Advanced Fluid Mechanics

Brief syllabus

hydrostatics, fluid flow basics, conservation laws, vorticity, potential flow, dimensional analysis, waves, instability, compressible flow, turbulence

Objectives

By the end of the course students should be able to:

• understand the concepts listed in the detailed syllabus

• solve problems in fluid mechanics

Prerequisites

Thermodynamics; Fluid Mechanics; one part of the course also uses results taught in Complex Analysis for Physicists/Mathematical Methods for Physicists.

Lectures

Week 1

Hydrostatics I: variation in pressure with position in static, uniformly accelerating, and rotating fluids; rotating fluid bodies; cavitation; forces on submerged objects

Week 2

Hydrostatics II: stability of submerged and floating objects; surface tension; capillary action

Week 3

Fluid flow basics: streamlines; flow rate; Newtonian fluid; viscosity; Reynolds number; types of flow; substantive derivative

Week 4

Conservation laws I: control volume; continuity equation; Newton's 2nd law in integral form; hydraulic jump

Week 5

Conservation laws II: Navier-Stokes equation for incompressible flow; steady-flow energy equation; Bernoulli equation; heat conduction and generation

Week 6

Vorticity: relation between vorticity and angular velocity; simple experimental test for vorticity; types of vortex; circulation; Kelvin's circulation theorem; interaction of vortices

Week 7

Potential flow I: velocity potential; stream function; complex potential for uniform flow, source, vortex, doublet; Rankine bodies; flow around a cylinder; method of images

Week 8

Exam 1 (on weeks 1-7).

Week 9

Potential flow II: conformal mapping; forces on bodies; Zhukovsky aerofoil; axisymmetric flow; flow around a sphere

Week 10

Dimensional analysis: Froude number; dynamically similar flows; drag coefficient; how to nondimensionalize a differential equation and obtain dimensionless parameters; velocity dependence of drag for very low and very high Reynolds numbers

Week 11

Real flow: types of drag; boundary layer thickness and nature; separation point; flow past cylinder for various Reynolds numbers; Strouhal number

Week 12

Waves I: linear gravity waves at the surface and interface between two fluids; capillary waves; effect of viscosity and nonlinearity

Week 13

Waves II: waves in continuously stratified fluid

Week 14

Instability

Week 15

Compressible flow

Week 16

Turbulence

Week 17

Final exam

Teaching methods

Full detailed lecture notes are provided. The course is designed to be mostly self study rather than lecture based. There will be a weekly meeting in which students can ask questions or get hints on homework questions.

Course assessment

Homework: 4% (students must hand in at least one homework assignment in order to be allowed to take the mid-term exam)

Exam 1: 48%

Exam 2: 48%

References

Pijush K Kundu and Ira M Cohen, "Fluid Mechanics", Elsevier Academic Press, 2004.

Frank M White, "Fluid Mechanics", McGraw-Hill, 1999.

Brian R Munson, Donald F Young, and Theodore K Okiishi, "Fundamentals of Fluid Mechanics", 4th edn, Wiley, 2002.