Stream filament theory

The streamline theory is a field of fluid mechanics . It deals with the flow along a stream filament , which is a model concept and which one has to imagine as a thin stream tube formed by streamlines with a variable cross-sectional area . 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 stream filament, but only in the direction of flow.

In streamline theory, compressible and incompressible fluids are considered.

An application example is the flow through a nozzle . In a nozzle, as a result of the change in cross-section of the flow channel, any desired flow filament also experiences a corresponding change in cross-section, which leads to a change in speed and consequently also in pressure. The mathematical description of these changes is a subject of stream filament theory.

When considering the current filament theory, u. a. uses a one-dimensional form of the continuity equation that takes into account the law of conservation of mass . In addition, the Bernoulli equation , which is derived from the law of conservation of momentum, plays a role for incompressible fluids . For compressible fluids, the one-dimensional relationships of gas dynamics also arise from the streamline theory.

When applying relationships from the streamline theory, it must be checked whether the idealizations that have been made describe the processes correctly, e.g. B. whether the changes in the state variables in the transverse direction are actually much smaller than in the flow direction.

literature

• Jürgen Zierep: Basics of fluid mechanics. Springer, Berlin 1997, ISBN 3540616152 .