1. Continuum Viewpoint and the Equation of Motion

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

Table of Fluid Physical Properties (PDF)

2. Static Fluids

Solution to Helium Balloon Problem (PDF)

3. Mass Conservation

Simple Example: Piston (PDF - 2.4 MB) - A simple example showing a number of different ways in which the conservation of mass equation for a material volume can be used.

4. Inviscid Flow

Streamline Coordinates (PDF) - This document provides a derivation of the Bernoulli equation in streamline coordinates and provides an example.

Roadmap of Inviscid Flow Equations (PDF) - This page shows the interconnections between different formulations of the Euler Equation and Bernoulli Equation together with the assumptions required to derive each representation.

5. Control Volume Theorems

Navier-Stokes Equation Sheet (PDF)

6. Navier-Stokes Equation and Viscous Flow

Viscous Flow (PDF) - Outline of the derivation of the Navier-Stokes equations plus discussions of the stress tensor and also the bulk viscosity.

Criteria for Locally Fully Developed Flow (PDF) - This document summarizes the scaling and nondimensional arguments used in deciding if a flow is locally fully developed.

Slider Block Example (PDF)

8. Potential Flow

Potential Flow Formula Sheet (PDF) (Courtesy of Brenden Epps. Used with permission.)

9. Boundary Layers, Separation and Drag

Generalized Boundary Layers (PDF) - Some notes on scaling the boundary layer equations.

10. Potential Flow, Lift, Drag and Thrust

Wingtip Vortices

General overview

NASA's Autonomous Formation Flight (AFF) Photos 

Vortex Ring Guns - A quick Web search shows that these "non-lethal weapons" are still actively being considered.

Quiz 1 2004 (PDF)

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Quiz 1 2003 (PDF)

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Quiz 2 2004 (PDF - 1.8 MB)

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Quiz 2 2003 (PDF)

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Final (PDF)

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Quiz 1 (PDF)

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Quiz 2 (PDF)

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Final Exam (PDF)

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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

Separation

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