MECH 846: Laminar and Inviscid Flow

Fall 2011                         Instructor: R.W. Sellens

 

Course Description

Equations of motion of incompressible fluids. Equations for ideal flow; sources; sinks and doublets; vortices; Kelvin and Helmholtz theorems; circulation; irrotational flows; velocity potential and stream function; two dimensional flows using complex variable methods; singularity distribution methods. Exact solutions for laminar flows; Couette and Poiseuille flows; Stokes' first and second problems. Instability of cylindrical jets; Rayleigh's solution; viscous flow approaches.
Three term-hours; lectures. R.W. Sellens. 

 

TIme & Location: TBA

This course will be offered in Fall 2009. The first meeting will be at 10:30 on Tuesday, September 15 in McLaughlin Hall Room 312. A study of inviscid and non-turbulent flows provides much of the fundamental understanding needed in all fluid mechanical studies. This course will provide you with that basis.

Topics to be covered include:

  • Full Lagrangian derivation of the equations of motion, based on an arbitrary control volume.
  • Simplification of general equations; incompressibility; ideal flow assumptions; stream function / velocity potential equations.
  • Classical forms; sources, sinks, doublets and vortices.
  • Complex variable techniques for solution of two dimensional ideal flows.
  • Laminar boundary layer flows
  • Some exact solutions for laminar flows and a comparison of inviscid and viscous flow solutions to the Rayleigh instability on a liquid ligament.
  • Instability in laminar flow.

The course text, I.G. Currie, Fundamental Mechanics of Fluids, McGraw Hill, provides thorough coverage of the vast majority of the lecture material.

It is intended that the course will meet Tuesdays and Thursdays from 10:30 to 12:00, however the scheduling will be flexible to fit into everybody's timetable. I will look forward to seeing you in the class. 

There will be about six assignments which will constitute 50% of the final mark.

There will be a 24 hour take-home final exam for the remaining 50% of the mark.

 

Revised by Rick Sellens, 09.08.24