# Fluid dynamics

The fluid dynamics is a branch of the fluid dynamics and is involved in moving fluids ( liquids and gases ). The sub-area for gases is aerodynamics , for liquids it is hydrodynamics . For example, laminar and turbulent flows in channels , pressures on bodies in flow as well as movements and force relationships in pressure pipes are examined . The fluid statics other hand, deals with non-moving fluids and is divided into the Hydrostatic (liquids) andAerostatics (gases).

The basic equation of hydrodynamics is the continuity equation :

${\ displaystyle {\ frac {\ partial \ rho} {\ partial t}} + \ operatorname {div} \ left (\ rho {\ vec {v}} \ right) = 0}$

with the mass density and the velocity vector . ${\ displaystyle \ rho}$${\ displaystyle {\ vec {v}}}$

Among other things, this equation states that the mass flow through an area is always the same. This can be clearly explained as follows: you pour water into a hose. To prevent it from bursting because water accumulates in it, the same amount of water must come out at the end of the hose as flows into it. If the hose is narrowed at one point, the same amount of water must still come out at the end. This means that the water in the narrower piece of hose must flow faster than in the further.

In general, the motion of a fluid is described by the Navier-Stokes equations . In the case of low viscosity and thus high Reynolds number , friction effects can be neglected and the equation of motion of the fluid is the Euler equation as a good approximation :

${\ displaystyle {\ frac {\ partial {\ vec {v}}} {\ partial t}} + \ left ({\ vec {v}} \ cdot \ nabla \ right) {\ vec {v}} = - {\ frac {\ nabla p} {\ rho}}}$

This relates the change in speed of the fluid at one location to the pressure in the environment . The Euler equation is often used for the calculation of moving gases, while the Navier-Stokes equations are mostly used for the calculation of moving liquids. ${\ displaystyle p}$