Hydrodynamics

This course aims to introduce the fundamentals of physical hydrodynamics. The kinematic aspects are covered first: Eulerian and Lagrangian formalisms, analysis of the motion of a fluid volume element, introduction to the stream and potential velocity functions, and applications to various types of flows. In the next section on fluid dynamics, we derive Euler’s equation and Bernoulli’s equation for the flow of ideal fluids, followed by the Navier-Stokes equation describing the flow of Newtonian viscous fluids. This section will lead us to define the stress tensor as well as the Reynolds number, which allows us to determine whether a flow is laminar or turbulent. The course concludes with an introduction to the mechanics of deformable solids: displacement field, strain tensor, and deformation tensor.

Master the Eulerian and Lagrangian formalisms and know how to switch between them. Be able to describe and combine flows based on their stream function or velocity potential. Master the Euler and Navier-Stokes equations and be able to solve them to describe laminar, around-an-obstacle, and turbulent flows. Be able to calculate deformations in 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: 1:30 p.m.

TD: 1:30 p.m.