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Since solid-body rotation is characterized by an azimuthal velocity , where is the constant angular velocity, one can also use the parameter = / to characterize the vortex. The vorticity field ( ω r , ω θ , ω z ) {\displaystyle (\omega _{r},\omega _{\theta },\omega _{z})} associated with the Rankine vortex is
In flow regions where vorticity is known to be important, such as wakes and boundary layers, potential flow theory is not able to provide reasonable predictions of the flow. [1] Fortunately, there are often large regions of a flow where the assumption of irrotationality is valid which is why potential flow is used for various applications.
The problem of potential compressible flow over circular cylinder was first studied by O. Janzen in 1913 [4] and by Lord Rayleigh in 1916 [5] with small compressibility effects. Here, the small parameter is the square of the Mach number M 2 = U 2 / c 2 ≪ 1 {\displaystyle \mathrm {M} ^{2}=U^{2}/c^{2}\ll 1} , where c is the speed of sound .
The rotation moves around in circles. In this example the rotation of the bucket creates extra force. The reason that the vortices can change shape is the fact that they have open particle paths. This can create a moving vortex. Examples of this fact are the shapes of tornadoes and drain whirlpools.
The problem has a cylindrical symmetry and can be treated in two dimensions on the orthogonal plane. Line sources and line sinks (below) are important elementary flows because they play the role of monopole for incompressible fluids (which can also be considered examples of solenoidal fields i.e. divergence free fields).
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.
A "reverse" or "inverse" sprinkler would operate by aspirating the surrounding fluid instead. The problem is commonly associated with theoretical physicist Richard Feynman, who mentions it in his bestselling memoirs Surely You're Joking, Mr. Feynman!. The problem did not originate with Feynman, nor did he publish a solution to it.