**Pressure ** is the force per unit

areaArea is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

applied in a direction

perpendicularIn geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...

to the surface of an object.

Gauge pressureMany techniques have been developed for the measurement of pressure and vacuum. Instruments used to measure pressure are called pressure gauges or vacuum gauges....

is the pressure relative to the local atmospheric or ambient pressure.

## Definition

Pressure is the effect of a force applied to a surface. Pressure is the amount of force acting per unit area. The symbol of pressure is

*P*.

### Formula

Mathematically:

where:

*P* is the pressure,
*F* is the normal forceIn mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...

,
*A* is the area of the surface area on contact

Pressure is a

scalarIn physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...

quantity. It relates the

vector surface elementA surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...

(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.

It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. It is the force given by the previous relationship to the quantity that has a direction, not the pressure. 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 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

thermodynamicsThermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

, and it is

conjugateIn thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature/entropy or pressure/volume. In fact all thermodynamic potentials are expressed in terms of conjugate pairs....

to volume.

### Units

The

SISi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

unit for pressure is the

pascalThe pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...

(Pa), equal to one newton per square meter (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 simply as N/m

^{2}.

Non-SI measures such as pounds per square inch and

*bar*The bar is a unit of pressure equal to 100 kilopascals, and roughly equal to the atmospheric pressure on Earth at sea level. Other units derived from the bar are the megabar , kilobar , decibar , centibar , and millibar...

are used in some parts of the world, primarily in the United States of America. The cgs unit of pressure is the

baryeThe barye , or sometimes barad, barrie, bary, baryd, baryed, or barie, is the centimetre-gram-second unit of pressure. It is equal to 1 dyne per square centimetre....

(ba), equal to 1 dyn·cm

^{−2} or 0.1 Pa. Pressure is sometimes expressed in grams-force/cm

^{2}, or as kg/cm

^{2} 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 atmosphereA technical atmosphere is a non-SI unit of pressure equal to one kilogram-force per square centimeter.The symbol "at" clashes with that of the katal , the SI unit of catalytic activity; a kilotechnical atmosphere would have the symbol "kat", indistinguishable from the symbol for the katal...

(symbol: at) is 1 kgf/cm

^{2} (14.223 psi).

Since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume measured in J·m

^{−3}, related to energy density.

Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilo pascals (kPa) in most other fields, where the hecto- prefix is rarely used. The

inch of mercuryInches of mercury, ' is a unit of measurement for pressure. It is still widely used for barometric pressure in weather reports, refrigeration and aviation in the United States, but is seldom used elsewhere....

is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because an increase in pressure of 1 dbar is approximately equal to an increase in depth of 1 meter.

Scuba diversScuba diving is a form of underwater diving in which a diver uses a scuba set to breathe underwater....

often use a manometric

rule of thumbA rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation. It is an easily learned and easily applied procedure for approximately calculating or recalling some value, or for making some determination...

: the pressure exerted by ten meters depth of water is approximately equal to one atmosphere. The increase in pressure at 34 feet of fresh water or 33 feet of sea water is one atm.

The

standard atmosphereThe standard atmosphere is an international reference pressure defined as 101325 Pa and formerly used as unit of pressure. For practical purposes it has been replaced by the bar which is 105 Pa...

(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 = 101,325 Pa
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...

= 101.325 kPa = 1,013.25 hPa.

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 (e.g., centimetres of water, mm or inches of mercury). The most common choices are

mercuryMercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...

(Hg) and

waterWater is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

; water is nontoxic and readily available, while mercury's high density allows a shorter column (and so a smaller manometer) 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

*p = ρgh*. 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

millimeters of mercuryThe torr is a non-SI unit of pressure with the ratio of 760 to 1 standard atmosphere, chosen to be roughly equal to the fluid pressure exerted by a millimetre of mercury, i.e., a pressure of 1 torr is approximately equal to 1 mmHg...

or inches 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 mmHg (millimeter of mercury) is 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 pressureBlood pressure is the pressure exerted by circulating blood upon the walls of blood vessels, and is one of the principal vital signs. When used without further specification, "blood pressure" usually refers to the arterial pressure of the systemic circulation. During each heartbeat, BP varies...

is measured in millimeters of mercury in most of the world, and lung pressures in centimeters of water are still common.

Gauge pressure is often given in units with 'g' appended, e.g. 'kPag' 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 TechnologyThe National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...

recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure For example, "

*P*_{g} = 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
The standard atmosphere is an international reference pressure defined as 101325 Pa and formerly used as unit of pressure. For practical purposes it has been replaced by the bar which is 105 Pa...

