stream function

Also found in: Wikipedia.

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 ?
p] - specific heatat constant pressure, J /kg [degrees]C; f - Reduced stream function defined by Eq.
The research will tackle issues including sudden aspen decline, stream function and sensitivity, restoration of stream and riparian areas, adaptive management of rangelands and wildlife habitat, and energy development impacts on large mammals in the Piceance Basin.
The stream function must now be made to satisfy the momentum equations (2) and (3) for steady flow (2) and (3) will now become
In the forgoing analysis, the stream function formulation is introduced in the mathematical model.
Experienced teachers of visually impaired children and orientation and mobility (O&M) specialists will appreciate much of the information included in the book, as it provides an excellent description of the visual system, and dorsal and ventral stream function and gives insight into the methods of clinical evaluation and issues faced by clinicians working with children with this condition.
Equation (5) is the elliptic equation represents the stream function in the cavity The Navier-Stokes equation in Vorticity--stream function using equation (3)
In the present work we consider unsteady flows which have the stream function, [psi] (x, y, t) = x[xi] (z, t), z = y + Kx.
Hence, it is possible to avoid some assumptions for pressure distribution by introducing the vorticity and stream function as dependent variables.
From the standpoint of future stream function, large-span bridges, or at the very least oversized culverts with natural channel bottoms, should be installed in areas slated for urbanization.
The Hele-Shaw (lubrication) approximation leads to a potential equation for pressure or stream function on the plane of the slit, which combines momentum and mass conservation.