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
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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.
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Partial derivatives with respect to time are null.
drond/drondt = 0
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### (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 = rho*v*D/mu > 2500 (for a tube)
Turbulent flows happen often but we'll find ways get around it.