Pressure

Opposes the pressure is a measure of the resistance of material to a reduction in the available space. Pressure is an intensive, scalar physical quantity with the SI unit Pascal. The usual symbols is modeled on the English word for printing (English pressure).

Pressure can be equated in most cases with the quotient of force and area:

More specifically, the amount of the force acting perpendicular to the reference surface area. From the perspective of the elasticity theory, the pressure is a normal voltage, and therefore a special case of mechanical stress.

The Pauli exclusion principle of quantum physics leads to a fermion degeneracy pressure, which preserves such as a white dwarf star from further collapse. In the context of general relativity also pressure to gravitational effect contributes.

• 7.1 conversion between the most common units
• 7.2 Other units

Simple definition

Pressure is the result of a force acting on a surface. The size of the print on the reference area A is exclusively from the perpendicular to the surface force component. Mathematically:

With:

It is wrong (though common) to say that the pressure in a certain direction acts. Because pressure is directionless as a scalar quantity. Rather, it would be useful to describe the pressure as " acting on all sides ." Is usually meant by this directional information, the direction of the force caused by the pressure at a location of interest. Pressure is a relationship between the vector element surface and the normal force acting on this element, and is thus the constant of proportionality between the two vectors.

This is the normal vector on the surface in the same direction as the force, namely, outwards.

Definition in the continuum mechanics

In general, the pressure on the trace of the stress tensor is defined as:

If the stress tensor exclusive compressive stress describes it reduces to a diagonal matrix and can be represented as a multiple of Einheitstensors:

The negative multiples called pressure and thus a special case of mechanical stress.

In any material, the force on any (small ) area is the normal vector is given by:

And in the special case of pressure is:

That in such a medium, the direction of the force on a surface is always normal.

The mechanical stress has the same physical dimensions as the pressure, namely, force / area.

Pressure in flowing media

The pressure in flowing media is composed of a static and a dynamic component. While both parts depend on the density, they differ in that the ( hydro) static pressure increases for fluids with constant density, linearly with the height of the fluid column. He is also of the acceleration due to gravity, so the gravity -dependent. The dynamic component, however, grows quadratically with the flow velocity of the fluid. The picture to the right illustrates the constancy of the sum of dynamic and static content in an inviscid flow. This is known as the consequence of the conservation of energy in the flow, and for this special case as Bernoulli's law.

Hydrostatic pressure

The hydrostatic pressure exercised on each face of which is in communication with the fluid, a force acting on the proportional size of the area - that is the larger the area, the greater the force acting on it. This form of printing is a special form of elastic stresses, the ideal liquids and gases is peculiar: In the ideal ( frictionless ) fluid only normal stresses exist, just that hydrostatic pressure. It is different in a real ( frictional, viscous ) fluid, because this can also tangential or shear stresses occur due to the friction forces. In Mohr's circle, the hydrostatic pressure thus provides a simple point dar. examples of a hydrostatic pressure are the water pressure and the air pressure.

The hydrostatic pressure in a standing column of liquid of height and density under the influence of the gravitational acceleration is calculated as a special case of the basic hydrostatic equation

Here, the pressure at the top of the liquid column.

Hydrodynamic pressure

The hydrodynamic pressure resulting from the kinetic energy of a fluid flowing on the surface of a body in this flow. It is according to Daniel Bernoulli the change in surface pressure relative to the hydrostatic pressure ( see also dynamic pressure ).

The hydrodynamic pressure increases with the velocity of the fluid. During the transition from a larger to a smaller cross section, the flow velocity must increase. The speed may only increase from larger to smaller cross-sections, when the hydrostatic pressure in the smaller cross sections is less and vice versa. The flow thus generated in the transition from a larger to a smaller cross section, a speed gain, connected thereto, a reduction of the hydrostatic pressure at the same time increase the hydrodynamic pressure. And vice versa.

The hydrodynamic pressure is not directly measurable. However, it can be determined from the measurement of the pressure difference between total and static pressure (see Prandtlsonde ). It is used for measuring the speed of a fluid.

The following applies: ( is the dynamic pressure, the density of the flowing fluid and the speed )

The relationship between hydrostatic and hydrodynamic pressure is explained by the Bernoulli law.