(atm)
- manometric units:
- centimeter, inch, and millimeter of mercury (torr
The torr is a non-SI unit of pressure with the ratio of 760 to 1 standard atmosphere, chosen to be roughly equal to the fluid pressure exerted by a millimetre of mercury, i.e., a pressure of 1 torr is approximately equal to 1 mmHg...

)

}Height of equivalent column of water, including millimeter (mm H

_{2}O), centimeter (cm H

_{2}O), meter, inch, and foot of water

- customary units:
- kip
A kip is a non-SI unit of force that equals 1,000 pounds-force, used primarily by architects and engineers to measure engineering loads. Although uncommon, it is occasionally also considered a unit of mass, equal to 1,000 pounds, i.e. one half of a U.S. ton...

, tonThe ton is a unit of measure. It has a long history and has acquired a number of meanings and uses over the years. It is used principally as a unit of weight, and as a unit of volume. It can also be used as a measure of energy, for truck classification, or as a colloquial term.It is derived from...

-force (short), ton-force (long), pound-force, ounce-force, and poundalThe poundal is a unit of force that is part of the foot-pound-second system of units, in Imperial units introduced in 1877, and is from the specialized subsystem of English Absolut ....

per square inch
- pound-force, ton-force (short), and ton-force (long)

- non-SI metric units:
- bar
The bar is a unit of pressure equal to 100 kilopascals, and roughly equal to the atmospheric pressure on Earth at sea level. Other units derived from the bar are the megabar , kilobar , decibar , centibar , and millibar...

, decibar, millibar
- kilogram-force, or kilopond, per square centimetre (technical atmosphere
A technical atmosphere is a non-SI unit of pressure equal to one kilogram-force per square centimeter.The symbol "at" clashes with that of the katal , the SI unit of catalytic activity; a kilotechnical atmosphere would have the symbol "kat", indistinguishable from the symbol for the katal...

)
- gram-force and tonne-force (metric ton-force) per square centimetre
- barye
The barye , or sometimes barad, barrie, bary, baryd, baryed, or barie, is the centimetre-gram-second unit of pressure. It is equal to 1 dyne per square centimetre....

(dyneIn physics, the dyne is a unit of force specified in the centimetre-gram-second system of units, a predecessor of the modern SI. One dyne is equal to exactly 10 µN...

per square centimetre)
- kilogram-force and tonne-force per square metre
- sthene
The sthène is the unit of force in the metre-tonne-second system of units , invented in France and used in the Soviet Union 1933-1955. The symbol is sn. It is also used to measure thrust. It is approximately 224 pounds force.1 sn := 1 t·m/s²...

per square metre (piezeThe pièze is the unit of pressure in the metre-tonne-second system of units , used, e.g., in the former Soviet Union 1933-1955. It is defined as one sthène per square metre. The symbol is pz....

)

### 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

thumbtackA drawing pin , thumbtack , or push pin is a short nail or pin with a circular, sometimes domed, head, used to fasten items such as documents to a wall or board for display. Various designs and names are used. They are inserted and removed by hand, hence the terms "thumbtack" and "push pin"...

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

stressIn continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

, pressure is defined as a

scalar quantityIn physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...

.

Another example is of a common

*knife.* If we try to cut a fruit with the flat side it obviously won't cut. But if we take the thin side, it will cut smoothly. The reason is that the flat side has a greater surface area (less pressure) and so it does not cut the fruit. When we take the thin side, the surface area is reduced and so it cuts the fruit easily and quickly. This is one example of a practical application of pressure.

The

gradientIn vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

of pressure is called the

force densityIn fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid...

. For gases, pressure is sometimes measured not as an

**absolute pressure**, but relative to

atmospheric pressureAtmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...

; such measurements are called

**gage pressure** (also spelled

*gauge pressure*). An example of this is the air pressure in an

automobileAn automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...

tireA tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...

, which might be said to be "220

kPaThe pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...

/32psi", but is actually 220 kPa/32 psi above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa/14.7 psi, the absolute pressure in the tire is therefore about 320 kPa/46.7 psi. In technical work, this is written "a gage pressure of 220 kPa/32 psi". 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 (gage)" or "kPa (absolute)", is permitted. In non-

SISi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

technical work, a gage pressure of 32 psi 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 100 kPa, a gas (such as helium) at 200 kPa (gage) (300 kPa [absolute]) is 50 % denser than the same gas at 100 kPa (gage) (200 kPa [absolute]). Focusing on gage values, one might erroneously conclude the first sample had twice the density of the second one.

