Pressure

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. 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; 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
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 exerted by collisions
Pressure as exerted by particle collisions inside a closed container

Definition

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.[1] The IUPAC recommendation for pressure is a lower-case p.[2] 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

Pressure force area

Mathematically:

[3]

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 surface 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.

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. 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.

Units

Barometer mercury column hg
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;[4] before that, pressure in SI was expressed simply 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 (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:

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 most other fields, where the hecto- prefix is rarely used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because pressure in the ocean increases by approximately one decibar per metre depth.

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.

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, millimetres of mercury or inches of mercury). The most common choices are mercury (Hg) and water; 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, 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 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 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 (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[5] (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.[6]

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.[7] 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
      2
      O
      ), centimetre (cm H
      2
      O
      ), metre, inch, and foot of water;
  • imperial and customary units:
  • non-SI metric units:
    • bar, decibar, millibar,
      • msw (metres sea water), used in underwater diving, particularly in connection with diving pressure exposure and decompression,
    • 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).
Pressure units
Pascal Bar Technical atmosphere Standard atmosphere Torr Pounds per square inch
(Pa) (bar) (at) (atm) (Torr) (lbf/in2)
1 Pa ≡ 1 N/m2 10−5 1.0197×10−5 9.8692×10−6 7.5006×10−3 0.000 145 037 737 730
1 bar 105 ≡ 100 kPa

≡ 106 dyn/cm2

1.0197 0.98692 750.06 14.503 773 773 022
1 at 98066.5 0.980665 ≡ 1 kgf/cm2 0.967 841 105 354 1 735.559 240 1 14.223 343 307 120 3
1 atm 101325 1.01325 1.0332 1 760 14.695 948 775 514 2
1 Torr 133.322 368 421 0.001 333 224 0.001 359 51 1/760 ≈ 0.001 315 789 1 Torr

≈ 1 mmHg

0.019 336 775
1 lbf/in2 6894.757 293 168 0.068 947 573 0.070 306 958 0.068 045 964 51.714 932 572 ≡ 1 lbf/in2
Pressure units
Pressure units as circles in log scale. 4 graphs show scaled P units to unitary mTorr, Pa, mbar, bar. A circle is to imagine a bubble, that such pressure would occupy.

Examples

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

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 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.

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 "220 kPa (32 psi)", 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 psi). In technical work, this is written "a gauge 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 (gauge)" or "kPa (absolute)", is permitted. In non-SI technical work, a gauge pressure of 32 psi (220 kPa) 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.[8]

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

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 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 a very small point (becoming less true as we approach the atomic scale), and 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 (at right angle) 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 (see stress–energy tensor) 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.[9]

Types

Fluid pressure

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.)

Defekter unterflurhydrant goettingen
Water shooting out a damaged hydrant 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.

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 negligible changes in the pressure. Such conditions conform with principles of fluid statics. 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 dynamics.

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[10] and incompressible.[10] An ideal fluid is a fluid in which there is no friction, it is inviscid [10] (zero viscosity).[10] The equation for all points of a system filled with a constant-density fluid is[11]

where:

p = pressure of the fluid,
= ρg = density · acceleration of gravity = specific weight of the fluid,[10]
v = velocity of the fluid,
g = acceleration of gravity,
z = elevation,
= pressure head,
= velocity head.

Applications

Explosion or deflagration pressures

Explosion or deflagration pressures are the result of the ignition of explosive gases, mists, dust/air suspensions, in unconfined and confined spaces.

Negative pressures

13-07-23-kienbaum-unterdruckkammer-33
Low-pressure chamber in Bundesleistungszentrum Kienbaum, Germany

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 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.[12]
  • The Casimir effect can create a small attractive force due to interactions with vacuum energy; this force is sometimes termed "vacuum pressure" (not to be confused with the negative gauge pressure of a vacuum).
  • For non-isotropic stresses in rigid bodies, depending on how the orientation of a surface is chosen, the same distribution of forces may have a component of positive pressure along one surface normal, with a component of negative pressure acting along another surface normal.
    • The stresses in an electromagnetic field are generally non-isotropic, with the pressure normal to one surface element (the normal stress) being negative, and positive for surface elements perpendicular to this.
  • In the cosmological constant.

