Hydrodynamics

This course aims at introducing the basics of physical hydrodynamics. The kinematic aspects are treated in a first step: Euler and Lagrange formalism, analysis of the motion of an element of fluid volume, introduction of the current and potential velocity functions, and applications to different types of flows. In the next part of fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of perfect fluids, then the Navier-Stokes equation describing the flow of viscous Newtonian fluids. This part will lead us to define the stress tensor and the Reynolds number to deduce the laminar or turbulent character of a flow. The course ends with an introduction to the mechanics of deformable solids : displacement field, expansion and deformation tensor.

Master the Euler and Lagrange formalism and know how to switch from one to the other. Know how to describe/combine flows from their current function or their velocity potential. Master the Euler and Navier-stokes equations and know how to solve them to describe liminal plane flows, around an obstacle, and vortex flows. Know how to calculate deformations in viscous fluids and deformable solids.   

Newtonian dynamics and fluid statics.

Recommended prerequisites*: Point mechanics, differential calculus, gradient, divergence and rotational operators, and integral calculus. 

100% CT

CM : 13.5 h

TD : 13.5 h