# Pressure (physics)

the pressure is an intensive physical variable of state of thermodynamic systems. Its symbol is p (from English. pressure) and its derived SI-UNIT is the Pascal Pa. The symbol may not here with the achievement P (from English. power) and/or with the impulse p to be confounded.

The pressure has a rather colloquial meaning apart from its meaning as scalar variable of state in physics also. One can exert for instance pressure on a nail, in order to strike it into a wood.The pressure (actually the compression stress) between wood and nail depends thereby beside of on the nail the exercised Kraft, also on the size of the contact surface between wood and nail. The smaller this contact surface is, is the largerthe pressure between nail and wood and the more easily is it to press the nail into the wood.

The compression stress is not contrary to the pressure scalar variable of state.

## pressure generally

under the pressure p (English. pressure) one understands the quotient from Kraft an F (English. force) and the surface A (English. AREA), which these Kraft perpendicularly to the surface affects (against the surface-normal). From this the equation results:

[itex]

p = \ frac {F} {A} [/itex]

Whereby both the surface and thoseKraft vectorial sizes are.

The pressure can be confounded in this conception easily with Kraft:

The terms pressure and Kraft can be often only badly from each other defined, there the effect of the different bearing surfaces in the everyday life are mostly inconspicuous andthus working Kraft is proportional to the resulting pressure and/or. as such one feels or one interprets. For this an example:

A nail has a very small bearing surface, which according to above formula with a small Kraft too at its pointa large pressure to lead can. One feels these when exercising Kraft on the nail, if one presses him with the point on the skin. If one turns the nail and exercises identical Kraft on it, then is the pressure due to the higher bearing surface substantially smaller. This effect is however often attributed to a higher Kraft, instead of that for this responsible person smaller bearing surface.

It is thus important to differentiate between pressure and Kraft because apart from the fact that it itself over, possesses Kraft a direction, the pressure acts entirely different sizes however not.

“Pressure is not a scalar size, only teacher and authors seems this in the reason of its heart to believe.” (McClelland, 1987)

the above concept is a simplification of the general Stress tensor, as it admits from the mechanics is.

## pressure in currents

static and dynamic pressure portion in a current

the pressure in currents consists of a static and a dynamic portion.While both parts depend on the density, they differ by the fact that (hydraulic) the static pressure, for fluids with constant density, rises linear with the height of the fluid column. Besides it depends on acceleration due to gravity, thus the gravitation. Thatdynamische Anteil hingegen wächst quadratisch mit derStrömungsgeschwindigkeit des Fluids. The picture to rights clarifies the Konstanz of the sum of dynamic and static portion in a frictionless current. This is the consequence from the energy conservation in the current and forthis special case as law of Bernoulli admits.

### hydrostatic pressure

the hydrostatic pressure exercises on each surface, which stands with the fluid in connection, a Kraft, which is directly proportional to the size of the surface. This formthe pressure is thus a special form of the flexible tensions, which is own to ideal liquids and gases: In the ideal, (smooth) liquid exist excluding standard voltages, evenly this hydrostatic pressure. Different it is in a tough liquid, because can here alsoTangential - or arise to shear stresses due to the friction forces. In the Mohr Spannungskreis the hydrostatic pressure presents itself therefore as simple point. Examples of a hydrostatic pressure are the water pressure and the air pressure.

The hydrostatic pressure in a fluid column thatHeight of h (on a y axis) and the density ρ under effect of acceleration due to gravity g, whereby with p (y=0) the pressure on the surface of the fluid column is meant, result as a special case from the hydrostatic principal equation too

< math>

p (y=h) = \ rho\ cdot g \ cdot h + p (y=0) [/itex]

### hydrodynamic pressure

measuring instrument in principle for the stagnation pressure, differential pressure measurement

the hydrodynamic, or also more briefly dynamic pressure, results from the kinetic energy of an mass-afflicted body, which itself with oneSpeed - which fluid speed - moves. It is therefore after Jakob Bernoulli the name for the increase or reduction of the hydrostatic pressure, which arises due to a movement of a liquid.

In the simplest case one can imagine a horizontal attached pipe,a variable diameter possesses. This is flowed through evenly by the liquid, whereby from the friction is to be refrained. In each time unit the same liquid quantity must flow by each cross section, and therefore the speed of the current the cross section must in reverse proportionallyits.

