Hydrodynamics

The aim of this course is to introduce the basics of physical hydrodynamics. The kinematic aspects are dealt with first: Euler and Lagrange formalism, analysis of the motion of an element of fluid volume, introduction of current and potential velocity functions, and applications to different types of flow. In the following section on fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of perfect fluids, followed by the Navier-Stokes equation describing the flow of viscous Newtonian fluids. This will lead to the definition of the stress tensor and the Reynolds number, enabling us to deduce whether a flow is laminar or turbulent. The course concludes with an introduction to the mechanics of deformable solids : displacement field, expansion and deformation tensors.

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