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Consortium for Mathematics and its Applications

Product ID: 99712
Supplementary Print
Undergraduate

The Drag Force on a Sphere (UMAP)

Author: H. Edward Donley


This module analyzes the drag force on a sphere moving through a fluid, by applying dimensional analysis to reduce the number of variables, experimental results to find a relationship between the drag coefficient and the Reynolds number, and the resulting log-log graph to develop two models for the drag force. These models are then used to derive differential equations for spheres falling through fluids.

Table of Contents:

INTRODUCTION

REDUCTION OF THE NUMBER OF VARIABLES
The Need for Reducing the Number of Variables
The Drag Coefficient and the Reynolds Number

GRAPH OF DRAG COEFFICIENT VS. REYNOLDS NUMBER
Log-Log Graphs
The Graph of CD vs. R

TWO MODELS FOR THE DRAG FORCE

THE MOTION OF A SPHERE THROUGH A FLUID
Development of the Differential Equations
Solutions of the Differential Equations
Comparison of the Two Models
An Example: Sand Settling in Water

CONCLUSION

APPENDIX I: TABLE OF PHYSICAL CONSTANTS

APPENDIX II: DIMENSIONAL ANALYSIS

SAMPLE EXAM

SOLUTIONS TO THE EXERCISES

ANSWERS TO THE SAMPLE EXAM

REFERENCES

ABOUT THE AUTHOR

©1999 by COMAP, Inc.
UMAP Module
33 pages

Mathematics Topics:

Calculus , Differential Equations

Application Areas:

Physical Sciences , Fluid Dynamics

Prerequisites:

Calculus through simple differential equations; familiarity with separation of varaibles; logarithms and exponentials; hyperbolic trigonometric functions

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