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48-401: Where p is the pressure , V is volume , n is the polytropic index , and C is a constant. The polytropic process equation describes expansion and compression processes which include heat transfer. Some specific values of n correspond to particular cases: In addition, when the ideal gas law applies: Where γ {\displaystyle \gamma } is the ratio of

96-553: A manometer . Depending on where the inlet holes are located on the probe, it can measure static pressures or stagnation pressures. 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

144-400: A gravitational well such as a planet, otherwise known as atmospheric pressure . In the case of planetary atmospheres , the pressure-gradient force of the gas pushing outwards from higher pressure, lower altitudes to lower pressure, higher altitudes is balanced by the gravitational force , preventing the gas from diffusing into outer space and maintaining hydrostatic equilibrium . In

192-423: 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 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

240-675: 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: Mayer%27s relation In the 19th century, German chemist and physicist Julius von Mayer derived a relation between the molar heat capacity at constant pressure and the molar heat capacity at constant volume for an ideal gas . Mayer's relation states that C P , m − C V , m = R , {\displaystyle C_{P,\mathrm {m} }-C_{V,\mathrm {m} }=R,} where C P ,m

288-520: A measured, rather than defined, quantity. These manometric units are still encountered in many fields. Blood pressure is measured in millimetres (or centimetres) 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 units for pressure gauges used to measure pressure exposure in diving chambers and personal decompression computers . A msw

336-411: A more complex dependence on the variables of state. 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

384-424: A physical container, the pressure of the gas originates from the molecules colliding with the walls of the container. The walls of the container can be anywhere inside the gas, and the force per unit area (the pressure) is the same. If the "container" is shrunk down to a very small point (becoming less true as the atomic scale is approached), the pressure will still have a single value at that point. Therefore, pressure

432-420: 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

480-495: 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. For example, " p g = 100 psi" rather than " p = 100 psig" . Differential pressure is expressed in units with "d" appended; this type of measurement

528-448: 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 (N/m ); similarly, the pound-force per square inch ( psi , symbol lbf/in ) 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 unit atmosphere (atm)

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576-424: Is "p" or P . The IUPAC recommendation for pressure is a lower-case p . 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. Mathematically: p = F A , {\displaystyle p={\frac {F}{A}},} where: Pressure

624-453: 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. In a static gas , the gas as a whole does not appear to move. The individual molecules of

672-463: Is a scalar quantity. It relates the vector area 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 d\mathbf {F} _{n}=-p\,d\mathbf {A} =-p\,\mathbf {n} \,dA.} The minus sign comes from

720-484: Is a constant, K = δ q δ w {\displaystyle K={\frac {\delta q}{\delta w}}} , γ = c p c v {\displaystyle \gamma ={\frac {c_{p}}{c_{v}}}} , and with the polytropic coefficient n = ( 1 − γ ) K + γ {\displaystyle n={(1-\gamma )K+\gamma }} . For certain values of

768-490: Is a fundamental parameter in thermodynamics , and it is conjugate to volume . The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N/m , or kg·m ·s ). This name for the unit was added in 1971; before that, pressure in SI was expressed in newtons per square metre. Other units of pressure, such as pounds per square inch (lbf/in ) and bar , are also in common use. The CGS unit of pressure

816-416: 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

864-449: Is an established constant. It is approximately equal to typical air pressure at Earth mean sea level and is defined as 101 325  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

912-485: Is defined as 0.1 bar (= 10,000 Pa), is not the same as a linear metre of depth. 33.066 fsw = 1 atm (1 atm = 101,325 Pa / 33.066 = 3,064.326 Pa). The pressure conversion from msw to fsw is different from the length conversion: 10 msw = 32.6336 fsw, while 10 m = 32.8083 ft. 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

960-407: 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. Pressure is the amount of force applied perpendicular to the surface of an object per unit area. The symbol for it

1008-421: 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

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1056-426: 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 .) Fluid pressure occurs in one of two situations: 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

1104-409: Is no friction, it is inviscid (zero viscosity ). The equation for all points of a system filled with a constant-density fluid is p γ + v 2 2 g + z = c o n s t , {\displaystyle {\frac {p}{\gamma }}+{\frac {v^{2}}{2g}}+z=\mathrm {const} ,} where: Explosion or deflagration pressures are

