2.25 | Fall 2013 | Graduate

Advanced Fluid Mechanics

Potential Flow Theory

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.

  • 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
  • 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
  • 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

Class Notes

Videos Seen During Class

Assignment

Problem Set 10

PROBLEMS SOLUTIONS
Problem 6.4 (PDF) Solution to Problem 6.4 (PDF)
Problem 6.8 (PDF) Solution to Problem 6.8 (PDF)
Problem 6.14 (PDF) Solution to Problem 6.14 (PDF)
The Magnus Effect (PDF) Solution to the Magnus Effect (PDF)

Course Info

As Taught In
Fall 2013
Level
Learning Resource Types
Problem Sets with Solutions
Exams with Solutions