# MTH737U Fluid Dynamics (Winter 2011)

## Announcements, Notices, Etc.

• ** REVISION LECTURE, 3pm, Tuesday, 26 Apr 2011, in Maths 203/103 **.
• ** MAKE-UP LECTURE, 11am, Tuesday, 22 Feb 2011, in Maths 203 **.

• in-course MIDTERM, 10am, Tuesday, 1 March 2011 [see below for a sample exam].

• Module Timetable

TU -- [1] 10:00 in Maths 203 (Lec); [2] 11:00 in Maths 203 (Tut); [3] 12:00 in Maths 513 (Lec)
TH -- [4] 11:00 in Maths 203 (Lec); [5] 12:00 in Laws G5 (Tut)

## Description, Syllabus, Notes, Etc.

(** DO NOT DISTRIBUTE and CAVEAT EMPTOR **)

## Exercises [may hand in starred problems for feedback.]

• Set 1: Verify vector identities and gradient/integral theorems, A.1--A.4: A.5* and A.6* in Section A.1
• Set 2: 1.1, 1.2, 1.4*, 1.5
• Set 3: 2.1, 2.6, 2.7*, 2.8, (2.14 optional)
• Set 4: 2.5, 2.6*, (2.12 optional), 2.14
• Set 5: 3.1, 3.2, 3.5*, (3.4, 3.6 optional)

## Solutions, Hints and Comments for Exercises

• Download the solutions to Probs 3.2, 3.4, 3.5 in pdf format.

## General Topics to Understand and Some Thinking Points

• Vector and gradient operations, Cartesian tensors and index notation and material derivative.
• Streamline, vorticity and circulation, Bernoulli streamfunction and point and Rankine vortices.
• Derive Eqs. (1.25), (1.27) and (1.29).
• Viscosity, Newtonian fluid and characteristic scales and Reynolds number.
• Boundary layer and diffusion of vorticity.
• Flow due to impulsively moved boundary and similarity solution.
• Diffusion of vorticity for flow bounded at the top and separation of variable (p.41).
• Simple model of a boundary layer and asymptotic matching (p.269).
• Read and understand section 3.1--3.3, 3.5--3.7, 3.9, 3.10 in the text.
• What is a wave? Frequency and wavelength, spectrum and superposition.
• Dispersion relation and phase and group velocities.