# 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 ?
NOMENCLATURE a = Constant g = Acceleration due to gravity k = Thermal Conductivity Pr = Prandtl Number T = Fluid Temperature Tw = Surface Temperature T8 = Free Stream Temperature u,v = Velocity Components x,y = Cartesian Coordinates f(x) = Dimensionless Stream Function Gr = Grashof Number qr = Heat Flux Radiation Bo = Magnetic Field of Constant Strength R = Radiation Parameter Ks = Rosseland Mean Absorption Coefficient K = Thermal Conductivity Coefficient GREEK SYMBOLS [beta] = Thermal Expansion Coefficient [micro] = Dynamic Coefficient of Viscosity [thera] ([bern]) = Dimensionless Temperature [eta] = Similarity Variable [rho] = Fluid Density [PSI] = Stream Function [sigma]' = Stefan-Bottzman Constant 2.
[4], [7], [17], [18], where the pressure is eliminate from the Navier-Stokes equations for viscous, incompressible and ideal, compressible flow by introducing the stream function and vorticity for the combustion process with simple exothermic chemical reaction.
In (1), f is the stream function; [[beta].sub.0] = ([[omega].sub.0]/[R.sub.0])/cos [[phi].sub.0], in which [R.sub.0] is the earth's radius, [[omega].sub.0] is the angular frequency of the earth's rotation, and 00 is the latitude; [[lambda].sub.0] = [f.sub.0]/[square root of gH], in which [f.sub.0] is the Coriolis parameter, g is the gravitational acceleration, and H is the atmospheric average height.
Discretization of Stream Function. Stream function equation is the elliptic equations; it can be dispersed by arrays of central difference with second-order accuracy.
13; [rho] - fluid density ,kg/[m.sup.3]; [sigma] - fluid electrical conductivity, A/V m; [phi] - angle inclination, [degrees]; [psi] - stream function, [m.sup.2]/s)
The numerical results for single and double lid driven cavity flow are presented by means of velocity, viscosity, and stream function plots in Section 4.
Two-dimensional ideal incompressible magnetohydrodynamics (MHD) equation can be described by a set of two scalar equations for the vorticity w and the magnetic stream function y; namely [1],
The velocity has two components that are described as u and v in terms of the stream function (x, y) as given below:
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.
Stream function formulation and suitable transformations reduce the arising problem to ordinary differential equation which has been solved by homotopy analysis method.

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