Fluid dynamics

Fluid dynamics is a branch of fluid mechanics and deals with moving fluids (liquids and gases). The subfield for gases is aerodynamics, for liquids hydrodynamics. For example, laminar and turbulent flows in channels, pressures on flowing bodies as well as movements and forces in pressure lines are investigated. Fluid statics, on the other hand, deals with immobile fluids and is divided into hydrostatics (liquids) and aerostatics (gases).

The basic equation of hydrodynamics is the continuity equation:

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

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

This equation states, among other things, that the mass flow through a surface is always the same. This can be explained as follows: water is introduced into a hose. To prevent it from bursting because water accumulates in it, the same amount of water must come out of 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 must flow faster in the narrower section of the hose than in the wider one.

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, frictional effects can be neglected and the Euler equation applies as the equation of motion of the fluid in a good approximation:

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

This relates the change in velocity of the fluid at a location to the pressure prevailing in the environment. The Euler equation is often used for the calculation of moving gases, while the Navier-Stokes equations are usually used for the calculation of moving fluids.

Questions and Answers

Q: What does Fluid Dynamics talk about?

A: Fluid Dynamics talks about how fluids (liquids and gases) work.

Q: Who studies Fluid Dynamics?

A: Fluid Dynamics is studied by physicists, mathematicians, and engineers.

Q: How can Mathematics describe how fluids move?

A: Mathematics can describe how fluids move using mathematical formulas called equations.

Q: What are the fluid dynamics of gases called?

A: The fluid dynamics of gases are called aerodynamics.

Q: Why is it important to understand how fluids behave?

A: Understanding how fluids behave helps us understand things like flight or ocean currents.

Q: How can computer programs use the mathematical equations of fluid dynamics?

A: Computer programs can use the mathematical equations of fluid dynamics to model and predict the actions of moving fluids.

Q: What is the name for studying how fluid dynamics can be done with computers?

A: Studying how fluid dynamics can be done with computers is called computational fluid dynamics (or CFD for short).