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# Pressure

Pressure is the application of force to a surface, and the concentration of that force in a given area. 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, even though the force applied is the same, because the point concentrates that force into a smaller area.

More formally, pressure (symbol: p or P) is the measure of the normal component of force that acts on a unit area, see also stress (physics):

$p = \frac{F}{A}$

where:

• p is the pressure
• F is the normal component of the force
• A is the area

Often F is taken to be the magnitude of the mean vector force normal to the surface of area A upon which it exerts; the "surface" not necessarily being a that of a body, but for example the cross sectional area of a conduit.

The gradient of pressure is force density.

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 tire of a car, which might be said to be "thirty PSI", but is actually thirty PSI above atmospheric pressure. In technical work, this is often written as "30 PSIG" or, more commonly, "30 psig", though other methods which avoid attaching this information to the unit of pressure are preferred. 1

In the human body, pressure is measured by baroreceptors.

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

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## Hydrostatic pressure

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

$p = {\rho}{g}{h} \,$

where:

• ρ (rho) is the density of the fluid
• g is the acceleration due to gravity
• h is the height of fluid above the point being measured

Also see Pascal's Law.

## Stagnation pressure

Stagnation pressure is the pressure a fluid exerts when it is motionless. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure. Static 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·s-2·m-1). This special name for the unit was added in 1971; before that, pressures in SI were 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 g/cm² (often as kg/cm² and g/cm² without properly identifying the force units). The technical atmosphere (symbol: at) is 1 kgf/cm².

In the United States air pressure is still measured in inHg — inches of mercury (as in the mercury barometer). Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, because it gives the same numbers as the older millibar (mbar).

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 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 which can be expressed exactly in terms of SI units, though there were considerable minor variations in earlier usage. 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 pressures at sea level and defined to be

standard atmosphere = 101 325 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:

• Atmospheres
• Manometric units:
• Customary and foot-pound-second units:
• Kips, tons-force (short), tons-force (long), pounds-force, ounces-force, and poundals per square inch
• Pounds-force, tons-force(short) and tons-force (long) per square foot
• Non-SI metric units:
• bars and millibars
• Kilograms-force (kiloponds), grams-force, tonnes-force (metric tons-force), newtons and dynes per square centimetre
• Baryes = dyn/cm² and technical atmospheres = kgf/cm²
• Kilograms-force and tonnes-force per square metre

### Conversion table

Some popular pressure units and conversion factors
Pascal bar N/mm2 kp/m2 kp/cm2 (=1 at) atm torr
1 Pa (N/m2)= 1 10-5 10-6 0.102 0.102×10-4 0.987×10-5 0.0075
1 bar (daN/cm2) = 105 1 0.1 10,200 1.02 0.987 750
1 N/mm2 = 106 10 1 1.02×105 10.2 9.87 7,501
1 kp/m2 = 9.81 9.81×10-5 9.81×10-6 1 10-4 0.968×10-4 0.0736
1 kp/cm2 (1 at) = 98,100 0.981 0.0981 10,000 1 0.968 736
1 atm (760 torr) = 101,325 1.013 0.1013 10,330 1.033 1 760
1 torr (mmHg) = 133 0.00133 1.33×10-4 13.6 0.00132 0.00132 1