Pressure


Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure.
Various [|units] are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal, for example, is one newton per square metre ; similarly, the pound-force per square inch is the traditional unit of pressure in the imperial and US customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the unit atmosphere is equal to this pressure, and the torr is defined as of this. Manometric units such as the centimetre of water, millimetre of mercury, and inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer.

Definition

Pressure is the amount of force applied perpendicular to the surface of an object per unit area. The symbol for it is p or P.
The IUPAC recommendation for pressure is a lower-case p.
However, upper-case P is widely used. The usage of P vs p depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, and on writing style.

Formula

Mathematically:
where:
  • is the pressure,
  • is the magnitude of the normal force,
  • is the area of the surface on contact.
Pressure is a scalar quantity. It relates the vector area element with the normal force acting on it. The pressure is the scalar proportionality constant that relates these two normal vectors:
The minus sign comes from the convention 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.
It is incorrect to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.
Pressure is distributed 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. It is defined as a derivative of the internal energy of a system:
where:
  • is the internal energy,
  • is the volume of the system,
  • The subscripts mean that the derivative is taken at fixed entropy and particle number.

    Units

The SI unit for pressure is the pascal, equal to one newton per square metre. This name for the unit was added in 1971; before that, pressure in SI was expressed in newtons per square metre.
Other units of pressure, such as pounds per square inch and bar, are also in common use. The CGS unit of pressure is the barye, equal to 1 dyn·cm−2, or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force as units of force is deprecated in SI. The technical atmosphere is 1 kgf/cm2.
Pressure is related to energy density and may be expressed in units such as joules per cubic metre.
Mathematically:
Some meteorologists prefer the hectopascal for atmospheric air pressure, which is equivalent to the older unit millibar. Similar pressures are given in kilopascals in most other fields, except aviation where the hecto- prefix is commonly used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars because pressure in the ocean increases by approximately one decibar per metre depth.
The standard atmosphere is an established constant. It is approximately equal to typical air pressure at Earth mean sea level and is defined as .
Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid. The most common choices are mercury and water; water is nontoxic and readily available, while mercury's high density allows a shorter column to be used to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely.
When millimetres of mercury are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units. One millimetre of mercury is approximately equal to one torr. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These manometric units are still encountered in many fields. Blood pressure is measured in millimetres of mercury in most of the world, and lung pressures in centimetres of water are still common.
Underwater divers use the metre sea water and foot sea water units of pressure, and these are the units for pressure gauges used to measure pressure exposure in diving chambers and personal decompression computers. A msw is defined as 0.1 bar, is not the same as a linear metre of depth. 33.066 fsw = 1 atm. The pressure conversion from msw to fsw is different from the length conversion: 10 msw = 32.6336 fsw, while 10 m = 32.8083 ft.
Gauge pressure is often given in units with "g" appended, e.g. "kPag", "barg" or "psig", and units for measurements of absolute pressure are sometimes given a suffix of "a", to avoid confusion, for example "kPaa", "psia". However, the US National Institute of Standards and Technology recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure. For example, rather than.
Differential pressure is expressed in units with "d" appended; this type of measurement is useful when considering sealing performance or whether a valve will open or close.
Presently or formerly popular pressure units include the following:
  • atmosphere
  • manometric units:
  • *centimetre, inch, millimetre and micrometre of mercury,
  • *height of equivalent column of water, including millimetre, centimetre, metre, inch, and foot of water;
  • imperial and customary units:
  • *kip, short ton-force, long ton-force, pound-force, ounce-force, and poundal per square inch,
  • *short ton-force and long ton-force per square inch,
  • *fsw used in underwater diving, particularly in connection with diving pressure exposure and decompression;
  • non-SI metric units:
  • *bar, decibar, millibar,
  • **msw, used in underwater diving, particularly in connection with diving pressure exposure and decompression,
  • *kilogram-force, or kilopond, per square centimetre,
  • *gram-force and tonne-force per square centimetre,
  • *barye,
  • *kilogram-force and tonne-force per square metre,
  • *sthene per square metre.

    Examples

As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity. The negative gradient of pressure is called the force density.
Another example is a knife. If the flat edge is used, force is distributed over a larger surface area resulting in less pressure, and it will not cut. Whereas using the sharp edge, which has less surface area, results in greater pressure, and so the knife cuts smoothly. This is one example of a practical application of pressure.
For gases, pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are called gauge pressure. An example of this is the air pressure in an automobile tire, which might be said to be "", but is actually 220 kPa above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa, the absolute pressure in the tire is therefore about. In technical work, this is written "a gauge pressure of ".
Where space is limited, such as on pressure gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa " or "kPa ", is permitted. In non-SI technical work, a gauge pressure of is sometimes written as "32 psig", and an absolute pressure as "32 psia", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.
Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluidics systems. However, whenever equation-of-state properties, such as densities or changes in densities, must be calculated, pressures must be expressed in terms of their absolute values. For instance, if the atmospheric pressure is, a gas at is 50% denser than the same gas at . Focusing on gauge values, one might erroneously conclude the first sample had twice the density of the second one.

Scalar nature

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 there are an extremely large number of molecules and because the motion of the individual molecules is random in every direction, no motion is detected. When the gas is at least partially confined, the gas will exhibit a hydrostatic pressure. This confinement can be achieved with either a physical container, or in the gravitational well of a large mass, such as a planet, otherwise known as atmospheric pressure.
In the case of planetary atmospheres, the pressure-gradient force of the gas pushing outwards from higher pressure, lower altitudes to lower pressure, higher altitudes is balanced by the gravitational force, preventing the gas from diffusing into outer space and maintaining hydrostatic equilibrium.
In a physical container, the pressure of the gas originates from the molecules colliding with the walls of the container. The walls of the container can be anywhere inside the gas, and the force per unit area is the same. If the "container" is shrunk down to a very small point, 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 force acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular to the surface.
A closely related quantity is the stress tensor σ, which relates the vector force to the
vector area via the linear relation.
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 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.