Pressure Measure

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A Pressure Measure is a physical measure of force per unit of area.

  • Context:
    • It is defined as [math]\displaystyle{ P=\frac{F}{A} }[/math]where F is the applied force on the surface of area (A).
    • In case the of fluid dynamics and thermodynamics, it is useful to re-defined pressure as energy (or work) per unit of volume:
[math]\displaystyle{ P=\frac{F}{A}=\frac{Force\times d}{Area \times d}= \frac{Work}{Volume}=\frac{Energy}{Volume} }[/math]
where d is unspecified distance value.
[math]\displaystyle{ [Pressure]=\frac{[Force]}{[Area]}=\frac{[mass][length]}{[time]^2}\times\frac{1}{[length]^2}=\frac{[mass]}{[time]^2[length]} }[/math]
where [math]\displaystyle{ [x] }[/math] symbolizes the conversion of the quantity [math]\displaystyle{ x }[/math] to its units of measurement. Thus, the units of measurement for pressure in International System of Units is kilograms per squared seconds per metre or Newton per square meter which is the Pascal Unit ([math]\displaystyle{ Pa=kg s^{-2}m{-1}=N/m{2} }[/math]).

References

2016

[math]\displaystyle{ d\mathbf{F}_n=-p\,d\mathbf{A} = -p\,\mathbf{n}\,dA }[/math]
The minus sign comes from the fact that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation(...) Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics, and it is conjugate to volume.
(...)In a static gas, the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant random motion. Because we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our "container" down to a very small point (becoming less true as we approach the atomic scale), and the pressure will still have a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has magnitude but no direction sense associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular (at right angle) to the surface.
A closely related quantity is the stress tensor σ, which relates the vector force [math]\displaystyle{ \vec{F} }[/math] to the vector area [math]\displaystyle{ \vec{A} }[/math] via the linear relation [math]\displaystyle{ \vec{F}=\sigma\vec{A}\, }[/math].
This tensor may be expressed as the sum of the viscous stress tensor minus the hydrostatic pressure. The negative of the stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure.
According to the theory of general relativity, pressure increases the strength of a gravitational field (see stress–energy tensor) and so adds to the mass-energy cause of gravity. This effect is unnoticeable at everyday pressures but is significant in neutron stars, although it has not been experimentally tested.

2005

For an object sitting on a surface, the force pressing on the surface is the weight of the object, but in different orientations it might have a different area in contact with the surface and therefore exert a different pressure.
There are many physical situations where pressure is the most important variable. If you are peeling an apple, then pressure is the key variable: if the knife is sharp, then the area of contact is small and you can peel with less force exerted on the blade. If you must get an injection, then pressure is the most important variable in getting the needle through your skin: it is better to have a sharp needle than a dull one since the smaller area of contact implies that less force is required to push the needle through the skin.
When you deal with the pressure of a liquid at rest, the medium is treated as a continuous distribution of matter. But when you deal with a gas pressure, it must be approached as an average pressure from molecular collisions with the walls.
Pressure in a fluid can be seen to be a measure of energy per unit volume by means of the definition of work. This energy is related to other forms of fluid energy by the Bernoulli equation.

1996

[math]\displaystyle{ P=\frac{F}{A} }[/math]
Pressure therefore has units of N m^{-2} = kg m^{-1} s{-2}. It is usually denoted P or p. Pressure can be measured in atmospheres, bars, inches of mercury, millimeters of mercury, Pascals, or Torr.
When pressure is measured by a gauge, the quantity obtained usually excludes the ambient atmospheric pressure and is therefore called overpressure,
[math]\displaystyle{ P_{overpressure}=P_{gauge} }[/math]
If atmospheric pressure is included, then the resulting pressure is called absolute pressure,
[math]\displaystyle{ P_{absolute}=P_{atmospheric}+P_{gauge} }[/math]
In a uniform fluid, the total pressure is the atmospheric pressure plus the weight of the fluid column,
[math]\displaystyle{ P_0=+g\rho h }[/math]
where [math]\displaystyle{ \rho }[/math] is the density of the fluid, g is the gravitational acceleration, and h is the height of the fluid column.
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