Textbook | Coding Tutorials | Code for Figures | Experiments | Other Resources | GitHub Site
Welcome! Here you will find everything you need to run an upper undergraduate course in fluid dynamics.
The textbook, code, and everything else is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Introduction to Fluid Dynamics is a textbook aimed at upper undergraduate physics and math students. It covers visualization, the Navier-Stokes equations and solutions to various simple problems, potential theory, the complex potential, aerodynamics, surface waves, and more.
Download the textbook in PDF format: Introduction to Fluid Dynamics by MacMillan.pdf
Order a copy of the textbook on Amazon: Introduction to Fluid Dynamics by MacMillan (I don't make any money from Amazon sales; you pay for printing and shipping only).
Solving problems and visualizing fluid dynamics requires some coding ability. There are a number of tutorials that demonstrate how to code various useful things: plotting, complex numbers, animations, and more. All tutorials use Jupyter Notebooks and are written in Python 3.
Tutorial 1 - Introduction to Jupyter and NumPy - View | Download
Tutorial 2 - Fluid Visualization - View | Download
Tutorial 3 - Advanced Plots - View | Download
Tutorial 4 - Solvingn ODEs - View | Download
Tutorial 5 - Fluids in the Complex Plane - View | Download
Tutorial 6 - A Simple Model of Vortex Shedding - View | Download
Tutorial 7 - Fourier Transforms - View | Download
Almost all of the figures in the textbook were created in Jupyter notebooks; for reference, the code is given here.
Chapter 1 - Introduction - View | Download
Chapter 2 - Viscous Fluids - View | Download
Chapter 3 - Ideal Fluids - View | Download
Chapter 3 - Ideal Fluids - View | Download
Chapter 4 - Potential Flow - View | Download
Chapter 5 - Waves - View | Download
Chapter 6 - Special Topics - View | Download
A few simple experiments you can do with household items and your phone.
The Cheerios Effect - measure the force between two cheerios attracting each other in a bowl of milk - Download
Hydraulic Jumps - measure the radius of the circle formed when a faucet is turned on in a sink - Download
The Hele-Shaw Cell - a two-dimensional unstable flow between two closely-spaced plates - Download
The Dam Break - how does water flow from a broken dam? - Download
Other possible ideas for experiments:
Instabilities in a soap film tunnel - P. Vorobieff and R. E. Ecke, Am. J. Phys. Vol. 67, No. 5, May 1999.
Surface waves in a ripple tank - G. Kuwabara, T. Hasegawa, K. Kono, Am. J. Phys. Vol. 54, No. 11, November 1986.
NSF Fluid Mechanics Series - a collection of old but very good videos on fluid mechanics.
Physics Girl's Pool Vortex Pair - an excellent video showing a vortex pair moving across a pool (and more).
Various videos showing vortex shedding (experiment and simulation): Vortex Shedding, Flow-induced vibrations, Von Karman Vortex Street, Stunning Flow Visualization Lab.
Group and Phase Velocity - comparing group and phase velocity for three cases.
Waves in Fluid - From NSF Fluid Mechanics Series, showing wave motion and particle paths.