Stagnation pressure

The resting pressure (even stagnation pressure or total pressure ) means the settled pressure of a gas flow when the flow velocity isentropic ( ie thermally insulated and free of friction ) is delayed to a negligibly small value. It is thus the equivalent of the total pressure of a hydraulic fluid ( liquid), which, according to Bernoulli is the sum of hydrostatic and hydrodynamic pressure.

Assuming that internal friction ( friction of gas molecules with each other ) and outer friction ( friction of the gas with the pipe wall ) are negligible, a constant height of the flow path, the static pressure over the entire flow path is constant, while the static pressure as a function of flow velocity can vary continuously.

Analogous to the definition of the static pressure exists to a one-dimensional gas flow, a corresponding resting temperature.

Classification and delimitation

The simple approach, according to Bernoulli on the pressure change within a flow is exact only for liquids.

At a gas flow takes place through the changes in the static pressure additional density and temperature changes of the medium, which are reflected in the internal and kinetic energy of the medium or the flow and therefore must be taken into account in the energy approach. The energy or power equation along the flow path of a friction- free flowing ideal gas is thus:

These are:

Or have the terms in the equation (1) the following meaning:

Assuming that the potential energy content is negligible ( the flow is horizontal, and the density of gas is generally much less than in the liquid), the last term of equation ( 1) can be removed and the basic equations, as follows be reshaped:

Influence of the speed of pressure and temperature of a stationary heat-insulated gas flow

Equation (2) states that in an ideal gas, the temperature of the gas is reduced with increasing flow velocity and, conversely, if there is no energy exchange takes place with the environment. With increasing flow rate, a part of the non-directional speed microscopic molecule (temperature) is transformed into a directed speed macroscopic quasi. The situation is similar with the pressure. Again, the static pressure decreases with increasing flow rate, as the molecule speed (and thus the momentum exchange ) is perpendicular to the wall is reduced in favor of the flow rate.

When flow velocity 0 static pressure and static pressure are identical, as static temperature and total temperature.

Calculation of the static pressure

Since the static pressure can be measured at only one point at which the flow velocity is negligibly small, which belongs to the static pressure static pressure usually has to be calculated. If the material data of a flowing ideal gas and its quiescent temperature known and continue to be the mass flow and the flow cross-section at which adjusts a certain static pressure, known as It raises the static pressure calculated as follows:

These are:

Since an ideal gas, the rest temperature along a heat-insulated flow path remains constant ( as well as in the pressure drop due to friction / orifice), the resting temperature can be typically detected at any point along the flow path, wherein the flow rate is negligible. Whether the flow can be considered as thermally insulated, depends not only on the thermal conductivity of the environment also depends on how large are the differences in temperature between the gas flow and the environment and how big is the ratio of surface area to mass flow. Equation (3 ) assumes further that the flow profile of the gas flow has a rectangular velocity distribution. For turbulent flow (which sets in at higher speeds and for which there ever comes only to significant differences between the resting pressure and the static pressure ), this is almost given. If the search matches the static pressure for any flow cross -section, so numerical methods must be applied because equation (3) obviously can not change after the static pressure.

Ausströmvorgang of a container and diffuser

When Ausströmvorgang from a container with a well- rounded nozzle ( → nearly frictionless Ausströmvorgang with usually negligible heat transfer) the corresponding to the static pressure in the nozzle neck resting pressure corresponding to the container internal pressure.

A diffuser with a small expansion angle, the static pressure at the diffuser inlet can also be recycled as far as possible to the static pressure while the flow rate at the inlet of the diffuser is less than the corresponding speed of sound.

Application of pressure at rest

In technical practice, it is often more useful to work with the "correct" static pressure, rather than with the usually simple and direct measurable static pressure. Unfortunately, this is often ignored and lead to further questions and problems. Two examples from the field of flow measurement and flow characteristics determination of pneumatic components are intended to illustrate this fact.

If the form is due to the different conductor cross-sections measured with a smaller pressure measuring tube (pipe, on which the static pressure of the flow can be at right angles to tap to the flow direction ) and the back pressure with a greater pressure measuring tube at a flow- diffuser, so the paradox occurs that the back pressure is greater than the inlet pressure (while the speed of sound in the diffuser is not exceeded ). Thus, the medium flows from the lower static pressure for higher static pressure. Looking at the flow from the point of resting pressures, the static pressure will never increase in the flow direction, but at best remain almost constant.

A common flow coefficient of pneumatic components is the qnN VDI 3290th When qnN correlating the flow to a static pre-or inlet pressure of 6 bar and a static output or outlet pressure of 5 bar is measured. If the qnN on a valve island determined ( unit with common supply terminal and several individually switchable individual valves), so the effect is that the quotient divided from flow -connected by number of ( identical ) Valves not remain constant (or even decreasing, as might be due to could suggest an internal limit), but increases progressively with each other through-connected valve. Cause of this effect is that the static supply pressure is kept constant by readjustment active, but the invisible resting pressure thus increases continuously and the last valve plates results in an increased back pressure, resulting in an increased flow rate.