Flow velocity

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The flow velocity , also flow velocity or flow velocity , is the velocity in a flow , a directed movement of particles or continuous bodies ( fluids ).

A distinction is made between the flow velocities of the individual particles and the mean flow velocity over a line, area or volume element or time interval.

The flow speed of water is the average speed at which the water moves downstream and is on the order of 1 meter per second. In contrast, that of groundwater is millimeters per second or centimeters per day, ie a few orders of magnitude lower.


The flow velocity is the change in location of the individual point (location) along its path .

: Flow
the point is the time derivative in physical notation

The flow velocity vectors carry one time line over into the next.

Average flow velocities can be determined using a streamline , the flow cross-section or the flow rate ( volume flow element , mass flow ).

Flow velocity in the potential field

In the potential field , the flow velocity follows the equation of motion

: Nabla operator
: Potential

The specific energy equation applies :

Flow velocity in the Newtonian fluid

The flow velocity in a field of a flow in a Newtonian fluid is calculated from the Navier-Stokes equations , in their general formulation:

: Density of the fluid
: Time
: Pressure
: 1. Lamé constant
: 2. Lamé constant, dynamic viscosity
: Partial derivative with respect to time
: Nabla operator

For this basic equation of fluid mechanics , a system of non-linear partial differential equations of the 2nd order, there are numerous simplifications, special cases and numerical approaches.

Non-Newtonian fluids such as blood, glycerine or dough, which show a non-proportional, erratic flow behavior (see rheology ), behave differently .

Application formulas

Examples of formulas in more specific application areas are:

  • The Bernoulli equation for smooth liquids and gases:
  • Bernoulli's general law for frictionless, eddy-free , stationary flows
  • The Bernoulli law at constant density
  • Bernoulli equation with acceleration term for non-stationary flow:
  • Bernoulli equation of relative motion
    : Circumferential speed - application for blade rings
  • Bernoulli equation at higher speeds (about> 150 m / s):

Typical formulas for measurement methods

  • Dynamic pressure in the open air flow:
: Back pressure
  • Lateral discharge from an open vessel:

Medium speeds

  • mean flow velocity with a non-constant cross-section
    Velocity at a point on the cross-section as a function of the location , with the direction of flow , so that .

The flow velocity has an influence on the velocity-dependent parameters Reynolds number and Froude number .

Measurement methods

The determination of the flow rate can be done with different techniques. Flow velocity in free air flow:

Flow velocity of currents in pipelines :

Flow velocity of bodies of water and currents in open channels :

General measurement methods:


See also