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The near-wall velocity gradient of the unburned reactants flowing from a tube is a key parameter for characterising flame stability. [5]: 1–3 The velocity gradient of a plasma can define conditions for the solutions to fundamental equations in magnetohydrodynamics. [4]
Defining equation SI units Dimension Flow velocity vector field u = (,) ... Equations Fluid statics, pressure gradient: r = Position;
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.
The gradient of a function is called a gradient field. A (continuous) gradient field is always a conservative vector field: its line integral along any path depends only on the endpoints of the path, and can be evaluated by the gradient theorem (the fundamental theorem of calculus for line integrals). Conversely, a (continuous) conservative ...
Potential flow describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field , which is a valid approximation for several applications.
The vorticity equation of fluid dynamics describes the evolution of the vorticity ω of a particle of a fluid as it moves with its flow; that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity). The governing equation is:
For example, the flow velocity is represented by a function (,). On the other hand, in the Lagrangian specification , individual fluid parcels are followed through time. The fluid parcels are labelled by some (time-independent) vector field x 0 .
The pressure gradient can be positive (adverse pressure gradient) or negative (favorable pressure gradient). In the limiting case of stationary plates ( U = 0 {\displaystyle U=0} ), the flow is referred to as Plane Poiseuille flow , and has a symmetric (with reference to the horizontal mid-plane) parabolic velocity profile.