Notes_cours-SdTA/Introduction to fluid dynamics.md

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Introduction to fluid dynamics

3 main laws

  • Momentum balance
  • Mass balance
  • Energy balance

The continuum assumption

Let lambda be the mean free path, L a characteristic dimension of the problem

Kn = lambda/L

Hypothesis: If Kn<<1, it is possible to use a model based on the continuum hypothesis

That hypothesis is often valid, but not always. Within this course's scope, this hypothesis is always valid.

Types of flows

Three ways flows can be be split:

(Un)Steady flows

Steady: flow variables do not depend on time.

Partial derivatives with respect to time are null.

drond/drondt = 0

(In)compressible flows

A flox can be considered incompressible is the Mach number is low enough:

Let v be the flow velocity, c be the celerity of sound

Approx. M = v/c <= 0.3

Turbulent or laminar flows

Turbulent flows : flow variable are stochastic and vary with space and time. This happens when the Reynolds number is high enough :

Re = rhovD/mu > 2500 (for a tube)

Turbulent flows happen often but we'll find ways get around it.