Steady flow of incompressible fluids


Fluid mechanics is concerned with the study of forces and movements of liquids and gases. Both substances are continua whose elements can easily move against each other. They are grouped together under the term ‘fluid’.

Incompressible flow

Liquids are incompressible. In technical fields of application of fluid mechanics, incompressibility is also assumed for gases as long as the flow velocity remains below Mach 0,3. Based on air at 20°C this limiting value corresponds to a velocity of approximately 100m/s and the change in density is roughly 4%. It is therefore broadly possible to treat liquid and gas flows with common fundamental principles in fluid mechanics.

Steady and transient flow

Steady flow: the velocity of a fluid particle changes with the position: v=f(s).

Transient flow: the velocity of a fluid particle changes with the time and the position: v=f(s,t).

Transient flows occur during discharge processes, during startup and shutdown processes of turbomachines or in the case of fluid oscillations and water hammer processes

To get a better understanding about the different states of fluids, take a look at the following video.

Velocity profile in fully developed flow

  • laminar (left)

  • turbulent (right)

Pressure losses in straight pipes

Pressure losses in pipe fittings

  • enlargement/constriction/change of direction

  • pipe bends

  • segment bends /pipe angles

Losses in single-strand and multi-strand pipe systems

Flow rate metrology: representation of the common industry measuring methods


Cavitation effects in industrial piping systems: formation and consequences

Flow from tanks

Special emphasis on technical issues

  • constructions

  • valve characteristics

  • Kvs values

  • subcritical and supercritical flow

  • control structures

  • discharge measurement