Flow field

The flow field is a concept of field theory and is among others in the electrodynamics and in the fluid mechanics used (fluid mechanics). The flow field describes rivers (currents) that transport material or other properties such as force effects (interactions) within a spatial area.

General

Since the densities of rivers in spatial areas are primarily of interest and rivers are described as area integrals that are usually more difficult to handle , the associated flux densities are primarily considered in flow fields . Depending on the specific area of ​​application, rivers and their densities can be e.g. B. to be electrical charge carriers , liquids, gases or magnetic fluxes.

One distinguishes

• stationary flow fields in which there is no change in the flow over time - these flows are usually relatively easy to model
• unsteady flow fields in which the flow distributions also change over time.

A distinction is also made:

• homogeneous flow fields, in which the flow distribution is constant in a certain space segment of the flow field. Only in this case is the density of the field equal to the simple quotient of river and area : ${\displaystyle D}$ ${\displaystyle F}$ ${\displaystyle A}$

${\displaystyle D_{\text{hom}}={\frac {F}{A}}}$

• inhomogeneous , d. H. spatially non- constant flow fields in which the flow density is different at every point in space. They are to be calculated as a derivative :

${\displaystyle D_{\text{inhom}}={\frac {dF}{dA}}}$

Flow field in electrodynamics

In electrodynamics, flow fields are used, among other things, to describe the spatial distribution of electrical currents, which is described by the current density . For example, the charge carrier current (electrons) in an electrical conductor (cable) results in a specific current density (current distribution) that is generally not constant over the location. The current of charge carriers represents the electric current , the associated density is the electric current density . ${\displaystyle I}$ ${\displaystyle J}$

Furthermore, a spatial distribution of electrical charges represents a flow field of the electrical flow . The current occurring corresponds to the distributed electrical charges (space charges) , the associated flux density is the electrical flux density . ${\displaystyle Q}$ ${\displaystyle D}$

A final example of a flow field in electrodynamics is the magnetic flux . This is primarily caused by spatially distributed currents, charge carrier movements. The associated magnetic flux density is given in Tesla . ${\displaystyle \Phi }$ ${\displaystyle B}$

Quasi-static flow field

Quasi- static flow fields occur in conductors through which alternating current flows or something in impulse current measuring resistors , as long as current displacement phenomena play no role. Whether or not a flow field can be described as quasi-static depends on the arrangement under consideration and the rate of change of the variable voltage driving the line current. Therefore, the same applies to the quasi-static flow field without current displacement as to a static flow field.

Flow field in mechanics

Fluid mechanics deals with flowing liquids and gases , the flow of which is caused by pressure differences and the effect of gravity . The flowing medium has a velocity distribution that is characterized by the flow field. A flow field is characterized by the fact that the velocity of the medium flowing there (gas or liquid particles) is assigned to each point in space at any point in time. Thus mass flows are observed in fluid mechanics .

A mechanical flow field is characterized by streamlines :

• the direction of the flow velocity at a point is given by the tangent to the streamline at this point.
• the following agreement was made for the amount of speed in one point: ${\displaystyle v}$ ${\displaystyle {\vec {v}}}$

${\displaystyle v={\frac {N}{A_{\perp }}}}$

d. H. the amount of flow velocity at a point is defined as the number of streamlines per vertically intersected area in the vicinity of this point (this is precisely the density of the streamlines). ${\displaystyle N}$ ${\displaystyle A}$

As already mentioned in the general introduction, a distinction is made between time-independent (stationary) and time-dependent (non-stationary) flow fields as well as location-independent (homogeneous) and location-dependent (inhomogeneous) flow fields.

literature

• Adolf J. Schwab: Conceptual World of Field Theory, Springer Verlag, ISBN 3-540-42018-5

Web links

Global map of wind currents