For a gas flow ( compressible fluid ) exists in addition to the hydrostatic pressure nor the static pressure, which approximately corresponds to the sum of hydrostatic and hydrodynamic pressure.

Definition in statistical physics and thermodynamics

In statistical physics, the pressure is generally given by the expectation value:

It is the Hamiltonian of the system, the volume of an ensemble average over the respective statistical ensemble.

This definition leads to the microcanonical ensemble

(The internal energy ) in the canonical ensemble

(The free energy ) and in the grand canonical ensemble

( Is the grand canonical potential).

Gas pressure

The gas pressure is produced as the sum of all active by a gas or gas mixture to a vessel wall forces. Initiates a gas particle to a wall, both exchange a pulse. The warmer gas is, the faster the particles and the greater the pressure. The momentum transfer depends namely on the kinetic energy of the gas particle. Also it is dependent on the direction with which meets the particles to the wall. These momentum transfers add up to a total force for many particles. This mainly depends on the number of particles per unit of time to make the wall. The gas pressure can also be obtained by adding all partial pressures of the components of the gas mixture. Also in this case the vapor pressure and the saturation vapor pressure of special shapes of the gas pressure dar. Air pressure is an example of a gas pressure.

The kinetic theory of gases delivered from the above-mentioned mechanical and statistical considerations, the equation of state:

Which also offers a definition of pressure for thermodynamics as an intensive variable ( see also fundamental equation ).

For the special case of an ideal gas equation of state, this leads to thermal:

On the basis of the kinetic theory of gases follows

The individual symbols stand for the following sizes:

• M - mass of gas
• M - molecular weight
• N - amount of substance
• T - temperature
• R - universal gas constant
• V - volume

The averaged momentum transfer is included in the product of the gas constant and temperature of the equation of state. Both terms can be transferred through the piston probe experiments with each other. The gas pressure can be equivalent to the above definition, as a hydrostatic stress tensor understood, as is well known in mechanics.

Absolute / Relative pressure

The absolute pressure pabs (English absolute pressure ) refers to the perfect vacuum. In this molecule absolutely clear the origin of the absolute pressure is defined. An example of a common "absolute" value indicated is the air pressure.

As a relative pressure is called a relative pressure relationship between two volumes. Often, the ambient pressure is used as a reference, however, offer depending on the context, different reference sizes. An example of a common "relative" given pressure is the inflation pressure of a tire.

To illustrate: If you fill at an air pressure of 1 bar, a tire with a relative pressure of 2 bar, prevails in the tires an absolute pressure of 3 bar.

Units

The SI unit of pressure is the Pascal with the unit symbol Pa. One Pascal equals a pressure of one newton per square meter:

For higher pressures also like the SI -conforming unit bar is used, this corresponds to 1 bar = 100,000 Pa 1.000 hPa or 100 kPa.

Engineering in the unit N / mm ² is used for pressure as well as for stress:

Conversion between the most common units

Exponential rounded to four digits.

More units

Pressure units, which can be found in literature, but not SI -compliant:

Pressure gauges and procedures

Pressure gauges ( manometers ) are based on different measurement principles:

• To measure the tire pressure on the car or the house water and house gas pressure simple Bourdon tube pressure gauge or Bourdon tube pressure gauges are used. This is the principle of the rolled tube to reason that the rolls are under pressure.
• Measuring instruments for measuring static pressure, the pressure difference usually based on the displacement of a mechanical separation by reducing the pressure with a reference pressure such as vacuum is compared. How to Measure around the barometer and the ring scale by the deflection is directly translated into a display, or differential pressure sensors by the force of deflection is measured.
• Indirect pressure measurement is based on effects of particle number density
• Measuring instruments for pressure in moving fluids ( fluids ) use the peculiarities of the Bernoulli equations, such as the Pitot tube ( Pitot tube ) or the venturi
• Sphygmomanometers measure indirectly by acoustic events are captured while relaxing the previously compressed veins
• Pressure transmitters, pressure gauges, which can be used in industrial environments. To the pressure measuring signal obtained is converted into a defined signal.

Other methods to measure pressures:

• Pressure-sensitive paint (English pressure sensitive paint PSP) is a measurement method to make local pressure distributions at interfaces visible