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Parouse.com

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 1⁄760 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.

Contents

1 Definition

1.1 Formula 1.2 Units 1.3 Examples 1.4 Scalar nature

2 Types

2.1
**Fluid** pressure

2.1.1 Applications

2.2
**Explosion**

Explosion or deflagration pressures
2.3 Negative pressures
2.4 Stagnation pressure
2.5 Surface pressure and surface tension
2.6
**Pressure**

Pressure of an ideal gas
2.7
**Vapour**

Vapour pressure
2.8
**Liquid**

Liquid pressure
2.9 Direction of liquid pressure
2.10 Kinematic pressure

3 See also 4 Notes 5 References 6 External links

Definition[edit]
**Pressure**

Pressure is the amount of force applied perpendicular 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[edit]

Conjugate variables of thermodynamics

Pressure Volume

(Stress) (Strain)

Temperature Entropy

Chemical potential Particle number

Mathematically:

p = −

F A

,

displaystyle p=- frac F A ,

where:

p

displaystyle p

is the pressure,

F

displaystyle F

is the magnitude of the normal force,

A

displaystyle A

is the area of the surface on contact.

**Pressure**

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:

d

F

n

= − p

d

A

= − p

n

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.
**Pressure**

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[edit]

Mercury column

The
**SI unit**

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;[3] 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**

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:

p =

F ×

distance

A ×

distance

=

work volume

=

energy (J)

volume

(

m

3

)

.

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
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.[citation needed] 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**

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[4] (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.[5]
**Gauge pressure**

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.[6] 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 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).

**Pressure**

Pressure units

v t e

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

6998193367800000000♠1.933678×10−2

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

Examples[edit]

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
area.
**Pressure**

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 a fruit with the flat
side, the force is distributed over a large area, and it will not cut.
But if we use the edge, 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.
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 (46.7 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 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.[7]
**Gauge pressure**

Gauge pressure is the relevant measure of pressure wherever one is
interested in the stress on storage vessels and the plumbing
components of fluidics systems. However, whenever equation-of-state
properties, such as densities or changes in densities, must be
calculated, pressures must be expressed in terms of their absolute
values. For instance, if the atmospheric pressure is 100 kPa, a
gas (such as helium) at 200 kPa (gauge) (300 kPa [absolute])
is 50% denser than the same gas at 100 kPa (gauge) (200 kPa
[absolute]). Focusing on gauge values, one might erroneously conclude
the first sample had twice the density of the second one.
Scalar nature[edit]
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

F

displaystyle mathbf F

to the vector area

A

displaystyle mathbf A

via the linear relation

F

= σ

A

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.[8]
Types[edit]
**Fluid** pressure[edit]
**Fluid** pressure is most often the compressive stress at some point
within a fluid. (The term fluid refers to both liquids and gases –
for more information specifically about liquid pressure, see section
below.)

Water 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.

**Pressure**

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**

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[9] and incompressible.[9] An
ideal fluid is a fluid in which there is no friction, it is inviscid
[9] (zero viscosity).[9] The equation for all points of a system
filled with a constant-density fluid is[10]

p γ

+

v

2

2 g

+ z =

c o n s t

,

displaystyle frac p gamma + frac v^ 2 2g +z=mathrm const ,

where:

p = pressure of the fluid, γ = ρg = density · acceleration of gravity = specific weight of the fluid,[9] v = velocity of the fluid, g = acceleration of gravity, z = elevation,

p γ

displaystyle frac p gamma

= pressure head,

v

2

2 g

displaystyle frac v^ 2 2g

= velocity head.

Applications[edit]

Hydraulic brakes Artesian well Blood pressure Hydraulic head Plant cell turgidity Pythagorean cup

**Explosion**

Explosion or deflagration pressures[edit]
**Explosion**

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

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.[11]
The
**Casimir effect**

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[edit]
**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:

p

0

=

1 2

ρ

v

2

+ p

displaystyle p_ 0 = frac 1 2 rho v^ 2 +p

where

p

0

displaystyle p_ 0

is the stagnation pressure

v

displaystyle v

is the flow velocity

p

displaystyle p

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**

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[edit]
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:

