**Pressure** is the amount of force applied normal to a surface divided by the area of that surface. 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.

More formally, **pressure** (symbol: *p*) is defined as the magnitude of the normal force divided by the area over which the normal force acts.

*p*=*F*/*A*

where *p* is the pressure, *F* is the normal force, and *A* is the 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 gradient of pressure is force density.

## Relative or gauge pressure[]

Pressure is sometimes measured, not as an **absolute pressure**, but relative to atmospheric pressure; such measurements are sometimes called **gauge pressure**. An example of this is the air pressure in a car tire, which might be said to be "220 kPa," 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 320 kPa. In technical work, this is written "a gauge pressure of 220 kPa." Where space is limited, such as on gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge)" or "kPa (absolute)," is permitted. In non-SI technical work, a gauge pressure is sometimes written as "32 psig," though the other methods explained above that avoid attaching characters to the unit of pressure are preferred. ^{1}

## Scalar quantity[]

Let us look at a static gas, one that does not appear to move or flow. While the gas as a whole does not appear to move, the individual molecules of the gas, which we cannot see, 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 an infinitely small point, and the pressure has a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has a magnitude but no direction 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 to the surface.

"Pressure is a scalar quantity, but teachers and authors do not appear to believe this in their hearts." (McClelland, 1987)

## Hydrostatic pressure[]

Hydrostatic pressure is the pressure due to the weight of a fluid.

*p*=*ρgh*

where *ρ* (rho) is density of the fluid, *g* is acceleration due to gravity, and *h* is height of the fluid above the point being measured. See also Pascal's law.

## Stagnation pressure[]

**Stagnation pressure** is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower **static pressure**, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by the Mach number of the fluid. In addition, there can be differences in pressure due to differences in the elevation (height) of the fluid. See Bernoulli's equation.

The pressure of a moving fluid can be measured using a Pitot probe, or one of its variations such as a Kiel probe or Cobra probe, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressure or stagnation pressure.

## Units[]

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N·m^{−2} or kg·m^{−1}·s^{−2}). This special name for the unit was added in 1971; before that, pressure in SI was expressed in units such as N/m².

Non-SI measures (still in use in some parts of the world) include the pound-force per square inch (psi) and the bar.

The cgs unit of pressure is barye (ba). It is equal to 1 dyn·cm^{−2}.

Pressure is still sometimes expressed in kgf/cm² or grams-force/cm² (sometimes as kg/cm² and g/cm² without properly identifying the force units). But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as a unit of force is expressly forbidden in SI; the unit of force in SI is the newton (N). The technical atmosphere (symbol: at) is 1 kgf/cm².

Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in practically all other fields, where the hecto prefix is hardly ever used. In Canadian weather reports, the normal unit is kPa. The obsolete unit *inch of mercury* (inHg) is still sometimes used in the United States.

Blood pressure is still measured in millimetres of mercury in most of the world, and lung pressures in centimeters of water are still common. These obsolete **manometric units** of pressure are based on the pressure exerted by the weight of some "standard" fluid under some "standard" gravity. They are effectively attempts to define a unit for expressing the readings of a manometer. When millimetres or inches of mercury are used today, they have precise definitions that can be expressed in terms of SI units. The water-based units depend on the density of water, a measured, rather than defined, quantity.

The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at earth mean sea level and is defined as follows.

- standard atmosphere = 101325 Pa = 101.325 kPa = 1013.25 hPa.

A rule of thumb commonly used by scuba divers is that one atmosphere is approximately equal to the pressure exerted by ten metres of water.

Non-SI units presently or formerly in use include the following.

- atmosphere.
- manometric units:
- centimetre, inch, and millimetre of mercury (Torr).
- millimetre, centimetre, metre, inch, and foot of water.

- imperial units:
- kip, ton-force (short), ton-force (long), pound-force, ounce-force, and poundal per square inch.
- pound-force, ton-force (short), and ton-force (long) per square foot.

- non-SI metric units:
- bar, millibar.
- kilogram-force, or kilopond, per square centimetre (technical atmosphere).
- gram-force and tonne-force (metric ton-force) per square centimetre.
- barye (dyne per square centimetre).
- kilogram-force and tonne-force per square metre.
- sthene per square metre (pieze).

### Conversion table[]

pascal | MPa | bar | kp/m^{2} |
at | atm | Torr | |
---|---|---|---|---|---|---|---|

1 Pa (N/m^{2}) = |
1 | 10^{−6} |
10^{−5} |
0.102 | 0.102×10^{−4} |
0.987×10^{−5} |
0.0075 |

1 MPa (N/mm^{2}) = |
10^{6} |
1 | 10 | 1.02×10^{5} |
10.2 | 9.87 | 7501 |

1 bar (daN/cm^{2}) = |
10^{5} |
0.1 | 1 | 10200 | 1.02 | 0.987 | 750 |

1 kp/m^{2} = |
9.81 | 9.81×10^{−6} |
9.81×10^{−5} |
1 | 10^{−4} |
0.968×10^{−4} |
0.0736 |

1 at (kp/cm^{2}) = |
98100 | 0.0981 | 0.981 | 10000 | 1 | 0.968 | 736 |

1 atm (760 Torr) = | 101325 | 0.1013 | 1.013 | 10330 | 1.033 | 1 | 760 |

1 Torr (mmHg) = | 133 | 1.33×10^{−4} |
0.00133 | 13.6 | 0.00132 | 0.00132 | 1 |

## See also[]

- Atmospheric pressure
- Blood pressure
- Conversion of units
- Kinetic theory#Pressure
- Partial pressure
- Sound pressure (audio)
- Microphone
- Timeline of temperature and pressure measurement technology
- Vacuum (or negative pressure)

## External links[]

- Online unit converter - conversion of many different units.
- An exercise in air pressure
- Pressure being a scalar quantity

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