Differential equation describing pressure distribution of thin viscous fluids
This article is about the equation in lubrication theory. For the dimensionless quantity, see Reynolds number. For the turbulence-modeling technique, see Reynolds-averaged Navier–Stokes equations.
In fluid mechanics (specifically lubrication theory), the Reynolds equation is a partial differential equation governing the pressure distribution of thin viscous fluid films. It was first derived by Osborne Reynolds in 1886.[1] The classical Reynolds Equation can be used to describe the pressure distribution in nearly any type of fluid film bearing; a bearing type in which the bounding bodies are fully separated by a thin layer of liquid or gas.
^Cite error: The named reference Reynolds1886 was invoked but never defined (see the help page).
mechanics (specifically lubrication theory), the Reynoldsequation is a partial differential equation governing the pressure distribution of thin viscous...
instability The definition of the Reynolds number is not to be confused with the Reynoldsequation or lubrication equation. Full development of the flow occurs...
Reynolds stress equation model (RSM), also referred to as second moment closures are the most complete classical turbulence model. In these models, the...
the particle Reynolds Number (based on superficial velocity).. To calculate the pressure drop in a given reactor, the following equation may be deduced:...
the Reynolds number; if the fluid is a gas, c d {\displaystyle c_{\rm {d}}} depends on both the Reynolds number and the Mach number. The equation is attributed...
phenomenological Colebrook–White equation (or Colebrook equation) expresses the Darcy friction factor f as a function of Reynolds number Re and pipe relative...
same time. Reynolds number Reynolds analogy ReynoldsequationReynolds transport theorem Reynolds decomposition Reynolds stress Reynolds-averaged Navier–Stokes...
the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier–Stokes equations to account...
flow as well as flow with low viscosity and a Reynolds number much greater than one. Using the Euler equation, many fluid dynamics problems involving low...
The classical elastohydrodynamic theory considers Reynoldsequation and the elastic deflection equation to solve for the pressure and deformation in this...
requires turbulence models for the foreseeable future. Reynolds-averaged Navier–Stokes equations (RANS) combined with turbulence modelling provides a model...
bearings). Gas-lubricated bearings are usually modeled using the Reynoldsequation to describe the evolution of pressure in the thin film domain. Unlike...
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\to 0} , the first term in the induction equation vanishes. This is equivalent to a very large magnetic Reynolds number. For example, it can be of order...
actually solve transport equations for the Reynolds stresses. This means introduction of several transport equations for all the Reynolds stresses and hence...
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non-dimensional form that relates the Darcy–Weisbach friction factor fD, Reynolds number Re, and surface roughness for fully developed flow in a circular...
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