# Study Materials

This section contains documents created from scanned original files and other documents that could not be made accessible to screen reader software. A "#" symbol is used to denote such documents.

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)