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Advanced Fluid Mechanics >> Content Detail



Study Materials



Readings

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The following table lists assigned readings. Note that additional reading materials are listed at the study materials page.

[K&C] = Amazon logo Kundu, Pijush K., and Ira M. Cohen. Fluid Mechanics. 3rd ed. Burlington, MA: Elsevier, 2004. ISBN: 9780121782535.

[Fay] = Amazon logo Fay, James A. Introduction to Fluid Mechanics. Cambridge, MA: MIT Press, 1994. ISBN: 9780262061650.


SES #TOPICSREADINGS
1. The Continuum Viewpoint and the Equation of Motion
L1Introduction: Continuum Hypothesis[K&C] Sections 1.1-1.6, 3.1-3.5, and 4.1-4.6.

[Fay] Chapters 1, 2, 3, and 4, pp. 39-44, 89-97, and 128-132.

Review: [K&C] "Vector Calculus." Chapter 2.
L2The Material Derivative

Lagrangian and Eulerian Descriptions

Thermophysical Properties

Compressibility Effects in Gases
T1Tutorial Session
L3Forces Acting on a Continuum

The Inviscid Fluid
2. Static Fluids
L4Static Fluids[K&C] Chapter 1 and sections 4.1-4.3.

[Fay] Chapter 2, pp. 44-75.

Note: There is little detail of hydrostatics in [K&C]; for a better in-depth review either see your own undergraduate text or the section of [Fay].
T2Tutorial Session
3. Mass Conservation in Flowing Media
L5Mass Conservation in Flowing Media[K&C] Sections 3.6, 3.7, 3.13, and 4.1-4.3.

[Fay] Chapter 3
4. Inviscid Flow
L6Steady Bernoulli Equation
T3Tutorial Session
L7Unsteady/Generalized Forms of the Bernoulli Equation
5. Control Volume Theorems and Applications
L8The Reynolds Transport Theorem[K&C] Chapter 4

Sonin, A. A. "Fundamental Laws of Motion for Particles, Material Volumes, and Control Volumes." (PDF - 1.5 MB)

Essential reading: This chapter is extremely detailed and you need to spend the time to go through it in some detail.
T4Tutorial Session
L9Conservation of Mass/Energy/Entropy
T5Tutorial Session
L10Conservation of Linear Momentum

Examples of Conservation of Linear Momentum
T6Tutorial Session
Quiz 1
L11Conservation of Angular Momentum
T7Tutorial Session
6. Navier-Stokes Equation and Viscous Flow
L12Kinematics of Deformation[K&C] Chapter 9
L13The Navier-Stokes Equation

Boundary Conditions for Navier-Stokes Equations
T8Tutorial Session
L14Fully Developed Flows, Stability of Viscous Flows
L15Start-up and Transient Flows Similarity Solution for a Flat Plate (The Rayleigh Problem)
T9Tutorial Session
L16Quasi-Fully Developed Flows: Lubrication Theory
T10Tutorial Session
7. Dimensional Analysis
L17The Buckingham Pi Theorem

Physical Significance of Dimensionless Variables
[K&C] Chapter 8

Buckingham Pi Theorem (PDF)

Sonin, A. A. "Physical Basis of Dimensional Analysis." Manuscript handout.
T11Tutorial Session
L18Asymptotic Limits of the Governing Equations and Scaling with Dimensionless Variables
8. Potential Flow Theory
L19The Velocity Potential and Streamfunction

Complex Variable Formulation
T12Tutorial Session
L20Examples of Potential Flow Solutions
Quiz 2
9. Boundary Layers, Separation and Drag
L21Boundary Layer on a Flat Plate

Effect of a Pressure Gradient

Separation
T13Tutorial Session
10. Vorticity and Circulation
L22Definition of Circulations

Kelvin's Circulation Theorems

Lift, Induced Drag
T14Tutorial Session
11. Surface Tension and its Importance
L23Free Surface Force Balance

Scaling and Dimensional Analysis
L24Sample Flows
T15Tutorial Session
12. Turbulence (v. Brief Introduction)
L25Mean and Fluctuating Quantities

Reynolds Stresses, Eddy Viscosity, Taylor Microscale

Homogeneous and Wall-Bounded Turbulence

Kolmogorov Energy Cascade
L26Turbulence (Conclusions)

Course Review
Final Exam

 








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