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The value of the stream function is constant along every streamline (streamlines represent the trajectories of particles in steady flow). That is, in two dimensions each streamline is a level curve of the stream function.
A scalar function whose contour lines define the streamlines is known as the stream function. Dye line may refer either to a streakline: dye released gradually from a fixed location during time; or it may refer to a timeline: a line of dye applied instantaneously at a certain moment in time, and observed at a later instant.
In fluid dynamics, the Stokes stream function is used to describe the streamlines and flow velocity in a three-dimensional incompressible flow with axisymmetry. A surface with a constant value of the Stokes stream function encloses a streamtube , everywhere tangential to the flow velocity vectors.
The stream function associated with source flow is – (,) =. The steady flow from a point source is irrotational, and can be derived from velocity potential. The velocity potential is given by – (,) = .
A practical example of this type of flow is a bridge pier or a strut placed in a uniform stream. The resulting stream function and velocity potential are obtained by simply adding the stream function and velocity potential for each individual flow.
These total flow conditions are a function of the fluid velocity and have different values in frames of reference with different motion. To avoid potential ambiguity when referring to the properties of the fluid associated with the state of the fluid rather than its motion, the prefix "static" is commonly used (such as static temperature and ...
New details about a study that warned against black plastic spatulas and other kitchen tools have come out. (Getty Creative) (Анатолий Тушенцов via Getty Images)
Pressure field (colors), stream function (black) with contour interval of 0.2Ur from bottom to top, velocity potential (white) with contour interval 0.2Ur from left to right. A cylinder (or disk) of radius R is placed in a two-dimensional, incompressible, inviscid flow.