# Basics

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This section provides a systematic explanation of the background ideas, notions, and facts needed for understanding fluid flows. It will grow. As of now, it includes the following pages:

Reynolds number and dynamic similarity of fluid flows

Experienced fluid dynamicists first of all calculate the Reynolds number when starting to analyse a particular flow, because its value tells them a lot. …

Understanding vorticity

Vorticity is one of the most important and most useful notions in fluid dynamics. Vorticity is the angular velocity of fluid particles multiplied by 2. …

The language of fluid dynamics

Fluid dynamicists use special terminology: velocity field and pressure field, fluid particles, material lines, streamlines and streak lines, vorticity, Eulerian and Lagrangian viewpoints and many more.

Lagrangian and Eulerian viewpoints

Mr. Euler, on a bridge, and Mr. Lagrange, in a boat carried by a river, are measuring the rate at which the temperature is varying. Their observations differ. Why?

Incompressibility

Everyone knows that mass is conserved. What does this mean for a fluid flow? …

The problem of pressure: the intrigue of hydrodynamics

Reasoning in terms of vorticity-velocity instead of pressure-velocity, and in terms of boundary layers when possible, is the key to intuitive understanding of hydrodynamics. …

Viscosity in shear flows

Friction is a force acting in fluids. In air and water friction is small. Should one pay attention to it? The answer is a very definite yes.

Viscosity as diffusion

The short story is that in incompressible fluid the action of viscosity is equivalent to diffusion of velocity. Each component of the velocity vector is diffused independently. The same applies for vorticity: the action of viscosity is equivalent to diffusion of vorticity.

The famous Navier-Stokes

This is the famous Navier-Stokes equation. In words, this can be described in the following way. …

What we need to know to determine the flow evolution

Suppose that we know the velocity and pressure distribution at a certain time. Can we decide, intuitively, what the velocity field will be later? …

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