The speed can increase from larger to smaller cross sections however only if the pressure is higher in the smaller cross sections and turned around. From the current thus hydrodynamic increases of the pressure result, in smaller cross sections reductions of in larger cross sectionsPressure, due to those the pressure ratios in peace - are changed which hydrostatic pressure -. The hydrodynamic pressure is not directly measurable thereby, however for the speed measurement of the fluid is used. It applies:

[itex]

p = \ frac {1} {2} \ \ rho \ cdotv^2 [/itex]

## gas pressure

the gas pressure develops as sum of all forces working by a gas or a gas mixture on a gefässwand. If a gas particle pushes to a wall, then these exchange an impulse. This Impulsübertragung hangs on the one hand ofthe kinetic energy of the gas particle and of the direction of the particle toward the wall off. For many particles these impulse transfers add themselves to a total force. This depends mainly on the number of particles, those per time unit on the wallmeet. One receives the gas pressure also by an addition of all partial pressure of the components to that of gas mixture. Here also steam pressure and Sättigungsdampfdruck represent special forms of the gas pressure. The air pressure is an example of a gas pressure.

The kinetic gas theory supplies from the mentionedmechanical and statistic considerations the equation of state:

[itex]

p = - \ frac {\ partial U (S, V, n)}{\ partial V} [/itex]

for thermodynamics also as definition of the pressure as intensive size offers itself (see also fundamental equation). For ideal a gas this leads to thermal equation of state:

[itex]

p \ cdot V = n \ cdot R \ cdot T [/itex]

From it different formulas for the gas pressure can be derived:

[itex]

p = \ frac {n \ cdot R \ cdot T} {V} [/itex]

[itex]

p = \ rho \ R_s cdot \ cdot T[/itex]

[itex]

p = \ frac {m \ cdot R_s \ cdot T} {V} \ qquad [/itex]

[itex]

p = \ frac {R \ cdot T} {V_m} [/itex]

From the kinetic gas theory follows:

[itex]

p = \ frac {n M \ overline {v^2}} {3 V} [/itex]

Here the individual symbols stand for the following sizes:

the averaged impulse transfer is contained in the product made of gas constant and temperature of the equation of state. Both terms can be transferred by piston sample experiments into one another. The gas pressure can do equivalent for above definition also as hydrostatic stress tensor, as it from the mechanicsadmits to be understood is.

## units

SI - unit of the pressure is the Pascal with the unit symbol Pa. A Pascal corresponds to a pressure of Newton per square meter:

[itex]

\ mathrm {1 \ Pa = 1 \ \ frac {N} {m^2} =1 \ \ frac {kg} {m \ cdot s^2}} [/itex]

The unit of pressure bar usually used in Western Europe corresponds to 100,000 Pa, 1,000 hPa or 100 kPa.

Other partial, but no longer permissible units of pressure still which can be found are:

 Pascal [2] bar technical/physical atmosphere torr Pound per square tariff 1 Pa ≡1 N/m ² = 10 −5 bar ≈ 10,2·10 −6 RK ≈ 9,87·10 −6 at ≈ 7,5·10 −3 torr ≈ 145·10 −6 psi = 100000 Pa ≡ 10 6 dyn /cm ² ≈ 1.02 RKs ≈ 0.987 at ≈ 750torr ≈ 14.504 psi = 98066.5 Pa = 0.980665 bar ≡ 1 kp /cm ² ≈ 0.968 at ≈ 736 torr ≈ 14.223 psi = 101325 Pa = 1.01325 bar ≈ 1.033 RKs ≡ p 0 =760 torr ≈ 14.696 psi ≈ 133.322 Pa ≈ 1,333·10 −3 bar ≈ 1,360·10 −3 RK ≈ 1,316·10 −3 at ≡ 1 mm Hg ≈ 19,337·10 −3 psi ≈ 6894.757 Pa ≈ 68,948·10 −3 bar ≈ 70,307·10 −3 RK ≈ 68,046·10 −3 at ≈ 51.7149 torr ≡ 1 lb f./in. ²
1. data are not specified by water gauge as well as simple multiple of other units such as MP/m ² = 0.1 kp/cm ² = 0.1 RKs.
2. Pascal is the SI-UNIT of the pressure, bar is accepted.

## gauges

major items: Gauge, barometer, manometer, venturi nozzle, pitot tube, blood pressure apparatus

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