# 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:INTRODUCTIONREDUCTION 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

THE MOTION OF A SPHERE THROUGH A FLUID

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

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

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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