User:Frank Rückert/sandbox

The theory of flow filament

The theory of flow filament is a objective of fluid mechanics. It deals with the flow along a streamline, which is a model idea and which must be imagined as a thin stream tube with variable cross-sectional area formed by streamlines. The flow along the flow filament is treated as a one-dimensional process. The state variables speed, pressure, density and temperature do not change over the cross-section of the current filament, but only in the direction of flow.

In current filament theory, compressible and incompressible fluids are considered.

An application example is the flow through a nozzle. In a nozzle, the cross-sectional change of the flow channel also causes a corresponding cross-sectional change in any current filament, which leads to a change in speed and consequently also in pressure. The mathematical description of these changes is an object of current filament theory. In the considerations of current filament theory, a one-dimensional form of the continuity equation is used, which takes into account the law of mass conservation. For incompressible fluids, the Bernoulli equation, which is derived from the principle of conservation of momentum, also plays a role. For compressible fluids, the one-dimensional relationships of gas dynamics also originate from current filament theory. When applying correlations from current filament theory, it must be checked whether the idealizations carried out accurately describe the processes, e.g. whether the changes in the state variables in the transverse direction are actually much smaller than in the flow direction.