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Lecture Notes

The following table presents lecture outlines for each section.

1. The Continuum Viewpoint and the Equation of Motion (PDF)
L1 Introduction: Continuum Hypothesis
L2 The Material Derivative

Lagrangian and Eulerian Descriptions

Thermophysical Properties

Compressibility Effects in Gases
L3 Forces Acting on a Continuum

The Inviscid Fluid
2. Static Fluids (PDF)
L4 Static Fluids
3. Mass Conservation in Flowing Media (PDF)
L5 Mass Conservation in Flowing Media
4. Inviscid Flow (PDF)
L6 Steady Bernoulli Equation
L7 Unsteady/Generalized Forms of the Bernoulli Equation
5. Control Volume Theorems and Applications (PDF)
L8 The Reynolds Transport Theorem
L9 Conservation of Mass/Energy/Entropy
L10 Conservation of Linear Momentum

Examples of Conservation of Linear Momentum
L11 Conservation of Angular Momentum
6. Navier-Stokes Equation and Viscous Flow (PDF)
L12 Kinematics of Deformation
L13 The Navier-Stokes Equation

Boundary Conditions for Navier-Stokes Equations
L14 Fully Developed Flows, Stability of Viscous Flows
L15 Start-up and Transient Flows Similarity Solution for a Flat Plate (The Rayleigh Problem)
L16 Quasi-Fully Developed Flows: Lubrication Theory
7. Dimensional Analysis (PDF)
L17 The Buckingham Pi Theorem

Physical Significance of Dimensionless Variables
L18 Asymptotic Limits of the Governing Equations and Scaling with Dimensionless Variables
8. Potential Flow Theory (PDF)
L19 The Velocity Potential and Streamfunction

Complex Variable Formulation
L20 Examples of Potential Flow Solutions
9. Boundary Layers, Separation and Drag (PDF)
L21 Boundary Layer on a Flat Plate

Effect of a Pressure Gradient

10. Vorticity and Circulation (PDF)
L22 Definition of Circulations

Kelvin's Circulation Theorems

Lift, Induced Drag
11. Surface Tension and its Importance (PDF)
L23 Free Surface Force Balance

Scaling and Dimensional Analysis
L24 Sample Flows
12. Turbulence (Brief Introduction)
L25 Mean and Fluctuating Quantities

Reynolds Stresses, Eddy Viscosity, Taylor Microscale

Homogeneous and Wall-Bounded Turbulence

Kolmogorov Energy Cascade
L26 Turbulence (Conclusions)

Course Review