π =

F l

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.
**Surface tension**

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

Pressure of an ideal gas[edit]
Main article:
**Ideal gas**

Ideal gas law
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:

p =

n R T

V

,

displaystyle p= frac nRT V ,

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.[12]
**Vapour**

Vapour pressure[edit]
Main article:
**Vapour**

Vapour pressure
**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**

Liquid pressure[edit]
See also:
**Fluid** statics §
**Pressure**

Pressure in fluids at rest

Continuum mechanics

Laws

Conservations

Energy Mass Momentum

Inequalities

Clausius–Duhem (entropy)

**Solid**

Solid mechanics

Stress Deformation Compatibility Finite strain Infinitesimal strain Elasticity (linear) Plasticity Bending Hooke's law Material failure theory Fracture mechanics

Contact mechanics (frictional)

**Fluid** mechanics

Fluids

Statics · Dynamics Archimedes' principle · Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure

Liquids

Surface tension Capillary action

Gases

Atmosphere Boyle's law Charles's law Gay-Lussac's law Combined gas law

Plasma

Rheology

Viscoelasticity Rheometry Rheometer

Smart fluids

Magnetorheological Electrorheological Ferrofluids

Scientists

Bernoulli Boyle Cauchy Charles Euler Gay-Lussac Hooke Pascal Newton Navier Stokes

v t e

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**

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. The pressure due to a liquid in liquid
columns of constant density or at a depth within a substance is
represented by the following formula:

p = ρ g h ,

displaystyle p=rho gh,

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:

p =

weight density

×

depth

.

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

weight density

=

weight volume

displaystyle text weight density = frac text weight text volume

we can express this weight of liquid as

weight

=

weight density

×

volume

,

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

pressure

=

force area

=

weight area

=

weight density

×

volume

area

,

displaystyle text pressure = frac text force text area = frac text weight text area = frac text weight density times text volume text area ,

pressure

=

weight density

×

(area

×

depth)

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

pressure

=

weight density

×

depth

.

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.
**Atmospheric pressure**

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
section of each dam, the 10 ft deep water will apply half the
force of 20 ft 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**

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.[13] Mathematically, it is described by
Bernoulli's equation, where velocity head is zero and comparisons per
unit volume in the vessel are

p γ

+ z =

c o n s t

.

displaystyle frac p gamma +z=mathrm const .

Terms have the same meaning as in section
**Fluid** pressure.
Direction of liquid pressure[edit]
An experimentally determined fact about liquid pressure is that it is
exerted equally in all directions.[14] 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**

Pressure is seen
acting sideways when water spurts sideways from a leak in the side of
an upright can.
**Pressure**

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.[14] 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

2 g h

displaystyle scriptstyle sqrt 2gh

, where h is the depth below the free surface.[14] Interestingly, this is the same speed the water (or anything else) would have if freely falling the same vertical distance h. Kinematic pressure[edit]

P = p

/

ρ

0

displaystyle P=p/rho _ 0

is the kinematic pressure, where

p

displaystyle p

is the pressure and

ρ

0

displaystyle rho _ 0

constant mass density. The
**SI unit**

SI unit of P is m2/s2. Kinematic pressure
is used in the same manner as kinematic viscosity

ν

displaystyle nu

in order to compute
**Navier–Stokes equation**

Navier–Stokes equation without explicitly
showing the density

ρ

0

displaystyle rho _ 0

.

**Navier–Stokes equation**

Navier–Stokes equation with kinematic quantities

∂ u

∂ t

+ ( u ∇ ) u = − ∇ P + ν

∇

2

u .

displaystyle frac partial u partial t +(unabla )u=-nabla P+nu nabla ^ 2 u.

See also[edit]

**Underwater diving**

Underwater diving portal

Atmospheric pressure
Blood pressure
Boyle's Law
Combined gas law
Conversion of units
Critical point (thermodynamics)
Dynamic pressure
Electron degeneracy pressure
Hydraulics
Internal pressure
Kinetic theory
Microphone
Orders of magnitude (pressure)
Partial pressure
**Pressure**

Pressure measurement
**Pressure**

Pressure sensor
Sound pressure
Spouting can
Static pressure
Timeline of temperature and pressure measurement technology
Units conversion by factor-label
Vacuum
**Vacuum**

Vacuum pump
Vertical pressure variation

Notes[edit]

^ 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[edit]

^ 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)

External links[edit]

Introduction to
**Fluid** Statics and Dynamics on Project PHYSNET
**Pressure**

Pressure being a scalar quantity
wikiUnits.org - Convert units of pressure

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