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:

where

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

The pressure of a moving fluid can be measured using a Pitot tube, 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 pressures or stagnation pressures.

Surface pressure and surface tension

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 law, πA = k, at constant temperature.

Surface tension is another example of surface pressure, but with a reversed sign, because "tension" is the opposite to "pressure".

Pressure of an ideal gas

In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume:

where:

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.[13]

Vapour pressure

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.

The atmospheric pressure boiling point 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 vapour bubbles inside the bulk of the substance. Bubble 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 pressure.

Liquid pressure

When a person swims under the water, water pressure is felt acting on the person's eardrums. The deeper that person swims, the greater the pressure. The pressure felt is due to the weight of the water above the person. As someone swims deeper, there is more water above the person and therefore greater pressure. The pressure a liquid exerts depends on its depth.

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:

where:

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 a liquid exerts against the sides and bottom of a container depends on the density and the depth of the liquid. If atmospheric pressure is neglected, liquid pressure against the bottom is twice as great at twice the depth; at three times the depth, the liquid pressure is threefold; etc. Or, if the liquid is two or three times as dense, the liquid pressure is correspondingly two or three times as great for any given depth. Liquids are practically incompressible – that is, their volume can hardly be changed by pressure (water volume decreases by only 50 millionths of its original volume for each atmospheric increase in pressure). Thus, except for small changes produced by temperature, the density of a particular liquid is practically the same at all depths.

Atmospheric pressure pressing on the surface of a liquid must be taken into account when trying to discover the total pressure acting on a liquid. The total pressure of a liquid, then, is ρgh plus the pressure of the atmosphere. When this distinction is important, the term total pressure is used. Otherwise, discussions of liquid pressure refer to pressure without regard to the normally ever-present atmospheric pressure.

It is important to recognize that 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 (note that 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) section of each dam, the 10 ft (3.0 m) deep water will apply half 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.[14] 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

An experimentally determined fact about liquid pressure is that it is exerted equally in all directions.[15] If someone is submerged in water, no matter which way that person tilts his/her head, the person will feel the same amount of water pressure on his/her ears. Because a liquid can flow, this pressure isn't only downward. Pressure is seen acting sideways when water spurts sideways from a leak in the side of an upright can. Pressure also acts upward, as demonstrated when someone tries to push a beach ball beneath the surface of the water. The bottom of a boat is pushed upward by water pressure (buoyancy).

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.[15] 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.[15] This is the same speed the water (or anything else) would have if freely falling the same vertical distance h.

Kinematic pressure

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 Navier–Stokes equation without explicitly showing the density .

Navier–Stokes equation with kinematic quantities

See also

Notes

  1. ^ The preferred spelling varies by country and even by industry. Further, both spellings are often used within a particular industry or country. Industries in British English-speaking countries typically use the "gauge" spelling.

References

  1. ^ Giancoli, Douglas G. (2004). Physics: principles with applications. Upper Saddle River, N.J.: Pearson Education. ISBN 978-0-13-060620-4.
  2. ^ 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.
  3. ^ "Pressure". Retrieved 2018-06-14.
  4. ^ "14th Conference of the International Bureau of Weights and Measures". Bipm.fr. Archived from the original on 2007-06-30. Retrieved 2012-03-27.
  5. ^ 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.
  6. ^ "U.S. Navy Diving Manual (Chapter 2:Underwater Physics)" (PDF). p. 2.32. Archived (PDF) from the original on 2017-02-02.
  7. ^ "Rules and Style Conventions for Expressing Values of Quantities". NIST. Archived from the original on 2009-07-10. Retrieved 2009-07-07.
  8. ^ NIST, Rules and Style Conventions for Expressing Values of Quantities Archived 2010-02-04 at the Wayback Machine, Sect. 7.4.
  9. ^ 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.
  10. ^ a b c d e Finnemore, John, E. and Joseph B. Franzini (2002). Fluid Mechanics: With Engineering Applications. New York: McGraw Hill, Inc. pp. 14–29. ISBN 978-0-07-243202-2.CS1 maint: Multiple names: authors list (link)
  11. ^ NCEES (2011). Fundamentals of Engineering: Supplied Reference Handbook. Clemson, South Carolina: NCEES. p. 64. ISBN 978-1-932613-59-9.
  12. ^ Karen Wright (March 2003). "The Physics of Negative Pressure". Discover. Archived from the original on 8 January 2015. Retrieved 31 January 2015.
  13. ^ P. Atkins, J. de Paula Elements of Physical Chemistry, 4th Ed, W. H. Freeman, 2006. ISBN 0-7167-7329-5.
  14. ^ Streeter, V. L., Fluid Mechanics, Example 3.5, McGraw–Hill Inc. (1966), New York.
  15. ^ a b c Hewitt 251 (2006)

