1.1 Formula 1.2 Units 1.3 Examples 1.4 Scalar nature
2.1 Fluid pressure
3 See also 4 Notes 5 References 6 External links
Conjugate variables of thermodynamics
Chemical potential Particle number
p = −
displaystyle p=- frac F A ,
is the pressure,
is the magnitude of the normal force,
is the area of the surface on contact.
= − p
= − p
d A .
displaystyle dmathbf F _ n =-p,dmathbf A =-p,mathbf n ,dA.
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.
displaystyle p= frac Ftimes text distance Atimes text distance = frac text work text volume = frac text energy (J) text volume ( text m ^ 3 ) .
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 7005101325000000000♠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
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.
atmosphere (atm) manometric units:
centimetre, inch, millimetre (torr) and micrometre (mTorr, micron) of mercury, height of equivalent column of water, including millimetre (mm H 2O), centimetre (cm H 2O), metre, inch, and foot of water;
imperial and customary units:
kip, short ton-force, long ton-force, pound-force, ounce-force, and poundal per square inch, short ton-force and long ton-force per square inch, fsw (feet sea water) used in underwater diving, particularly in connection with diving pressure exposure and decompression;
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).
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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 6995101970000000000♠1.0197×10−5 6994986919999999999♠9.8692×10−6 6997750060000000000♠7.5006×10−3 6996145037700000000♠1.450377×10−4
1 bar 105 ≡ 100 kPa ≡ 106 dyn/cm2
7000101970000000000♠1.0197 6999986920000000000♠0.98692 7002750060000000000♠750.06 7001145037700000000♠14.50377
1 at 7004980665000000000♠9.80665×104 6999980665000000000♠0.980665 ≡ 1 kgf/cm2 6999967841100000000♠0.9678411 7002735559200000000♠735.5592 7001142233400000000♠14.22334
1 atm 7005101325000000000♠1.01325×105 7000101325000000000♠1.01325 7000103319999999999♠1.0332 1 ≡ 7002760000000000000♠760 7001146959500000000♠14.69595
1 Torr 7002133322399999999♠133.3224 6997133322400000000♠1.333224×10−3 6997135955100000000♠1.359551×10−3 ≡ 1/760 ≈ 6997131578900000000♠1.315789×10−3 ≡ 1 Torr ≈ 1 mmHg
1 lbf/in2 7003689480000000000♠6.8948×103 6998689480000000000♠6.8948×10−2 6998703069000000000♠7.03069×10−2 6998680460000000000♠6.8046×10−2 7001517149300000000♠51.71493 ≡ 1 lbf /in2
The effects of an external pressure of 700 bar on an aluminum cylinder with 5 mm 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
displaystyle mathbf F
to the vector area
displaystyle mathbf A
via the linear relation
displaystyle mathbf F =sigma mathbf A
. 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. 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.)
Water shooting out a damaged hydrant at high pressure
Fluid pressure occurs in one of two situations:
An open condition, called "open channel flow", e.g. the ocean, a swimming pool, or the atmosphere. A closed condition, called "closed conduit", e.g. a water line or gas line.
+ z =
c o n s t
displaystyle frac p gamma + frac v^ 2 2g +z=mathrm const ,
p = pressure of the fluid, γ = ρg = density · acceleration of gravity = specific weight of the fluid, v = velocity of the fluid, g = acceleration of gravity, z = elevation,
displaystyle frac p gamma
= pressure head,
displaystyle frac v^ 2 2g
= velocity head.
Hydraulic brakes Artesian well Blood pressure Hydraulic head Plant cell turgidity Pythagorean cup
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
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.
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:
displaystyle p_ 0 = frac 1 2 rho v^ 2 +p
displaystyle p_ 0
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
displaystyle pi = frac F l
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.
n R T
displaystyle p= frac nRT V ,
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
Energy Mass Momentum
Stress Deformation Compatibility Finite strain Infinitesimal strain Elasticity (linear) Plasticity Bending Hooke's law Material failure theory Fracture mechanics
Contact mechanics (frictional)
Statics · Dynamics Archimedes' principle · Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure
Surface tension Capillary action
Atmosphere Boyle's law Charles's law Gay-Lussac's law Combined gas law
Viscoelasticity Rheometry Rheometer
Magnetorheological Electrorheological Ferrofluids
Bernoulli Boyle Cauchy Charles Euler Gay-Lussac Hooke Pascal Newton Navier Stokes
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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.
p = ρ g h ,
displaystyle p=rho gh,
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:
displaystyle p= text weight density times text depth .