### Scalar nature

In a static

gasGas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

, the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant

random motionBrownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...

. 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 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

stressIn continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

tensor

**σ**, which relates the vector force

**F** to the

vector area **A** via

This

tensorTensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...

may be divided up into a scalar part (pressure) and a traceless tensor part

shearA shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

. The shear tensor gives the force in directions

*parallel* to the surface, usually due to viscous or frictional forces. 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 relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

pressure increases the strength of a gravitational field (see

stress-energy tensorThe stress–energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields...

) and so adds to the mass-energy cause of gravity. This effect is unnoticeable at every-day pressures but is significant in

neutron starA neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

s, although it has not been experimentally tested.

### Fluid pressure

**Fluid pressure** is the pressure at some point within a

fluidIn physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

, such as water or air.

Fluid pressure occurs in one of two situations:

- 1. an open condition, called "open channel flow"
- a. the ocean, or
- b. swimming pool, or
- c. the atmosphere.

- 2. a closed condition, called closed conduits
- a. water line, or
- b. gas line.

Pressure in open conditions usually can be approximated as the pressure in "static" or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only

negligibleNegligible refers to the quantities so small that they can be ignored when studying the larger effect. Although related to the more mathematical concepts of infinitesimal, the idea of negligibility is particularly useful in practical disciplines like physics, chemistry, mechanical and electronic...

changes in the pressure. Such conditions conform with principles of

fluid staticsFluid statics is the science of fluids at rest, and is a sub-field within fluid mechanics. The term usually refers to the mathematical treatment of the subject. It embraces the study of the conditions under which fluids are at rest in stable equilibrium...

. The pressure at any given point of a non-moving (static) fluid is called the

**hydrostatic pressure**.

Closed bodies of fluid are either "static," when the fluid is not moving, or "dynamic," when the fluid can move as in either a pipe or by compressing an air gap in a closed container. The pressure in closed conditions conforms with the principles of

fluid dynamicsIn physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

.

The concepts of fluid pressure are predominantly attributed to the discoveries of

Blaise Pascal Blaise Pascal , was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen...

and

Daniel BernoulliDaniel Bernoulli was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics...

.

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 and incompressible. An ideal fluid is a fluid in which there is no friction, it is inviscid, zero

viscosityViscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

. The equation is written between any two points in a system that contain the same fluid.

Where:

- p = pressure of the fluid
- γ = ρg= density*acceleration of gravity = specific weight
The specific weight is the weight per unit volume of a material. The symbol of specific weight is γ ....

of the fluid.
- v = velocity of the fluid
- g = acceleration of gravity
- z = elevation

= pressure head

= velocity head

#### Applications

- Artesian well
- Blood pressure
Blood pressure is the pressure exerted by circulating blood upon the walls of blood vessels, and is one of the principal vital signs. When used without further specification, "blood pressure" usually refers to the arterial pressure of the systemic circulation. During each heartbeat, BP varies...

- Hydraulic head
Hydraulic head or piezometric head is a specific measurement of water pressure above a geodetic datum. It is usually measured as a water surface elevation, expressed in units of length, at the entrance of a piezometer...

- Plant cell turgidity
Turgor Pressure or turgidity is the main pressure of the cell contents against the cell wall in plant cells and bacteria cells, determined by the water content of the vacuole, resulting from osmotic pressure, i.e...

- Pythagorean cup
A Pythagorean cup is a form of drinking cup which forces its user to imbibe only in moderation. Credited to Pythagoras of Samos, it allows the user to fill the cup with wine up to a certain level. If the user fills the cup only up to that level he may enjoy his drink in peace...

### Explosion or deflagration pressures

ExplosionAn explosion is a rapid increase in volume and release of energy in an extreme manner, usually with the generation of high temperatures and the release of gases. An explosion creates a shock wave. If the shock wave is a supersonic detonation, then the source of the blast is called a "high explosive"...

or

deflagrationDeflagration is a term describing subsonic combustion that usually propagates through thermal conductivity; hot burning material heats the next layer of cold material and ignites it. Most "fire" found in daily life, from flames to explosions, is deflagration...

pressures are the result of the ignition of explosive

gasGas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

es, mists, dust/air suspensions, in unconfined and confined spaces.