External links

Bar (unit)

The bar is a metric unit of pressure, but is not approved as part of the International System of Units (SI). It is defined as exactly equal to 100,000 Pa, which is slightly less than the current average atmospheric pressure on Earth at sea level.The bar and the millibar were introduced by the Norwegian meteorologist Vilhelm Bjerknes, who was a founder of the modern practice of weather forecasting.The International Bureau of Weights and Measures (BIPM) lists the bar as one of the "non-SI units [that authors] should have the freedom to use", but has declined to include it among the "Non-SI units accepted for use with the SI". The bar has been legally recognised in countries of the European Union since 2004. The US National Institute of Standards and Technology (NIST) deprecates its use except for "limited use in meteorology" and lists it as one of several units that "must not be introduced in fields where they are not presently used". The International Astronomical Union (IAU) also lists it under "Non-SI units and symbols whose continued use is deprecated".Units derived from the bar include the megabar (symbol: Mbar), kilobar (symbol: kbar), decibar (symbol: dbar), centibar (symbol: cbar), and millibar (symbol: mbar or mb). The notation bar(g), though deprecated by various bodies, represents gauge pressure, i.e., pressure in bars above ambient or atmospheric pressure.

Bernoulli's principle

In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler who derived Bernoulli's equation in its usual form in 1752. The principle is only applicable for isentropic flows: when the effects of irreversible processes (like turbulence) and non-adiabatic processes (e.g. heat radiation) are small and can be neglected.

Bernoulli's principle can be applied to various types of fluid flow, resulting in various forms of Bernoulli's equation; there are different forms of Bernoulli's equation for different types of flow. The simple form of Bernoulli's equation is valid for incompressible flows (e.g. most liquid flows and gases moving at low Mach number). More advanced forms may be applied to compressible flows at higher Mach numbers (see the derivations of the Bernoulli equation).

Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy, potential energy and internal energy remains constant. Thus an increase in the speed of the fluid – implying an increase in its kinetic energy (dynamic pressure) – occurs with a simultaneous decrease in (the sum of) its potential energy (including the static pressure) and internal energy. If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ρ g h) is the same everywhere.Bernoulli's principle can also be derived directly from Isaac Newton's Second Law of Motion. If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline.Fluid particles are subject only to pressure and their own weight. If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can only be because the fluid on that section has moved from a region of higher pressure to a region of lower pressure; and if its speed decreases, it can only be because it has moved from a region of lower pressure to a region of higher pressure. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest.

Blood pressure

Blood pressure (BP) is the pressure of circulating blood on the walls of blood vessels. Most of this pressure is due to work done by the heart by pumping blood through the circulatory system. Used without further specification, "blood pressure" usually refers to the pressure in large arteries of the systemic circulation. Blood pressure is usually expressed in terms of the systolic pressure (maximum during one heartbeat) over diastolic pressure (minimum in between two heartbeats) and is measured in millimeters of mercury (mmHg), above the surrounding atmospheric pressure.

Blood pressure is one of the vital signs, along with respiratory rate, heart rate, oxygen saturation, and body temperature. Normal resting blood pressure in an adult is approximately 120 millimetres of mercury (16 kPa) systolic, and 80 millimetres of mercury (11 kPa) diastolic, abbreviated "120/80 mmHg". Globally, the average blood pressure, age standardized, has remained about the same since 1975 to the present, at approx. 127/79 mmHg in men and 122/77 mmHg in women.Traditionally, blood pressure was measured non-invasively using ausculation with a mercury-tube sphygmomanometer. Ausculation is still generally considered to be the gold standard of accuracy for non-invasive blood pressure readings in clinic. However, semi-automated methods have become common, largely due to concerns about potential mercury toxicity, although cost, ease of use and applicability to ambulatory blood pressure or home blood pressure measurements have also influenced this trend. Early automated alternatives to mercury-tube sphygmomanometers were often seriously inaccurate, but modern devices validated to international standards achieve an average difference between two standardized reading methods of 5 mm Hg or less and a standard deviation of less than 8 mm Hg. Most of these semi-automated methods measure blood pressure using oscillometry.Blood pressure is influenced by cardiac output, total peripheral resistance and arterial stiffness and varies depending on situation, emotional state, activity, and relative health/disease states. In the short term, blood pressure is regulated by baroreceptors which act via the brain to influence the nervous and the endocrine systems.