1152-437: 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

1200-584: Is related to energy density and may be expressed in units such as joules per cubic metre (J/m , which is equal to Pa). Mathematically: p = F ⋅ distance A ⋅ distance = Work Volume = Energy (J) Volume  ( m 3 ) . {\displaystyle p={\frac {F\cdot {\text{distance}}}{A\cdot {\text{distance}}}}={\frac {\text{Work}}{\text{Volume}}}={\frac {\text{Energy (J)}}{{\text{Volume }}({\text{m}}^{3})}}.} Some meteorologists prefer

1248-463: Is the barye (Ba), equal to 1 dyn·cm , or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre ("g/cm " or "kg/cm ") 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 deprecated in SI. The technical atmosphere (symbol: at) is 1 kgf/cm (98.0665 kPa, or 14.223 psi). Pressure

1296-654: Is the molar heat at constant pressure , C V ,m is the molar heat at constant volume and R is the gas constant . For more general homogeneous substances, not just ideal gases, the difference takes the form, C P , m − C V , m = V m T α V 2 β T {\displaystyle C_{P,\mathrm {m} }-C_{V,\mathrm {m} }=V_{\mathrm {m} }T{\frac {\alpha _{V}^{2}}{\beta _{T}}}} (see relations between heat capacities ), where V m {\displaystyle V_{\mathrm {m} }}

1344-434: 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

1392-401: Is useful when considering sealing performance or whether a valve will open or close. Presently or formerly popular pressure units include the following: 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,

1440-401: 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

1488-478: The Lane–Emden equation using a polytropic fluid is known as a polytrope . 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) is the pressure relative to the ambient pressure. Various units are used to express pressure. Some of these derive from

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1536-424: 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

1584-447: The convention 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

1632-480: The flat edge is used, 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

1680-404: 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 . 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

1728-419: 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. Fluid pressure

1776-425: The gas, however, are in constant random motion . Because there are an extremely large number of molecules and because the motion of the individual molecules is random in every direction, no motion is detected. When the gas is at least partially confined (that is, not free to expand rapidly), the gas will exhibit a hydrostatic pressure. This confinement can be achieved with either a physical container of some sort, or in

1824-537: The heat capacity at constant pressure ( C P {\displaystyle C_{P}} ) to heat capacity at constant volume ( C V {\displaystyle C_{V}} ). For an ideal gas in a closed system undergoing a slow process with negligible changes in kinetic and potential energy the process is polytropic, such that p v ( 1 − γ ) K + γ = C {\displaystyle pv^{(1-\gamma )K+\gamma }=C} where C

1872-548: 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, except aviation where the hecto- prefix is commonly 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)

1920-412: 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,

1968-454: 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

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2016-851: The polytropic index, the process will be synonymous with other common processes. Some examples of the effects of varying index values are given in the following table. When the index n is between any two of the former values (0, 1, γ , or ∞), it means that the polytropic curve will cut through (be bounded by ) the curves of the two bounding indices. For an ideal gas, 1 <  γ  < 5/3, since by Mayer's relation γ = c p c v = c v + R c v = 1 + R c v = c p c p − R . {\displaystyle \gamma ={\frac {c_{p}}{c_{v}}}={\frac {c_{v}+R}{c_{v}}}=1+{\frac {R}{c_{v}}}={\frac {c_{p}}{c_{p}-R}}.} A solution to

2064-415: 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 and incompressible. An ideal fluid is a fluid in which there

2112-428: The result of the ignition of explosive gases , mists, dust/air suspensions, in unconfined and confined spaces. While pressures are, in general, positive, there are several situations in which negative pressures may be encountered: 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

2160-399: 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

2208-537: 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". 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: Real gases exhibit

2256-416: The unit of pressure are preferred. Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluidics systems. However, whenever equation-of-state properties, such as densities or changes in densities, must be calculated, pressures must be expressed in terms of their absolute values. For instance, if the atmospheric pressure

2304-463: 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

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