### Negative pressures

While

**pressures** are, in general, positive, there are several situations in which negative pressures may be encountered:

- When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of -21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa).
- When attractive forces (e.g., van der Waals force
In physical chemistry, the van der Waals force , named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral...

s) between the particles of a fluid exceed repulsive forces. Such scenarios are generally unstable since the particles will move closer together until repulsive forces balance attractive forces. Negative pressure exists in the transpiration pull of plants, and is used to suction water even higher than the ten metres that it rises in a pure vacuum.
- The Casimir effect
In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, like capacitors placed a few micrometers apart, without any external electromagnetic field...

can create a small attractive force due to interactions with vacuum energyVacuum energy is an underlying background energy that exists in space even when the space is devoid of matter . The concept of vacuum energy has been deduced from the concept of virtual particles, which is itself derived from the energy-time uncertainty principle...

; this force is sometimes termed 'vacuum pressure' (not to be confused with the negative *gauge pressure* of a vacuum).
- Depending on how the orientation of a surface is chosen, the same distribution of forces may be described either as a positive pressure along one surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...

, or as a negative pressure acting along the opposite surface normal.
- In the cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

.

### Stagnation pressure

Stagnation pressureIn fluid dynamics, stagnation pressure is the static pressure at a stagnation point in a fluid flow.At a stagnation point the fluid velocity is zero and all kinetic energy has been converted into pressure energy . Stagnation pressure is equal to the sum of the free-stream dynamic pressure and...

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 pressureIn fluid mechanics the term static pressure has several uses:* In the design and operation of aircraft, static pressure is the air pressure in the aircraft’s static pressure system....

, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by the

Mach numberMach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...

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 (note: Bernoulli's equation only applies for incompressible, inviscid flow).

The pressure of a moving fluid can be measured using a

Pitot tubeA pitot tube is a pressure measurement instrument used to measure fluid flow velocity. The pitot tube was invented by the French engineer Henri Pitot Ulo in the early 18th century and was modified to its modern form in the mid-19th century by French scientist Henry Darcy...

, or one of its variations such as a

Kiel probeA Kiel probe is a device for measuring total pressure/or temperature in fluid dynamics. It is a variation of a Pitot probe where the inlet is protected by a "shroud". Unlike the Pitot probe, it is not so sensitive to changes in yaw angle, and is therefore useful when the probe's alignment with the...

or

Cobra probeA Cobra probe is a device to measure the pressure of a moving fluid. In this kind of instrument, there are two yaw direction tubes which are chamfered and silver soldered symmetrically on the two sides of a pitot tube. It is otherwise similar to the other kinds of yawmeters....

, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressure or stagnation pressures.

### Surface pressure

There is a two-dimensional analog of pressure – the lateral force per unit length applied on a line perpendicular to the force.

Surface pressure is denoted by π and shares many similar properties with three-dimensional pressure. Properties of surface chemicals can be investigated by measuring pressure/area isotherms, as the two-dimensional analog of

Boyle's lawBoyle's law is one of many gas laws and a special case of the ideal gas law. Boyle's law describes the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system...

,

*πA* =

*k*, at constant temperature.

### Pressure of an ideal gas

In an

ideal gasAn ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...

, molecules have no volume and do not interact. Pressure varies linearly with temperature, volume, and quantity according to the

ideal gas lawThe ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...

,

where:

*P* is the absolute pressure of the gas
*n* is the amount of substanceAmount of substance is a standards-defined quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, and other particles. It is sometimes referred to as chemical amount. The International System of Units defines the amount of substance to be...

*T* is the absolute temperature
*V* is the volume
*R* is the ideal gas constant.

Real gasReal gases – as opposed to a perfect or ideal gas – exhibit properties that cannot be explained entirely using the ideal gas law. To understand the behaviour of real gases, the following must be taken into account:* compressibility effects;...

es exhibit a more complex dependence on the variables of state.

### Vapor pressure

Vapor pressure is the pressure of a

vaporA vapor or vapour is a substance in the gas phase at a temperature lower than its critical point....

in

thermodynamic equilibriumIn thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

with its condensed

phaseIn the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...

s in a closed system. All

liquidLiquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

s and

solidSolid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

s have a tendency to evaporate into a gaseous form, and all

gasGas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

es have a tendency to

condenseCondensation is the change of the physical state of matter from gaseous phase into liquid phase, and is the reverse of vaporization. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition....

back to their liquid or solid form.