Blood pressure that is too low is called hypotension, and pressure that is consistently high is hypertension. Both have many causes and may be of sudden onset or of long duration. Long-term hypertension is a risk factor for many diseases, including heart disease, stroke and kidney failure. Long-term hypertension is more common than long-term hypotension, which is usually only diagnosed when it causes symptoms.

Boiling point

The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.

The boiling point of a liquid varies depending upon the surrounding environmental pressure. A liquid in a partial vacuum has a lower boiling point than when that liquid is at atmospheric pressure. A liquid at high pressure has a higher boiling point than when that liquid is at atmospheric pressure. For example, water boils at 100 °C (212 °F) at sea level, but at 93.4 °C (200.1 °F) at 1,905 metres (6,250 ft) altitude. For a given pressure, different liquids will boil at different temperatures.

The normal boiling point (also called the atmospheric boiling point or the atmospheric pressure boiling point) of a liquid is the special case in which the vapor pressure of the liquid equals the defined atmospheric pressure at sea level, 1 atmosphere. At that temperature, the vapor pressure of the liquid becomes sufficient to overcome atmospheric pressure and allow bubbles of vapor to form inside the bulk of the liquid. The standard boiling point has been defined by IUPAC since 1982 as the temperature at which boiling occurs under a pressure of 1 bar.The heat of vaporization is the energy required to transform a given quantity (a mol, kg, pound, etc.) of a substance from a liquid into a gas at a given pressure (often atmospheric pressure).

Liquids may change to a vapor at temperatures below their boiling points through the process of evaporation. Evaporation is a surface phenomenon in which molecules located near the liquid's edge, not contained by enough liquid pressure on that side, escape into the surroundings as vapor. On the other hand, boiling is a process in which molecules anywhere in the liquid escape, resulting in the formation of vapor bubbles within the liquid.

Edema

Edema, also spelled oedema or œdema, is an abnormal accumulation of fluid in the interstitium, located beneath the skin and in the cavities of the body, which can cause severe pain. Clinically, hyperaldosteronism, edema manifests as swelling. The amount of interstitial fluid is determined by the balance of fluid homeostasis and the increased secretion of fluid into the interstitium. The word is from Greek οἴδημα oídēma meaning "swelling". The condition is also known (mostly archaic) as dropsy.

Hypertension

Hypertension (HTN or HT), also known as high blood pressure (HBP), is a long-term medical condition in which the blood pressure in the arteries is persistently elevated. High blood pressure typically does not cause symptoms. Long-term high blood pressure, however, is a major risk factor for coronary artery disease, stroke, heart failure, atrial fibrillation, peripheral vascular disease, vision loss, chronic kidney disease, and dementia.High blood pressure is classified as either primary (essential) high blood pressure or secondary high blood pressure. About 90–95% of cases are primary, defined as high blood pressure due to nonspecific lifestyle and genetic factors. Lifestyle factors that increase the risk include excess salt in the diet, excess body weight, smoking, and alcohol use. The remaining 5–10% of cases are categorized as secondary high blood pressure, defined as high blood pressure due to an identifiable cause, such as chronic kidney disease, narrowing of the kidney arteries, an endocrine disorder, or the use of birth control pills.Blood pressure is expressed by two measurements, the systolic and diastolic pressures, which are the maximum and minimum pressures, respectively. For most adults, normal blood pressure at rest is within the range of 100–130 millimeters mercury (mmHg) systolic and 60–80 mmHg diastolic. For most adults, high blood pressure is present if the resting blood pressure is persistently at or above 130/80 or 140/90 mmHg. Different numbers apply to children. Ambulatory blood pressure monitoring over a 24-hour period appears more accurate than office-based blood pressure measurement.Lifestyle changes and medications can lower blood pressure and decrease the risk of health complications. Lifestyle changes include weight loss, physical exercise, decreased salt intake, reducing alcohol intake, and a healthy diet. If lifestyle changes are not sufficient then blood pressure medications are used. Up to three medications can control blood pressure in 90% of people. The treatment of moderately high arterial blood pressure (defined as >160/100 mmHg) with medications is associated with an improved life expectancy. The effect of treatment of blood pressure between 130/80 mmHg and 160/100 mmHg is less clear, with some reviews finding benefit and others finding unclear benefit. High blood pressure affects between 16 and 37% of the population globally. In 2010 hypertension was believed to have been a factor in 18% of all deaths (9.4 million globally).

