From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Common symbols
p, P
SI unitPascal [Pa]
In SI base unitsN/m2, 1 kg/(m·s2), or 1 J/m3
Derivations from
other quantities
p = F / A
DimensionM L−1 T−2
Pressure as exerted by particle collisions inside a closed container

Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.:445[1] Gauge pressure (also spelled gage pressure)[a] 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 (Pa), for example, is one newton per square metre (N/m2); similarly, the pound-force per square inch (psi) 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 atmosphere (atm) is equal to this pressure, and the torr is defined as ​1760 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.


Pressure is the amount of force applied at right angles to the surface of an object per unit area. The symbol for it is p or P.[2] The IUPAC recommendation for pressure is a lower-case p.[3] 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.


Pressure force area.svg




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 (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:

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.




Mercury column

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N/m2, or kg·m−1·s−2). This name for the unit was added in 1971;[5] before that, pressure in SI was expressed simply in newtons per square metre.

Other units of pressure, such as pounds per square inch (Ibf/in2) and bar, are also in common use. The CGS unit of pressure is the barye (Ba), equal to 1 dyn·cm−2, or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre (g/cm2 or kg/cm2) and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as units of force is expressly forbidden in SI. The technical atmosphere (symbol: at) is 1 kgf/cm2 (98.0665 kPa, or 14.223 psi).

Since a system under pressure has the potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to energy density and may be expressed in units such as joules per cubic metre (J/m3, which is equal to Pa). Mathematically:


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 101325 Pa.


Underwater divers use the metre sea water (msw or MSW) and foot sea water (fsw or FSW) units of pressure, and these are the standard units for pressure gauges used to measure pressure exposure in diving chambers and personal decompression computers. A msw is defined as 0.1 bar (= 100000 Pa = 10000 Pa), is not the same as a linear metre of depth. 33.066 fsw = 1 atm[6] (1 atm = 101325 Pa / 33.066 = 3064.326 Pa). Note that the pressure conversion from msw to fsw is different from the length conversion: 10 msw = 32.6336 fsw, while 10 m = 32.8083 ft.[7]

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.[8] For example, "pg = 100 psi" rather than "p = 100 psig".

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 (atm)
  • manometric units:
    • centimetre, inch, millimetre (torr) and micrometre (mTorr, micron) of mercury,
    • height of equivalent column of water, including millimetre (mm H
      ), centimetre (cm H
      ), metre, inch, and foot of water;
  • imperial and customary units:
  • non-SI metric units:
    • bar, decibar, millibar,
    • kilogram-force, or kilopond, per square centimetre (technical atmosphere),
    • barye (dyne per square centimetre),
    • kilogram-force and tonne-force per square metre,
    • sthene per square metre (pieze).


The effects of an external pressure of 700 bar on an aluminum cylinder with 5 mm (0.197 in) wall thickness


Another example is a knife. If we try to cut with the flat edge, 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.


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 100 kPa (15 psi), a gas (such as helium) at 200 kPa (29 psi) (gauge) (300 kPa or 44 psi [absolute]) is 50% denser than the same gas at 100 kPa (15 psi) (gauge) (200 kPa or 29 psi [absolute]). Focusing on gauge values, one might erroneously conclude the first sample had twice the density of the second one.

Scalar nature[edit]


A closely related quantity is the stress tensor σ, which relates the vector force to the vector area via the linear relation .




Fluid pressure[edit]

Fluid pressure is most often the compressive stress at some point within a fluid. (The term fluid refers to both liquids and gases – for more information specifically about liquid pressure, see section below.)

Water escapes at high speed from a damaged hydrant that contains water at high pressure

Fluid pressure occurs in one of two situations:

  1. An open condition, called "open channel flow", e.g. the ocean, a swimming pool, or the atmosphere.
  2. A closed condition, called "closed conduit", e.g. a water line or gas line.



