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When we consider 2-D flows on the perpendicular plane, a line source appears as a point source. By symmetry, we can assume that the fluid flows radially outward from the source. The strength of a source can be given by the volume flow rate Q {\displaystyle Q} that it generates.
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.
Two solutions of the three-dimensional Euler equations with cylindrical symmetry have been presented by Gibbon, Moore and Stuart in 2003. [29] These two solutions have infinite energy; they blow up everywhere in space in finite time.
They differ only when the flow changes with time, that is, when the flow is not steady. [1] [2] Considering a velocity vector field in three-dimensional space in the framework of continuum mechanics: Streamlines are a family of curves whose tangent vectors constitute the velocity vector field of the flow.
The equation above is a vector equation in a three-dimensional flow, but it can be expressed as three scalar equations in three coordinate directions. The conservation of momentum equations for the compressible, viscous flow case is called the Navier–Stokes equations. [2] Conservation of energy
Shock waves at the pointed leading edge of two-dimensional wedge or three-dimensional cone (Taylor–Maccoll flow) has constant intensity. 2) For weak shock waves, the entropy jump across the shock wave is a third-order quantity in terms of shock wave strength and therefore can be neglected. Shock waves in slender bodies lies nearly parallel to ...
In fluid dynamics, a stagnation point flow refers to a fluid flow in the neighbourhood of a stagnation point (in two-dimensional flows) or a stagnation line (in three-dimensional flows) with which the stagnation point/line refers to a point/line where the velocity is zero in the inviscid approximation. The flow specifically considers a class of ...
In the larger context of the Navier-Stokes equations (and especially in the context of potential theory), elementary flows are basic flows that can be combined, using various techniques, to construct more complex flows. In this article the term "flow" is used interchangeably with the term "solution" due to historical reasons.