stream function

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Stream function

In fluid mechanics, a mathematical idea which satisfies identically, and therefore eliminates completely, the equation of mass conservation. If the flow field consists of only two space coordinates, for example, x and y, a single and very useful stream function ψ(x, y) will arise. If there are three space coordinates, such as (x, y, z), multiple stream functions are needed, and the idea becomes much less useful and is much less widely employed.

The stream function not only is mathematically useful but also has a vivid physical meaning. Lines of constant ψ are streamlines of the flow; that is, they are everywhere parallel to the local velocity vector. No flow can exist normal to a streamline; thus, selected ψ lines can be interpreted as solid boundaries of the flow.

Further, ψ is also quantitatively useful. In plane flow, for any two points in the flow field, the difference in their stream function values represents the volume flow between the points. See Creeping flow, Fluid flow

stream function

[′strēm ‚fəŋk·shən]
(fluid mechanics)
References in periodicals archive ?
Our aim is to initially eliminate the appearance of the pressure term in the equations, and to this end, we introduce streamfunction and vorticity formulae in two-dimensional coordinates to enable computation of the velocity components without any assumptions on the pressure.
The axial velocity a and radial velocity v are defined as derivatives of the streamfunction, i.
3), the initial condition for the streamfunction is given by
In studying Riabouchinsky flows [4] the streamfunction is taken to be linear in one of the space dimensions.
We introduce the streamfunction and vorticity formulas in the two-dimensional cylindrical coordinates for the governing equations in order to avoid the explicit appearance of the pressure term.
The axial velocity a and radial velocity v are defined as the derivatives of the streamfunction, i.