The Use of Dimensionless Analysis in Mathematical Modeling (UMAP)

This module demonstrates how dimensional analysis can be incorporated in the various stages of the modeling process. The problem of determining the period of an undamped pendulum is posed. Different assumptions about the nature of drag forces are suggested. The concepts underlying dimensional analysis are reviewed while applying dimensional analysis to the undamped pendulum in an intuitive manner. Dimensional analysis is then applied to the damped pendulum using the methodology developed in UMAP Unit 526. Experimental results are presented to determine which of the three models considered is most appropriate for particular cases.

Table of Contents:

INTRODUCTION

AN UNDAMPED PENDULUM
Problem Identification
Model Outline
Model Determination
Dimensional Analysis
Initial Test of the Model
Making the Model Useful

A DAMPED PENDULUM
Problem Identification
Model Outline
Buckingham's Theorem
Application of Dimensional Analysis
Testing the Model
Presenting the Results

CHOOSING AMONG COMPETING MODELS

SUMMARY
Determination of a Model
Initial Test of Assumptions
Usefulness of the Model
Similitude

REFERENCES

ANSWERS TO EXERCISES