Difference between revisions of "Fluid dynamics"
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(Euler equation added; I might try to expand the article a bit: Navier-Stokes equation, Bernoulli equations and their consequences, and so on. Nothing too fancy... I will also add references.) |
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| − | '''Fluid dynamics''' is the study of how [[fluid]]s move. Fluids include [[water]] and [[Gas|gases]] (such as [[air]]).<ref>http://virtualskies.arc.nasa.gov/glossary/F.html</ref> | + | '''Fluid dynamics''' is the study of how [[fluid]]s move. Fluids include [[water]] and [[Gas|gases]] (such as [[air]]).<ref>http://virtualskies.arc.nasa.gov/glossary/F.html</ref> Fluid dynamics is also known as continuum mechanics, as fluids cannot be treated as point objects; [[Newton]]'s second law thus becomes Euler equation |
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| + | <math>\frac{D\mathbf{u}}{Dt} = - \frac{1}{\rho}\nabla p + \mathbf{g},</math> | ||
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| + | where <math>\rho</math> is the [[density]] of the fluid, '''u''' its velocity and '''g''' the gravitational acceleration. The [[operator]] <math>D/Dt = \partial/\partial t + (\mathbf{u}\cdot\nabla)</math> is the convective derivative, the rate of change of a certain quantity ''A(t)'' of the fluid as it is carried by the fluid (hence the presence of '''u'''). Euler equation is then a differential operation explicitly relating the effects of the gravity and the gradient of pressure on the velocity of the fluid. | ||
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| + | As long as the [[speed of sound]] is much larger than '''u''', the density <math>\rho</math> of the fluid can be considered as constant (incompressible). | ||
==References== | ==References== | ||
Revision as of 16:49, February 25, 2010
Fluid dynamics is the study of how fluids move. Fluids include water and gases (such as air).[1] Fluid dynamics is also known as continuum mechanics, as fluids cannot be treated as point objects; Newton's second law thus becomes Euler equation
<math>\frac{D\mathbf{u}}{Dt} = - \frac{1}{\rho}\nabla p + \mathbf{g},</math>
where <math>\rho</math> is the density of the fluid, u its velocity and g the gravitational acceleration. The operator <math>D/Dt = \partial/\partial t + (\mathbf{u}\cdot\nabla)</math> is the convective derivative, the rate of change of a certain quantity A(t) of the fluid as it is carried by the fluid (hence the presence of u). Euler equation is then a differential operation explicitly relating the effects of the gravity and the gradient of pressure on the velocity of the fluid.
As long as the speed of sound is much larger than u, the density <math>\rho</math> of the fluid can be considered as constant (incompressible).