From Wikipedia, the free encyclopedia
|Navier–Stokes equations |
Relationship to continuum mechanicsFluid mechanics is a sub discipline of continuum mechanics, as illustrated in the following table.
|Continuum mechanics the study of the physics of continuous materials||Solid mechanics: the study of the physics of continuous materials with a defined rest shape.||Elasticity: which describes materials that return to their rest shape after an applied stress.|
|Plasticity: which describes materials that permanently deform after a large enough applied stress.||Rheology: the study of materials with both solid and fluid characteristics|
|Fluid mechanics: the study of the physics of continuous materials which take the shape of their container.||Non-Newtonian fluids|
The continuum hypothesis
General form of the equation
- is the fluid density,
- is the substantive derivative (also called the material derivative),
- is the velocity vector,
- is the body force vector, and
- is a tensor that represents the surface forces applied on a fluid particle (the comoving stress tensor).
- are normal stresses, and
- are tangential stresses (shear stresses).
Newtonian vs. non-Newtonian fluids
Equations for a Newtonian fluid
- τ is the shear stress exerted by the fluid ("drag")
- μ is the fluid viscosity - a constant of proportionality
- is the velocity gradient perpendicular to the direction of shear
- τij is the shear stress on the ith face of a fluid element in the jth direction
- vi is the velocity in the ith direction
- xj is the jth direction coordinate
|Wikibooks has more on the topic of |
- ^ Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", p. 642, in Rashed, Roshdi & Régis Morelon (1996), Encyclopedia of the History of Arabic Science, vol. 1 & 3, Routledge, 614-642, ISBN 0415124107: "Using a whole body of mathematical methods (not only those inherited from the antique theory of ratios and infinitesimal techniques, but also the methods of the contemporary algebra and fine calculation techniques), Arabic scientists raised statics to a new, higher level. The classical results of Archimedes in the theory of the centre of gravity were generalized and applied to three-dimensional bodies, the theory of ponderable lever was founded and the 'science of gravity' was created and later further developed in medieval Europe. The phenomena of statics were studied by using the dynamic apporach so that two trends - statics and dynamics - turned out to be inter-related withina single science, mechanics. The combination of the dynamic apporach with Archimedean hydrostatics gave birth to a direction in science which may be called medieval hydrodynamics. [...] Numerous fine experimental methods were developed for determining the specific weight, which were based, in particular, on the theory of balances and weighing. The classical works of al-Biruni and al-Khazini can by right be considered as the beginning of the application of experimental methods in medieval science."
- White, Frank M. (2003). Fluid Mechanics. McGraw-Hill. ISBN 0072402172
- Cramer, Mark. "The Gallery of Fluid Mechanics" [link appears dead]
- Massey, B. & Ward-Smith, J. (2005). Mechanics of Fluids - 8th ed. Taylor & Francis, ISBN 978-0-415-36206-1.
- Annual Review of Fluid Mechanics
- CFDWiki -- the Computational Fluid Dynamics reference wiki.
- Educational Particle Image Velocimetry - resources and demonstrations