The concepts of fluid pressure are predominantly attributed to the discoveries of Blaise Pascal and Daniel Bernoulli. Bernoulli's equation can be used in almost any situation to determine the pressure at any point in a fluid. The equation makes some assumptions about the fluid, such as the fluid being ideal[11] and incompressible.[11] An ideal fluid is a fluid in which there is no friction, it is inviscid [11] (zero viscosity).[11] The equation for all points of a system filled with a constant-density fluid is[12]


p = pressure of the fluid,
= ρg = density · acceleration of gravity = specific weight of the fluid,[11]
v = velocity of the fluid,
g = acceleration of gravity,
z = elevation,
= pressure head,
= velocity head.


Explosion or deflagration pressures[edit]


Negative pressures[edit]

Low-pressure chamber in Bundesleistungszentrum Kienbaum, Germany


  • When attractive intermolecular forces (e.g., van der Waals forces or hydrogen bonds) between the particles of a fluid exceed repulsive forces due to thermal motion. These forces explain ascent of sap in tall plants. A negative pressure acts on water molecules at the top of any tree taller than 10 m, which is the pressure head of water that balances the atmospheric pressure. Intermolecular forces maintain cohesion of columns of sap that run continuously in xylem from the roots to the top leaves.[13]
  • In the cosmological constant.

Stagnation pressure[edit]



is the stagnation pressure
is the flow velocity
is the static pressure.


Surface pressure and surface tension[edit]


Surface pressure is denoted by π:



Pressure of an ideal gas[edit]



p is the absolute pressure of the gas,
n is the amount of substance,
T is the absolute temperature,
V is the volume,
R is the ideal gas constant.

Real gases exhibit a more complex dependence on the variables of state.[14]

Vapour pressure[edit]

Vapour pressure is the pressure of a vapour in thermodynamic equilibrium with its condensed phases in a closed system. All liquids and solids have a tendency to evaporate into a gaseous form, and all gases have a tendency to condense back to their liquid or solid form.



Liquid pressure[edit]


Liquid pressure also depends on the density of the liquid. If someone was submerged in a liquid more dense than water, the pressure would be correspondingly greater. Thus, we can say that the depth, density and liquid pressure are directly proportionate. The pressure due to a liquid in liquid columns of constant density or at a depth within a substance is represented by the following formula:


p is liquid pressure,
g is gravity at the surface of overlaying material,
ρ is density of liquid,
h is height of liquid column or depth within a substance.

Another way of saying the same formula is the following:



The pressure does not depend on the amount of liquid present. Volume is not the important factor – depth is. The average water pressure acting against a dam depends on the average depth of the water and not on the volume of water held back. For example, a wide but shallow lake with a depth of 3 m (10 ft) exerts only half the average pressure that a small 6 m (20 ft) deep pond does. (The total force applied to the longer dam will be greater, due to the greater total surface area for the pressure to act upon. But for a given 5-foot (1.5 m)-wide section of each dam, the 10 ft (3.0 m) deep water will apply one quarter the force of 20 ft (6.1 m) deep water). A person will feel the same pressure whether his/her head is dunked a metre beneath the surface of the water in a small pool or to the same depth in the middle of a large lake. If four vases contain different amounts of water but are all filled to equal depths, then a fish with its head dunked a few centimetres under the surface will be acted on by water pressure that is the same in any of the vases. If the fish swims a few centimetres deeper, the pressure on the fish will increase with depth and be the same no matter which vase the fish is in. If the fish swims to the bottom, the pressure will be greater, but it makes no difference what vase it is in. All vases are filled to equal depths, so the water pressure is the same at the bottom of each vase, regardless of its shape or volume. If water pressure at the bottom of a vase were greater than water pressure at the bottom of a neighboring vase, the greater pressure would force water sideways and then up the narrower vase to a higher level until the pressures at the bottom were equalized. Pressure is depth dependent, not volume dependent, so there is a reason that water seeks its own level.

Restating this as energy equation, the energy per unit volume in an ideal, incompressible liquid is constant throughout its vessel. At the surface, gravitational potential energy is large but liquid pressure energy is low. At the bottom of the vessel, all the gravitational potential energy is converted to pressure energy. The sum of pressure energy and gravitational potential energy per unit volume is constant throughout the volume of the fluid and the two energy components change linearly with the depth.[15] Mathematically, it is described by Bernoulli's equation, where velocity head is zero and comparisons per unit volume in the vessel are

Terms have the same meaning as in section Fluid pressure.

