This section covers lectures 17-18.
Readings
Textbooks
Reading in: Panton, Ronald L. Incompressible Flow. 4th ed. Wiley, 2013. ISBN: 9781118013434. [Preview with Google Books]
- Chapter 18: Ideal Flows in a Plane
- 18.1: Problem Formulation for Plane Idea Flows
- 18.2: Simple Plane Flows
- 18.3: Line Source and Line Vortex
- 18.4: Flow over a Nose of a Cliff
- 18.5: Doublets
- 18.6: Cylinder in a Stream
Reading in: Kundu, Pijush K., and Ira M. Cohen. Fluid Mechanics. 6th ed. Academic Press, 2015. ISBN: 9780124059351.
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Chapter 4: Conservation Laws
- 4.8: Conservation of Energy
- 4.9: Special Forms of the Equations; Angular Momentum Principle for a Stationary Control Volume; Bernoulli Equations; Neglect of Gravity in Constant Density Flows; The Boussinesq Approximation; Summary
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Chapter 5: Vorticity Dynamics
- 5.1: Introduction
- 5.2: Kelvin’s Circulation Theorem
- 5.3: Helmhotz’s Vortex Theorems
- 5.4: Vorticity Equation in a Nonrotating Frame
- 5.5: Velocity Induces by a Vortex Filament: Law of Biot and Savart
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Chapter 6: Ideal Flow
- 6.1: Relevance of Irrotational Constant-Density Flow Theory
- 6.2: Two-Dimensional Stream Function and Velocity Potential
- 6.3: Construction of Elementary Flows in Two Dimensions
- 6.4: Complex Potential
- 6.5: Forces on a Two-Dimensional Body; Blasius Theorem; Kutta-Zhukhovsky Lift Theorem
- 6.8: Axisymmetric Ideal Flow
Additional Readings
Newman, John Nicholas. “Hydrodynamic Pressure Forces.” Section 4.12 in Marine Hydrodynamics. MIT Press, 1977. ISBN: 9780262140263. [Preview with Google Books]- Astarita, Gianni, and Michael E. Mackay. “The Generalized Engineering Bernoulli Equation (GEBE) and the First and Second Laws of Thermodynamics for Viscoelastic Fluids.” Journal of Rheology 40, no. 3 (1996): 335–46.
- Professor Jane Wang’s website on dragonfly flight and the role of vorticity shedding in fluttering and tumbling.
- Vortex Ring Gun website. A quick web-search shows that these “non-lethal weapons” are still actively being considered.
- NASA Aircraft Complete Wingtip Vortex Study
Class Notes
- Equation of Motion in Streamline Coordinates (PDF)
- Fluid Mechanics Equation Sheet (PDF)
- Inviscid Flow Equation Sheet (PDF)
Videos Seen During Class
- Pressure Fields and Fluid Acceleration Video and Film Notes (PDF - 1.3MB)
- Vorticity, Part 1 Video, Part 2 Video, and Film Notes (PDF - 2.8MB)