Hypotension

Hypotension is low blood pressure, especially in the arteries of the left sided systemic circulation. Blood pressure is the force of blood pushing against the walls of the arteries as the heart pumps out blood. A systolic blood pressure of less than 90 millimeters of mercury (mm Hg) or diastolic of less than 60 mm Hg is generally considered to be hypotension. However, in practice, blood pressure is considered too low only if noticeable symptoms are present.Hypotension is the opposite of hypertension, which is high blood pressure. It is best understood as a physiological state, rather than a disease. Severely low blood pressure can deprive the brain and other vital organs of oxygen and nutrients, leading to a life-threatening condition called shock.

For some people who exercise and are in top physical condition, low blood pressure is a sign of good health and fitness. A single session of exercise can induce hypotension and water-based exercise can induce important hypotension response.

For many people, excessively low blood pressure can cause dizziness and fainting or indicate serious heart, endocrine or neurological disorders.

Treatment of hypotension may include the use of intravenous fluids or vasopressors. When using vasopressors, trying to achieve a mean arterial pressure (MAP) of greater than 70 mm Hg does not appear to result in better outcomes than trying to achieve a MAP of greater than 65 mm Hg in adults.

Osmosis

Osmosis () is the spontaneous net movement of solvent molecules through a selectively permeable membrane into a region of higher solute concentration, in the direction that tends to equalize the solute concentrations on the two sides. It may also be used to describe a physical process in which any solvent moves across a selectively permeable membrane (permeable to the solvent, but not the solute) separating two solutions of different concentrations. Osmosis can be made to do work. Osmotic pressure is defined as the external pressure required to be applied so that there is no net movement of solvent across the membrane. Osmotic pressure is a colligative property, meaning that the osmotic pressure depends on the molar concentration of the solute but not on its identity.

Osmosis is a vital process in biological systems, as biological membranes are semipermeable. In general, these membranes are impermeable to large and polar molecules, such as ions, proteins, and polysaccharides, while being permeable to non-polar or hydrophobic molecules like lipids as well as to small molecules like oxygen, carbon dioxide, nitrogen, and nitric oxide. Permeability depends on solubility, charge, or chemistry, as well as solute size. Water molecules travel through the plasma membrane, tonoplast membrane (vacuole) or protoplast by diffusing across the phospholipid bilayer via aquaporins (small transmembrane proteins similar to those responsible for facilitated diffusion and ion channels). Osmosis provides the primary means by which water is transported into and out of cells. The turgor pressure of a cell is largely maintained by osmosis across the cell membrane between the cell interior and its relatively hypotonic environment.

Oxygen

Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group on the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as well as with other compounds. By mass, oxygen is the third-most abundant element in the universe, after hydrogen and helium. At standard temperature and pressure, two atoms of the element bind to form dioxygen, a colorless and odorless diatomic gas with the formula O2. Diatomic oxygen gas constitutes 20.8% of the Earth's atmosphere. As compounds including oxides, the element makes up almost half of the Earth's crust.

Dioxygen is used in cellular respiration and many major classes of organic molecules in living organisms contain oxygen, such as proteins, nucleic acids, carbohydrates, and fats, as do the major constituent inorganic compounds of animal shells, teeth, and bone. Most of the mass of living organisms is oxygen as a component of water, the major constituent of lifeforms. Oxygen is continuously replenished in Earth's atmosphere by photosynthesis, which uses the energy of sunlight to produce oxygen from water and carbon dioxide. Oxygen is too chemically reactive to remain a free element in air without being continuously replenished by the photosynthetic action of living organisms. Another form (allotrope) of oxygen, ozone (O3), strongly absorbs ultraviolet UVB radiation and the high-altitude ozone layer helps protect the biosphere from ultraviolet radiation. However, ozone present at the surface is a byproduct of smog and thus a pollutant.

