Hydrodynamics

This course aims to introduce the basics of physical hydrodynamics. Kinematic aspects are covered first: Euler and Lagrange formalism, analysis of the motion of a fluid volume element, introduction of velocity current and potential 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 ideal fluids, then Navier-Stokes' equation describing the flow of viscous Newtonian fluids. This section will lead us to define the stress tensor and the Reynolds number, which can be used to determine whether a flow is laminar or turbulent. The course ends with an introduction to the mechanics of deformable solids: displacement field, dilation tensor, and deformation tensor.

Master Euler and Lagrange formalism and know how to switch between the two. Be able to describe/combine flows based on their current function or velocity potential. Master Euler and Navier-Stokes equations and know how to solve them to describe plane boundary flows, flows around an obstacle, and turbulent flows. Know how to calculate deformations during viscous fluid flows 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 hours

Tutorial: 13.5 hours