The

atmospheric pressureAtmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...

boiling pointThe boiling point of an element or a substance is the temperature at which the vapor pressure of the liquid equals the environmental pressure surrounding the liquid....

of a liquid (also known as the normal boiling point) is the temperature at which the vapor pressure equals the ambient atmospheric pressure. With any incremental increase in that temperature, the vapor pressure becomes sufficient to overcome atmospheric pressure and lift the liquid to form vapor bubbles inside the bulk of the substance.

BubbleA bubble is a globule of one substance in another, usually gas in a liquid.Due to the Marangoni effect, bubbles may remain intact when they reach the surface of the immersive substance.-Common examples:...

formation deeper in the liquid requires a higher pressure, and therefore higher temperature, because the fluid pressure increases above the atmospheric pressure as the depth increases.

The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called

partial vapor pressureIn a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....

.

### Liquid pressure or pressure at depth

Used with liquid columns of constant density or at a depth within a substance (example: pressure at 20 km depth in the Earth).

Where:

*P* is Pressure
*g* is gravity at the surface of overlaying material is density of liquid or overlaying material
*h* is height of liquid or depth within a substance

## See also

- Atmospheric pressure
Atmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...

- Blood pressure
Blood pressure is the pressure exerted by circulating blood upon the walls of blood vessels, and is one of the principal vital signs. When used without further specification, "blood pressure" usually refers to the arterial pressure of the systemic circulation. During each heartbeat, BP varies...

- Boyle's Law
Boyle's law is one of many gas laws and a special case of the ideal gas law. Boyle's law describes the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system...

- Combined gas law
The combined gas law is a gas law which combines Charles's law, Boyle's law, and Gay-Lussac's law. These laws each relate one thermodynamic variable to another mathematically while holding everything else constant. Charles's law states that volume and temperature are directly proportional to each...

- Conversion of units
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.- Process :...

- Critical point (thermodynamics)
In physical chemistry, thermodynamics, chemistry and condensed matter physics, a critical point, also called a critical state, specifies the conditions at which a phase boundary ceases to exist...

- Dynamic pressure
- Hydraulics
Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. In fluid power, hydraulics is used for the generation, control,...

- Internal pressure
Internal pressure is a measure of how the internal energy of a system changes when it expands or contracts at constant temperature. It has the same dimensions as pressure, the SI unit of which is 1 pascal.Internal pressure is usually given the symbol \pi_T...

- Kinetic theory
- Microphone
A microphone is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal. In 1877, Emile Berliner invented the first microphone used as a telephone voice transmitter...

- Orders of magnitude (pressure)
This is a tabulated listing of the orders of magnitude in relation to pressure expressed in pascals....

- Partial pressure
In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....

- Pressure measurement
Many techniques have been developed for the measurement of pressure and vacuum. Instruments used to measure pressure are called pressure gauges or vacuum gauges....

- Pressure sensor
A pressure sensor measures pressure, typically of gases or liquids. Pressure is an expression of the force required to stop a fluid from expanding, and is usually stated in terms of force per unit area. A pressure sensor usually acts as a transducer; it generates a signal as a function of the...

- Sound pressure
Sound pressure or acoustic pressure is the local pressure deviation from the ambient atmospheric pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water...

- Spouting can
The spouting can experiment is a physics experiment designed to show that, according to Torricelli's Law, in a liquid with an open surface, pressure increases with depth. It consists of a tube with three separate holes in and an open surface. The three holes are blocked, then the tube is filled...

- Timeline of temperature and pressure measurement technology
Timeline of temperature and pressure measurement technology A history of temperature measurement and pressure measurement technology.-1500s:* 1592-1593 — Galileo Galilei builds a device showing variation of hotness known as the thermoscope using the contraction of air to draw water up a...

- Units conversion by factor-label
Many, if not most, parameters and measurements in the physical sciences and engineering are expressed as a numerical quantity and a corresponding dimensional unit; for example: 1000 kg/m³, 100 kPa/bar, 50 miles per hour, 1000 Btu/lb. Converting from one dimensional unit to another is often...

- Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

- Vacuum pump
A vacuum pump is a device that removes gas molecules from a sealed volume in order to leave behind a partial vacuum. The first vacuum pump was invented in 1650 by Otto von Guericke.- Types :Pumps can be broadly categorized according to three techniques:...

- Vertical pressure variation
Vertical pressure variation is the variation in pressure as a function of elevation. Depending on the fluid in question and the context being referred to, it may also vary significantly in dimensions perpendicular to elevation as well, and these variations have relevance in the context of pressure...

## External links