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The curl of the vector field at any point is given by the rotation of an infinitesimal area in the xy-plane (for z-axis component of the curl), zx-plane (for y-axis component of the curl) and yz-plane (for x-axis component of the curl vector). This can be seen in the examples below.
In fluid dynamics, the Taylor number (Ta) is a dimensionless quantity that characterizes the importance of centrifugal "forces" or so-called inertial forces due to rotation of a fluid about an axis, relative to viscous forces. [1] In 1923 Geoffrey Ingram Taylor introduced this quantity in his article on the stability of flow. [2]
Examples of common boundary conditions include the velocity of the fluid, determined by =, being 0 on the boundaries of the system. There is a great amount of overlap with electromagnetism when solving this equation in general, as the Laplace equation also models the electrostatic potential in a vacuum.
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.
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.
For example, in the laminar flow within a pipe with constant cross section, all particles travel parallel to the axis of the pipe; but faster near that axis, and practically stationary next to the walls. The vorticity will be zero on the axis, and maximum near the walls, where the shear is largest.
Informally, a flow may be viewed as a continuous motion of points over time. More formally, a flow is a group action of the real numbers on a set. The idea of a vector flow, that is, the flow determined by a vector field, occurs in the areas of differential topology, Riemannian geometry and Lie groups.
Rotation of an object in two dimensions around a point O. Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point.