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The red particle moves in a flowing fluid; its pathline is traced in red; the tip of the trail of blue ink released from the origin follows the particle, but unlike the static pathline (which records the earlier motion of the dot), ink released after the red dot departs continues to move up with the flow. (This is a streakline.)
Because = everywhere (e.g., see In terms of vector rotation), each streamline corresponds to the intersection of a particular stream surface and a particular horizontal plane. Consequently, in three dimensions, unambiguous identification of any particular streamline requires that one specify corresponding values of both the stream function and ...
File:Lagrangian vs Eulerian [further explanation needed] Eulerian perspective of fluid velocity versus Lagrangian depiction of strain. In classical field theories , the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time.
which is a (counter-clockwise) rigid body rotation with a superposed constant horizontal translation. A streakline starting at = (,) will intersect itself twice. See also animation below which shows the pathlines of the emitted particles (emitted every 0.5 time units) and the streaklines.
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases.It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of water and other liquids in motion).
In physics, drawings of field lines are mainly useful in cases where the sources and sinks, if any, have a physical meaning, as opposed to e.g. the case of a force field of a radial harmonic. For example, Gauss's law states that an electric field has sources at positive charges , sinks at negative charges, and neither elsewhere, so electric ...
Symbol Name Meaning SI unit of measure nabla dot : the divergence operator often pronounced "del dot" per meter (m −1) : nabla cross : the curl operator often pronounced "del cross"
Since a streamline is a curve that is tangent to the velocity vector of the flow, the left-hand side of the above equation, the convective derivative of velocity, can be described as follows: = = +, where =,, =, and is the radius of curvature of the streamline.