Breaking News

# Pressure

### topic elements

Notes

simple explanation
From Wikipedia the free encyclopedia

## Definition

Pressure is the amount of force applied at right angles to the surface of an object per unit area. The symbol for it is "p" or P. 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. Formula 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 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 the fact that the force is considered towards the surface element while the normal vector points outward. The equation has meaning in that for any surface S in contact with the fluid the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation. It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure as a scalar has no direction. The force given by the previous relationship to the quantity has a direction but the pressure does not. If we change the orientation of the surface element the direction of the normal force changes accordingly but the pressure remains the same. Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics and it is conjugate to volume. Units The SI unit for pressure is the pascal (Pa) equal to one newton per square metre (N/m2 or kg·m−1·s−2). This name for the unit was added in 1971; before that pressure in SI was expressed simply in newtons per square metre. Other units of pressure such as pounds per square inch (Ibf/in2) and bar are also in common use. The CGS unit of pressure is the barye (Ba) equal to 1 dyn·cm−2 or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre (g/cm2 or kg/cm2) and the like without properly identifying the force units. But using the names kilogram gram kilogram-force or gram-force (or their symbols) as units of force is expressly forbidden in SI. The technical atmosphere (symbol: at) is 1 kgf/cm2 (98.0665 kPa or 14.223 psi). Since a system under pressure has the potential to perform work on its surroundings pressure is a measure of potential energy stored per unit volume. It is therefore related to energy density and may be expressed in units such as joules per cubic metre (J/m3 which is equal to Pa). Mathematically: 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 the hectopascal (hPa) for atmospheric air pressure which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in most other fields where the hecto- prefix is rarely used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because pressure in the ocean increases by approximately one decibar per metre depth. The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at Earth mean sea level and is defined as 101325 Pa. Because pressure is commonly measured by its ability to displace a column of liquid in a manometer pressures are often expressed as a depth of a particular fluid (e.g. centimetres of water millimetres of mercury or inches of mercury). The most common choices are mercury (Hg) and water; water is nontoxic and readily available while mercury's high density allows a shorter column (and so a smaller manometer) to be used to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors so the height of a fluid column does not define pressure precisely. When millimetres of mercury or inches of mercury are quoted today these units are not based on a physical column of mercury; rather they have been given precise definitions that can be expressed in terms of SI units.[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 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 (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. 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. 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 H2O) centimetre (cm H2O) 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). Examples As an example of varying pressures a finger can be pressed against a wall without making any lasting impression; however the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress pressure is defined as a scalar quantity. The negative gradient of pressure is called the force density. Another example is a knife. If we try to cut with the flat edge force is distributed over a larger surface area resulting in less pressure and it will not cut. Whereas using the sharp edge which has less surface area results in greater pressure and so the knife cuts smoothly. This is one example of a practical application of pressure. For gases pressure is sometimes measured not as an absolute pressure but relative to atmospheric pressure; such measurements are called gauge pressure. An example of this is the air pressure in an automobile tire which might be said to be "220 kPa (32 psi)" but is actually 220 kPa (32 psi) above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa (14.7 psi) the absolute pressure in the tire is therefore about 320 kPa (46 psi). In technical work this is written "a gauge pressure of 220 kPa (32 psi)". Where space is limited such as on pressure gauges name plates graph labels and table headings the use of a modifier in parentheses such as "kPa (gauge)" or "kPa (absolute)" is permitted. In non-SI technical work a gauge pressure of 32 psi (220 kPa) is sometimes written as "32 psig" and an absolute pressure as "32 psia" though the other methods explained above that avoid attaching characters to the unit of pressure are preferred. Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluidics systems. However whenever equation-of-state properties such as densities or changes in densities must be calculated pressures must be expressed in terms of their absolute values. For instance if the atmospheric pressure is 100 kPa (15 psi) a gas (such as helium) at 200 kPa (29 psi) (gauge) (300 kPa or 44 psi [absolute]) is 50% denser than the same gas at 100 kPa (15 psi) (gauge) (200 kPa or 29 psi [absolute]). Focusing on gauge values one might erroneously conclude the first sample had twice the density of the second one. Scalar nature In a static gas the gas as a whole does not appear to move. The individual molecules of the gas however are in constant random motion. Because we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction we do not detect any motion. If we enclose the gas within a container we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas and the force per unit area (the pressure) is the same. We can shrink the size of our "container" down to a very small point (becoming less true as we approach the atomic scale) and the pressure will still have a single value at that point. Therefore pressure is a scalar quantity not a vector quantity. It has magnitude but no direction sense associated with it. Pressure force acts in all directions at a point inside a gas. At the surface of a gas the pressure force acts perpendicular (at right angle) to the surface. A closely related quantity is the stress tensor σ which relates the vector force 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.