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In fluid mechanics, a two-dimensional flow is a form of fluid flow where the flow velocity at every point is parallel to a fixed plane. The velocity at any point on a ...
The first two scale factors of the coordinate system are independent of the last coordinate: ∂h 1 / ∂x 3 = ∂h 2 / ∂x 3 = 0, otherwise extra terms appear. The stream function has some useful properties: Since −∇ 2 ψ = ∇ × (∇ × ψ) = ∇ × u, the vorticity of the flow is just the negative of the Laplacian of ...
Shown is a sphere in Stokes flow, at very low Reynolds number. Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, [1] is a type of fluid flow where advective inertial forces are small compared with viscous forces. [2] The Reynolds number is low, i.e. . This is a typical situation in flows where the ...
The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange in 1781, [1] is defined for incompressible (divergence-free), two-dimensional flows. The Stokes stream function , named after George Gabriel Stokes , [ 2 ] is defined for incompressible, three-dimensional flows with axisymmetry .
In real life, there will be a huge pressure at the point, which depends on the geometry of the contact. The stresses are shown in the figure as given in the Taylor's original paper. The stress in the direction parallel to the lower wall decreases as α {\displaystyle \alpha } increases, and reaches its minimum value σ x = 2 μ U / r ...
A typical example of this flow is the forward stagnation point appearing in a flow past a sphere. Paul A. Libby (1974) [ 16 ] (1976) [ 17 ] extended Homann's work by allowing the solid wall to translate along its own plane with a constant speed and allowing constant suction or injection at the solid surface.
The Kutta–Joukowski theorem is a fundamental theorem in aerodynamics used for the calculation of lift of an airfoil (and any two-dimensional body including circular cylinders) translating in a uniform fluid at a constant speed so large that the flow seen in the body-fixed frame is steady and unseparated.
Generic flow patterns can be also de-composed in terms of multipole expansions, in the same manner as for electric and magnetic fields where the monopole is essentially the first non-trivial (e.g. constant) term of the expansion. This flow pattern is also both irrotational and incompressible. This is characterized by a cylindrical symmetry: