Parouse.com
 Parouse.com



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
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
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

v t e

Diving medicine, physiology, physics and environment

Diving medicine

Injuries and disorders

Pressure

Oxygen

Freediving blackout Hyperoxia Hypoxia (medical) Oxygen toxicity

Inert gases

Atrial septal defect Avascular necrosis Decompression sickness Dysbaric osteonecrosis High-pressure nervous syndrome Hydrogen narcosis Isobaric counterdiffusion Nitrogen narcosis Taravana Uncontrolled decompression

Carbon dioxide

Hypercapnia Hypocapnia

Aerosinusitis Air embolism Alternobaric vertigo Barodontalgia Barostriction Barotrauma Compression arthralgia Decompression illness Dental barotrauma Dysbarism Ear clearing Frenzel maneuver Valsalva maneuver

Immersion

Asphyxia Drowning Hypothermia Immersion diuresis Instinctive drowning response Laryngospasm Salt water aspiration syndrome Swimming-induced pulmonary edema

List of signs and symptoms of diving disorders Cramps Diving disorders Motion sickness Surfer's ear

Treatments

Diving chamber Diving medicine Hyperbaric medicine Hyperbaric treatment schedules In-water recompression Oxygen therapy

Fitness to dive

Diving physiology

Artificial gills (human) Blood–air barrier Blood shift Breathing Circulatory system CO₂ retention Cold shock response Dead space (physiology) Decompression (diving) Decompression theory Diving reflex Gas
Gas
exchange History of decompression research and development Lipid Maximum operating depth Metabolism Normocapnia Oxygen window in diving decompression Perfusion Physiological response to water immersion Physiology of decompression Pulmonary circulation Respiratory exchange ratio Respiratory quotient Respiratory system Systemic circulation Tissue (biology)

Diving physics

Ambient pressure Amontons' law Anti-fog Archimedes' principle Atmospheric pressure Boyle's law Breathing
Breathing
performance of regulators Buoyancy Charles's law Combined gas law Dalton's law Diffusion Force Gay-Lussac's law Henry's law Hydrophobe Hydrostatic pressure Ideal gas
Ideal gas
law Molecular diffusion Neutral buoyancy Oxygen fraction Partial pressure Permeation Pressure Psychrometric constant Snell's law Solubility Solution Supersaturation Surface tension Surfactant Torricellian chamber Underwater vision Weight

Diving environment

Algal bloom Breaking wave Ocean current Current (stream) Ekman transport Halocline List of diving hazards and precautions Longshore drift Rip current Stratification Surf Surge (wave action) Thermocline Tides Turbidity Undertow (water waves) Upwelling

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

Aerospace Medical Association Divers Alert Network
Divers Alert Network
(DAN) Diving Diseases Research Centre
Diving Diseases Research Centre
(DDRC) Diving Medical Advisory Council (DMAC European Diving Technology Committee
European Diving Technology Committee
(EDTC) European Underwater and Baromedical Society
European Underwater and Baromedical Society
(EUBS) National Board of Diving and Hyperbaric Medical Technology Naval Submarine Medical Research Laboratory Royal Australian Navy School of Underwater Medicine Rubicon Foundation South Pacific Underwater Medicine Society
South Pacific Underwater Medicine Society
(SPUMS) Southern African Underwater and Hyperbaric Medical Association
Southern African Underwater and Hyperbaric Medical Association
(SAUHMA

Undersea and Hyperbaric Medical Society
Undersea and Hyperbaric Medical Society
(UHMS) United States Navy Experimental Diving Unit
United States Navy Experimental Diving Unit
(NEDU)

Categories: Diving medicine Underwater diving
Underwater diving
physiology Underwater diving
Underwater diving
physics Physical oceanography Glossary Portal

Authority control