chosen, the same force distribution may have a positive pressure component along one normal to the surface, with a negative pressure component acting along another normal to the surface;
- stresses in an electromagnetic field are generally non-isotropic, with the pressure normal to a surface element (normal stress) being negative and positive for surface elements perpendicular to it.

## Dynamic pressure

Dynamic pressure is the dynamic component of the pressure of a fluid in motion, i.e., it indicates the pressure increase resulting from the fluid’s kinetic energy. A classic example of dynamic pressure is represented by the energy source of sailing boats, windmills and wind turbines. It acts in the same direction as the fluid motion and is always considered to have a positive sign.

The dynamic pressure depends on the velocity and specific gravity of the fluid. To know the resistance of an object moving at a certain speed or the thrust on an object hit by the wind, it is necessary to calculate the dynamic pressure.

Dynamic pressure \(q\) is measured in the International System in Pascal, and is given by the following relationship:

\[q=\dfrac{1}{2}\rho u^2\]

Where (rho) is the density and (u) is the flow velocity of the fluid. To determine the pressure at a point in the fluid, the dynamic pressure must be added to the hydrostatic pressure.

In space launches, the point of maximum dynamic pressure is the point corresponding to the maximum mechanical stress condition for spacecraft.