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The Lorenz equations are derived from the Oberbeck–Boussinesq approximation to the equations describing fluid circulation in a shallow layer of fluid, heated uniformly from below and cooled uniformly from above. [26] This fluid circulation is known as Rayleigh–Bénard convection. The fluid is assumed to circulate in two dimensions (vertical ...
In fluid mechanics, non-dimensionalization of the Navier–Stokes equations is the conversion of the Navier–Stokes equation to a nondimensional form. This technique can ease the analysis of the problem at hand, and reduce the number of free parameters. Small or large sizes of certain dimensionless parameters indicate the importance of certain ...
Lattice Boltzmann methods. The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy- Pomeau -Pazzis and Frisch - Hasslacher - Pomeau models), is a class of computational fluid dynamics (CFD) methods for fluid simulation. Instead of solving the Navier–Stokes equations directly, a fluid density on a ...
Analysis Situs (PDF), archived (PDF) from the original on 27 March 2012. The first systematic study of topology. On celestial mechanics: 1890. Poincaré, Henri (2017). The three-body problem and the equations of dynamics: Poincaré's foundational work on dynamical systems theory. Translated by Popp, Bruce D. Cham, Switzerland: Springer ...
Moody chart. In engineering, the Moody chart or Moody diagram (also Stanton diagram) is a graph in non-dimensional form that relates the Darcy–Weisbach friction factor fD, Reynolds number Re, and surface roughness for fully developed flow in a circular pipe. It can be used to predict pressure drop or flow rate down such a pipe.
The Herschel–Bulkley fluid is a generalized model of a non-Newtonian fluid, in which the strain experienced by the fluid is related to the stress in a complicated, non-linear way. Three parameters characterize this relationship: the consistency k , the flow index n , and the yield shear stress τ 0 {\displaystyle \tau _{0}} .
The history of fluid mechanics is a fundamental strand of the history of physics and engineering. The study of the movement of fluids (liquids and gases) and the forces that act upon them dates back to pre-history. The field has undergone a continuous evolution, driven by human dependence on water, meteorological conditions and internal ...
Bow-tie diagram. A bow-tie diagram is a graphic tool used to describe a possible damage process in terms of the mechanisms that may initiate an event in which energy is released, creating possible outcomes, which themselves produce adverse consequences such as injury and damage. The diagram is centred on the (generally unintended) event with ...