# Fluid dynamics

$\frac{D\mathbf{u}}{Dt} = - \frac{1}{\rho}\nabla p + \mathbf{g},$
where $\rho$ is the density of the fluid, u its velocity and g the gravitational acceleration. The operator $D/Dt = \partial/\partial t + (\mathbf{u}\cdot\nabla)$ 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 $\rho$ of the fluid can assumed to be constant (incompressible) in most situations.