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The Rankine vortex is a simple mathematical model of a vortex in a viscous fluid. It is named after its discoverer, William John Macquorn Rankine. The vortices observed in nature are usually modelled with an irrotational (potential or free) vortex. However, in a potential vortex, the velocity becomes infinite at the vortex center.
The Rankine vortex is a model that assumes a rigid-body rotational flow where r is less than a fixed distance r 0, and irrotational flow outside that core regions. In a viscous fluid, irrotational flow contains viscous dissipation everywhere, yet there are no net viscous forces, only viscous stresses. [ 7 ]
A vortex tube is the surface in the continuum formed by all vortex lines passing through a given (reducible) closed curve in the continuum. The 'strength' of a vortex tube (also called vortex flux ) [ 10 ] is the integral of the vorticity across a cross-section of the tube, and is the same everywhere along the tube (because vorticity has zero ...
William John Macquorn Rankine FRSE FRS (/ ˈ r æ ŋ k ɪ n /; 5 July 1820 – 24 December 1872) was a Scottish mathematician and physicist. He was a founding contributor, with Rudolf Clausius and William Thomson (Lord Kelvin), to the science of thermodynamics , particularly focusing on its First Law.
In fluid dynamics, the Lamb–Oseen vortex models a line vortex that decays due to viscosity. This vortex is named after Horace Lamb and Carl Wilhelm Oseen. [1] [2] Vector plot of the Lamb–Oseen vortex velocity field. Evolution of a Lamb–Oseen vortex in air in real time. Free-floating test particles reveal the velocity and vorticity pattern.
A schematic diagram of a shock wave situation with the density , velocity , and temperature indicated for each region.. The Rankine–Hugoniot conditions, also referred to as Rankine–Hugoniot jump conditions or Rankine–Hugoniot relations, describe the relationship between the states on both sides of a shock wave or a combustion wave (deflagration or detonation) in a one-dimensional flow in ...
T-s diagram for the ideal/real ORC. The working principle of the organic Rankine cycle is the same as that of the Rankine cycle: the working fluid is pumped to a boiler where it is evaporated, passed through an expansion device (turbine, [3] screw, [4] scroll, [5] or other expander), and then through a condenser heat exchanger where it is finally re-condensed.
Rankine's theory (maximum-normal stress theory), developed in 1857 by William John Macquorn Rankine, [1] is a stress field solution that predicts active and passive earth pressure. It assumes that the soil is cohesionless, the wall is frictionless, the soil-wall interface is vertical, the failure surface on which the soil moves is planar , and ...