The Drag Force on a Sphere (UMAP)

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