Fluid dynamics

Fluid dynamics is the study of how fluids move. Fluids include water and gases (such as air). Fluid dynamics is also known as continuum mechanics, as fluids cannot be treated as point objects; Newton's second law thus becomes Euler equation

${\frac {D\mathbf {u} }{Dt}}=-{\frac {1}{\rho }}\nabla p+\mathbf {g} ,$

where $\rho$ is the density of the fluid, u its velocity and g the gravitational acceleration. The operator Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D/Dt = \partial/\partial t + (\mathbf{u}\cdot\nabla)} 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho} of the fluid can assumed to be constant (incompressible) in most situations.