Oxygen was isolated by Michael Sendivogius before 1604, but it is commonly believed that the element was discovered independently by Carl Wilhelm Scheele, in Uppsala, in 1773 or earlier, and Joseph Priestley in Wiltshire, in 1774. Priority is often given for Priestley because his work was published first. Priestley, however, called oxygen "dephlogisticated air", and did not recognize it as a chemical element. The name oxygen was coined in 1777 by Antoine Lavoisier, who first recognized oxygen as a chemical element and correctly characterized the role it plays in combustion.

Common uses of oxygen include production of steel, plastics and textiles, brazing, welding and cutting of steels and other metals, rocket propellant, oxygen therapy, and life support systems in aircraft, submarines, spaceflight and diving.

Pascal (unit)

The pascal (symbol: Pa) is the SI derived unit of pressure used to quantify internal pressure, stress, Young's modulus and ultimate tensile strength. It is defined as one newton per square metre. It is named after the French polymath Blaise Pascal.

Common multiple units of the pascal are the hectopascal (1 hPa = 100 Pa) which is equal to one millibar, and the kilopascal (1 kPa = 1000 Pa) which is equal to one centibar.

The unit of measurement called standard atmosphere (atm) is defined as 101325 Pa. Meteorological reports in the United States typically state atmospheric pressure in millibars. In Canada these reports are given in kilopascals.

Relative humidity

Relative humidity (RH) is the ratio of the partial pressure of water vapor to the equilibrium vapor pressure of water at a given temperature. Relative humidity depends on temperature and the pressure of the system of interest. The same amount of water vapor results in higher relative humidity in cool air than warm air. A related parameter is that of dewpoint.

Respiratory system

The respiratory system (also respiratory apparatus, ventilatory system) is a biological system consisting of specific organs and structures used for gas exchange in animals and plants. The anatomy and physiology that make this happen varies greatly, depending on the size of the organism, the environment in which it lives and its evolutionary history. In land animals the respiratory surface is internalized as linings of the lungs. Gas exchange in the lungs occurs in millions of small air sacs called alveoli in mammals and reptiles, but atria in birds. These microscopic air sacs have a very rich blood supply, thus bringing the air into close contact with the blood. These air sacs communicate with the external environment via a system of airways, or hollow tubes, of which the largest is the trachea, which branches in the middle of the chest into the two main bronchi. These enter the lungs where they branch into progressively narrower secondary and tertiary bronchi that branch into numerous smaller tubes, the bronchioles. In birds the bronchioles are termed parabronchi. It is the bronchioles, or parabronchi that generally open into the microscopic alveoli in mammals and atria in birds. Air has to be pumped from the environment into the alveoli or atria by the process of breathing which involves the muscles of respiration.

In most fish, and a number of other aquatic animals (both vertebrates and invertebrates) the respiratory system consists of gills, which are either partially or completely external organs, bathed in the watery environment. This water flows over the gills by a variety of active or passive means. Gas exchange takes place in the gills which consist of thin or very flat filaments and lammelae which expose a very large surface area of highly vascularized tissue to the water.

Other animals, such as insects, have respiratory systems with very simple anatomical features, and in amphibians even the skin plays a vital role in gas exchange. Plants also have respiratory systems but the directionality of gas exchange can be opposite to that in animals. The respiratory system in plants includes anatomical features such as stomata, that are found in various parts of the plant.

