Analysis on Spreadsheets

Dimensional analysis involves four steps. First, one derives a set of dimensionless groups. Next, one performs experiments on a convenient system. Third, one analyzes the data. Finally, one applies dynamic similarity to predict the behavior of the system of interest. 

An engineer will often pose two fundamental questions when performing the third step, the analysis of the data. First, an engineer may want to know the certainty that the data exhibit a specific relationship. For example, experiments on walking will yield a collection of Froude numbers and reduced strides. What is the certainty that reduced stride versus Froude number data lie on a straight line on a log-log plot That is, what is the certainty that s/1 (X Fr If the certainty is low, perhaps a different functional form is needed. 

An engineer s second question is similar, but there is a subtle, important difference. Given a specific functional relationship, what is the certainty of the fitted parameters in the equation For example, given that data for walking are represented by the functional form s/1 oc Fr, what is the certainty that m is a specific value Are the confidence limits on m 0.01, or 0.1, or 1, for example  

This tutorial illustrates the proficiency of spreadsheets for reducing experimental data, plotting the reduced data, and analyzing trends. Like the tutorial on spreadsheets for mass balances, this tutorial assumes a basic knowledge of spreadsheets, such as how to use a mouse to select a cell and how to copy and paste. However, the tutorial on spreadsheets for mass balances is not a prerequisite. 

Spreadsheet Example I Experimental data for the terminal velocities of spheres in water, vegetable oil, and glycerin are presented in three tables below and on the following page. The data are a subset of the experimental data measured by Cornell first-year engineers to obtain a general correlation between the Reynolds number. 

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