Direction of liquid pressure[edit]


When a liquid presses against a surface, there is a net force that is perpendicular to the surface. Although pressure doesn't have a specific direction, force does. A submerged triangular block has water forced against each point from many directions, but components of the force that are not perpendicular to the surface cancel each other out, leaving only a net perpendicular point.[16] This is why water spurting from a hole in a bucket initially exits the bucket in a direction at right angles to the surface of the bucket in which the hole is located. Then it curves downward due to gravity. If there are three holes in a bucket (top, bottom, and middle), then the force vectors perpendicular to the inner container surface will increase with increasing depth – that is, a greater pressure at the bottom makes it so that the bottom hole will shoot water out the farthest. The force exerted by a fluid on a smooth surface is always at right angles to the surface. The speed of liquid out of the hole is , where h is the depth below the free surface.[16] This is the same speed the water (or anything else) would have if freely falling the same vertical distance h.

Kinematic pressure[edit]

is the kinematic pressure, where is the pressure and constant mass density. The SI unit of P is m2/s2. Kinematic pressure is used in the same manner as kinematic viscosity in order to compute the Navier–Stokes equation without explicitly showing the density .

Navier–Stokes equation with kinematic quantities

See also[edit]




  1. ^ Knight, PhD, Randall D. (2007). "Fluid Mechanics". Physics for Scientists and Engineers: A Strategic Approach (google books) (2nd ed.). San Francisco: Pearson Addison Wesley. p. 1183. ISBN 978-0-321-51671-8. Retrieved 6 April 2020. Pressure itself is not a Force, even though we sometimes talk "informally" about the "force exerted by the pressure. The correct statement is that the Fluid exerts a force on a surface. In addition, Pressure is a scalar, not a vector.
  2. ^ Giancoli, Douglas G. (2004). Physics: principles with applications. Upper Saddle River, N.J.: Pearson Education. ISBN 978-0-13-060620-4.
  3. ^ McNaught, A. D.; Wilkinson, A.; Nic, M.; Jirat, J.; Kosata, B.; Jenkins, A. (2014). IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). 2.3.3. Oxford: Blackwell Scientific Publications. doi:10.1351/goldbook.P04819. ISBN 978-0-9678550-9-7. Archived from the original on 2016-03-04.
  4. ^ "Pressure". Retrieved 2018-06-14.
  5. ^ "14th Conference of the International Bureau of Weights and Measures". Archived from the original on 2007-06-30. Retrieved 2012-03-27.
  6. ^ US Navy (2006). US Navy Diving Manual, 6th revision. United States: US Naval Sea Systems Command. pp. 2–32. Archived from the original on 2008-05-02. Retrieved 2008-06-15.
  7. ^ "U.S. Navy Diving Manual (Chapter 2:Underwater Physics)" (PDF). p. 2.32. Archived (PDF) from the original on 2017-02-02.
  8. ^ "Rules and Style Conventions for Expressing Values of Quantities". NIST. Archived from the original on 2009-07-10. Retrieved 2009-07-07.
  9. ^ NIST, Rules and Style Conventions for Expressing Values of Quantities Archived 2010-02-04 at the Wayback Machine, Sect. 7.4.
  10. ^ Vishwakarma, Ram Gopal (2009). "Einstein's gravity under pressure". Astrophysics and Space Science. 321 (2): 151–156. arXiv:0705.0825. Bibcode:2009Ap&SS.321..151V. doi:10.1007/s10509-009-0016-8. Retrieved 2012-03-27.
  13. ^ Karen Wright (March 2003). "The Physics of Negative Pressure". Discover. Archived from the original on 8 January 2015. Retrieved 31 January 2015.
  14. ^ P. Atkins, J. de Paula Elements of Physical Chemistry, 4th Ed, W. H. Freeman, 2006. ISBN 0-7167-7329-5.
  15. ^ Streeter, V. L., Fluid Mechanics, Example 3.5, McGraw–Hill Inc. (1966), New York.
  16. ^ a b c Hewitt 251 (2006)

External links[edit]