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
displaystyle text weight density = frac text weight text volume
we can express this weight of liquid as
displaystyle text weight = text weight density times text volume ,
where the volume of the column is simply the area multiplied by the depth. Then we have
displaystyle text pressure = frac text force text area = frac text weight text area = frac text weight density times text volume text area ,
displaystyle text pressure = frac text weight density times text (area times text depth) text area .
With the "area" in the numerator and the "area" in the denominator canceling each other out, we are left with
displaystyle text pressure = text weight density times text depth .
Written with symbols, this is our original equation:
p = ρ g h .
displaystyle p=rho gh.
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.
+ z =
c o n s t
displaystyle frac p gamma +z=mathrm const .
Terms have the same meaning as in section
Direction of liquid pressure
An experimentally determined fact about liquid pressure is that it is
exerted equally in all directions. 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.
2 g h
displaystyle scriptstyle sqrt 2gh
, where h is the depth below the free surface. Interestingly, this is the same speed the water (or anything else) would have if freely falling the same vertical distance h. Kinematic pressure
P = p
displaystyle P=p/rho _ 0
is the kinematic pressure, where
is the pressure and
displaystyle rho _ 0
constant mass density. The
in order to compute
displaystyle rho _ 0
+ ( u ∇ ) u = − ∇ P + ν
displaystyle frac partial u partial t +(unabla )u=-nabla P+nu nabla ^ 2 u.
Combined gas law
Conversion of units
Critical point (thermodynamics)
Electron degeneracy pressure
Orders of magnitude (pressure)
^ 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.
^ Giancoli, Douglas G. (2004). Physics: principles with applications. Upper Saddle River, N.J.: Pearson Education. ISBN 0-13-060620-0. ^ 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 0-9678550-9-8. Archived from the original on 2016-03-04. ^ "14th Conference of the International Bureau of Weights and Measures". Bipm.fr. Archived from the original on 2007-06-30. Retrieved 2012-03-27. ^ 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. ^ "U.S. Navy Diving Manual (Chapter 2:Underwater Physics)" (PDF). p. 2.32. Archived (PDF) from the original on 2017-02-02. ^ "Rules and Style Conventions for Expressing Values of Quantities". NIST. Archived from the original on 2009-07-10. Retrieved 2009-07-07. ^ NIST, Rules and Style Conventions for Expressing Values of Quantities Archived 2010-02-04 at the Wayback Machine., Sect. 7.4. ^ "Einstein's gravity under pressure". Astrophysics and Space Science. 321: 151–156. arXiv:0705.0825 . Bibcode:2009Ap&SS.321..151V. doi:10.1007/s10509-009-0016-8. Retrieved 2012-03-27. ^ 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) ^ NCEES (2011). Fundamentals of Engineering: Supplied Reference Handbook. Clemson, South Carolina: NCEES. p. 64. ISBN 978-1-932613-59-9. ^ Karen Wright (March 2003). "The Physics of Negative Pressure". Discover. Archived from the original on 8 January 2015. Retrieved 31 January 2015. ^ P. Atkins, J. de Paula Elements of Physical Chemistry, 4th Ed, W. H. Freeman, 2006. ISBN 0-7167-7329-5. ^ Streeter, V. L., Fluid Mechanics, Example 3.5, McGraw–Hill Inc. (1966), New York. ^ a b c Hewitt 251 (2006)
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Researchers in diving medicine and physiology
Arthur J. Bachrach Albert R. Behnke Paul Bert George F. Bond Robert Boyle Albert A. Bühlmann John R Clarke William Paul Fife John Scott Haldane Robert William Hamilton Jr. Leonard Erskine Hill Brian Andrew Hills Felix Hoppe-Seyler Christian J. Lambertsen Simon Mitchell Charles Momsen John Rawlins R.N. Charles Wesley Shilling Edward D. Thalmann Jules Triger
Diving medical research organisations
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