Sepsis

Sepsis is a life-threatening condition that arises when the body's response to infection causes injury to its own tissues and organs. Common signs and symptoms include fever, increased heart rate, increased breathing rate, and confusion. There may also be symptoms related to a specific infection, such as a cough with pneumonia, or painful urination with a kidney infection. In the very young, old, and people with a weakened immune system, there may be no symptoms of a specific infection and the body temperature may be low or normal, rather than high. Severe sepsis is sepsis causing poor organ function or insufficient blood flow. Insufficient blood flow may be evident by low blood pressure, high blood lactate, or low urine output. Septic shock is low blood pressure due to sepsis that does not improve after fluid replacement.Sepsis is caused by an inflammatory immune response triggered by an infection. Most commonly, the infection is bacterial, but it may also be fungal, viral, or protozoan. Common locations for the primary infection include the lungs, brain, urinary tract, skin, and abdominal organs. Risk factors include very young age, older age, a weakened immune system from conditions such as cancer or diabetes, major trauma, or burns. An older method of diagnosis was based on meeting at least two systemic inflammatory response syndrome (SIRS) criteria due to a presumed infection. In 2016, SIRS was replaced with a shortened sequential organ failure assessment score (SOFA score) known as the quick SOFA score (qSOFA) which is two of the following three: increased breathing rate, change in level of consciousness, and low blood pressure. Blood cultures are recommended preferably before antibiotics are started, however, infection of the blood is not required for the diagnosis. Medical imaging should be used to look for the possible location of infection. Other potential causes of similar signs and symptoms include anaphylaxis, adrenal insufficiency, low blood volume, heart failure, and pulmonary embolism.Sepsis is usually treated with intravenous fluids and antibiotics. Typically, antibiotics are given as soon as possible. Often, ongoing care is performed in an intensive care unit. If fluid replacement is not enough to maintain blood pressure, medications that raise blood pressure may be used. Mechanical ventilation and dialysis may be needed to support the function of the lungs and kidneys, respectively. To guide treatment, a central venous catheter and an arterial catheter may be placed for access to the bloodstream. Other measurements such as cardiac output and superior vena cava oxygen saturation may be used. People with sepsis need preventive measures for deep vein thrombosis, stress ulcers and pressure ulcers, unless other conditions prevent such interventions. Some might benefit from tight control of blood sugar levels with insulin. The use of corticosteroids is controversial, with some reviews finding benefit, and others not.Disease severity partly determines the outcome. The risk of death from sepsis is as high as 30%, from severe sepsis as high as 50%, and from septic shock as high as 80%. The number of cases worldwide is unknown as there is little data from the developing world. Estimates suggest sepsis affects millions of people a year. In the developed world approximately 0.2 to 3 people per 1000 are affected by sepsis yearly, resulting in about a million cases per year in the United States. Rates of disease have been increasing. Sepsis is more common among males than females. The medical condition has been described since the time of Hippocrates. The terms "septicemia" and "blood poisoning" have been used in various ways and are no longer recommended.

Sound

In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid.

In human physiology and psychology, sound is the reception of such waves and their perception by the brain. Humans can only hear sound waves as distinct pitches when the frequency lies between about 20 Hz and 20 kHz. Sound waves above 20 kHz are known as ultrasound and is not perceptible by humans. Sound waves below 20 Hz are known as infrasound. Different animal species have varying hearing ranges.

Standard conditions for temperature and pressure

Standard conditions for temperature and pressure are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST), although these are not universally accepted standards. Other organizations have established a variety of alternative definitions for their standard reference conditions.

In chemistry, IUPAC changed the definition of standard temperature and pressure (STP) in 1982:

Until 1982, STP was defined as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of exactly 1 atm (101.325 kPa).

Since 1982, STP is defined as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of exactly 105 Pa (100 kPa, 1 bar).STP should not be confused with the standard state commonly used in thermodynamic evaluations of the Gibbs energy of a reaction.

NIST uses a temperature of 20 °C (293.15 K, 68 °F) and an absolute pressure of 1 atm (14.696 psi, 101.325 kPa). This standard is also called normal temperature and pressure (abbreviated as NTP).

The International Standard Metric Conditions for natural gas and similar fluids are 288.15 K (15.00 °C; 59.00 °F) and 101.325 kPa.In industry and commerce, standard conditions for temperature and pressure are often necessary to define the standard reference conditions to express the volumes of gases and liquids and related quantities such as the rate of volumetric flow (the volumes of gases vary significantly with temperature and pressure) – standard cubic meters per second (sm3/s), and normal cubic meters per second (nm3/s). However, many technical publications (books, journals, advertisements for equipment and machinery) simply state "standard conditions" without specifying them, often leading to confusion and errors. Good practice always incorporates the reference conditions of temperature and pressure.

