# Study Materials

The page contains supplemental study materials for many topics covered in the class, and a collection of exams and solutions from previous terms.

## Supplemental Materials

SECTIONS STUDY MATERIALS
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.

## Previous Exams and Solutions

EXAMS SOLUTIONS
Quiz 1 2004 (PDF) (PDF)
Quiz 1 2003 (PDF) (PDF)
Quiz 2 2004 (PDF - 1.8 MB) (PDF - 1.6 MB)
Quiz 2 2003 (PDF) (PDF)
Final (PDF) (PDF)