# Stationary flow

A steady flow is present if the flow velocity and the cross-sectional area of the flow (and thus also the flow ) are not subject to any change over time , i.e. if the following applies at each individual location:

${\ displaystyle {\ frac {{\ text {d}} v} {{\ text {d}} t}} = 0}$ and ${\ displaystyle {\ frac {{\ text {d}} A} {{\ text {d}} t}} = 0}$

With

• ${\ displaystyle v}$ the flow velocity
• ${\ displaystyle A}$ the cross-sectional area flowed through
• ${\ displaystyle t}$the time .

The flow velocity and cross-sectional area can vary between different locations. In this case, the system can be described by a speed field. In a steady flow, orbital and streamlines are the same; only then will the particles move on streamlines that remain constant over time, as if on fixed tracks.

## Stationary uniform flow

Flow velocity and flow height are not subject to any local change along a streamline , but they can vary from streamline to streamline: ${\ displaystyle v}$${\ displaystyle h}$

${\ displaystyle {\ frac {{\ text {d}} v} {{\ text {d}} x}} = 0}$ and ${\ displaystyle {\ frac {{\ text {d}} h} {{\ text {d}} x}} = 0}$

## Stationary irregular flow

Flow velocity and flow height are subject to local changes:

${\ displaystyle {\ frac {{\ text {d}} v} {{\ text {d}} x}} \ neq 0}$ and ${\ displaystyle {\ frac {{\ text {d}} h} {{\ text {d}} x}} \ neq 0}$

## Individual evidence

1. Wolfgang Demtröder : Experimentalphysik. Volume 1: Mechanics and Warmth. 4th, revised and updated edition. Springer Spectrum, Berlin 2006, ISBN 3-540-26034-X , pp. 225-226.
2. ^ Karl Wieghardt: Theoretical Fluid Mechanics . Universitätsverlag Göttingen, Göttingen 2005, ISBN 3-938616-33-4 . , P. 19