Steam engine

A steam engine is a heat engine that performs mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a cylinder. This pushing force is transformed, by a connecting rod and flywheel, into rotational force for work. The term "steam engine" is generally applied only to reciprocating engines as just described, not to the steam turbine.

Steam engines are external combustion engines, where the working fluid is separated from the combustion products. The ideal thermodynamic cycle used to analyze this process is called the Rankine cycle.

In general usage, the term steam engine can refer to either complete steam plants (including boilers etc.) such as railway steam locomotives and portable engines, or may refer to the piston or turbine machinery alone, as in the beam engine and stationary steam engine.

Steam-driven devices were known as early as the aeliopile in the first century AD, with a few other uses recorded in the 16th and 17th century. Thomas Savery's dewatering pump used steam pressure operating directly on water. The first commercially-successful engine that could transmit continuous power to a machine was developed in 1712 by Thomas Newcomen. James Watt made a critical improvement by removing spent steam to a separate vessel for condensation, greatly improving the amount of work obtained per unit of fuel consumed. By the 19th century, stationary steam engines powered the factories of the Industrial Revolution. Steam engines replaced sail for ships, and steam locomotives operated on the railways.

Reciprocating piston type steam engines were the dominant source of power until the early 20th century, when advances in the design of electric motors and internal combustion engines gradually resulted in the replacement of reciprocating (piston) steam engines in commercial usage. Steam turbines replaced reciprocating engines in power generation, due to lower cost, higher operating speed, and higher efficiency.

Turbocharger

A turbocharger, colloquially known as a turbo, is a turbine-driven forced induction device that increases an internal combustion engine's efficiency and power output by forcing extra compressed air into the combustion chamber. This improvement over a naturally aspirated engine's power output is due to the fact that the compressor can force more air—and proportionately more fuel—into the combustion chamber than atmospheric pressure (and for that matter, ram air intakes) alone.

Turbochargers were originally known as turbosuperchargers when all forced induction devices were classified as superchargers. Today the term "supercharger" is typically applied only to mechanically driven forced induction devices. The key difference between a turbocharger and a conventional supercharger is that a supercharger is mechanically driven by the engine, often through a belt connected to the crankshaft, whereas a turbocharger is powered by a turbine driven by the engine's exhaust gas. Compared with a mechanically driven supercharger, turbochargers tend to be more efficient, but less responsive. Twincharger refers to an engine with both a supercharger and a turbocharger.

Turbochargers are commonly used on truck, car, train, aircraft, and construction equipment engines. They are most often used with Otto cycle and Diesel cycle internal combustion engines.

Vapor pressure

Vapor pressure (or vapour pressure in British spelling) or equilibrium vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indication of a liquid's evaporation rate. It relates to the tendency of particles to escape from the liquid (or a solid). A substance with a high vapor pressure at normal temperatures is often referred to as volatile. The pressure exhibited by vapor present above a liquid surface is known as vapor pressure. As the temperature of a liquid increases, the kinetic energy of its molecules also increases. As the kinetic energy of the molecules increases, the number of molecules transitioning into a vapor also increases, thereby increasing the vapor pressure.

The vapor pressure of any substance increases non-linearly with temperature according to the Clausius–Clapeyron relation. The atmospheric pressure boiling point 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. Bubble formation deeper in the liquid requires a higher temperature due to the higher fluid pressure, because fluid pressure increases above the atmospheric pressure as the depth increases. More important at shallow depths is the higher temperature required to start bubble formation. The surface tension of the bubble wall leads to an overpressure in the very small, initial bubbles. Thus, thermometer calibration should not rely on the temperature in boiling water.

The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called partial pressure. For example, air at sea level, and saturated with water vapor at 20 °C, has partial pressures of about 2.3 kPa of water, 78 kPa of nitrogen, 21 kPa of oxygen and 0.9 kPa of argon, totaling 102.2 kPa, making the basis for standard atmospheric pressure.

Derivation of this equation
This is derived from the definitions of pressure and weight density. Consider an area at the bottom of a vessel of liquid. The weight of the column of liquid directly above this area produces pressure. From the definition

we can express this weight of liquid as

where the volume of the column is simply the area multiplied by the depth. Then we have

With the "area" in the numerator and the "area" in the denominator canceling each other out, we are left with

Written with symbols, this is our original equation:

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