Dimensional Analysis Made Easy DESN 100 Christine Griffith Spring 2009

So what is dimensional analysis? Dimensional analysis is the process used by scientists, mathematicians, engineers to change from one unit of measure to another

An example problem Convert 60 mph into feet per second Notice that the original units of miles per hour are multiplied by fractions that are equal to 1. 1 hour = 60 minutes 5280ft=1mile 1 minute = 60 seconds

Cancelling on the diagonal Hour on top cancels with hour on the bottom Minute on top cancels with minute on the bottom Miles on top cancels with mile on the bottom

Finish the problem… Now notice that the cancelled units turned into 1’s The 60’s also cancel

Procedure summary 1.Write the original number with dimensions as a fraction. Example: 60 miles/hour 2.Multiply by fractions with equivalent units in the top and bottom of the fraction. Example: 1 hour/60 minutes. 3.Make sure the units cancel top and bottom until you are left with the units you want

Another problem to practice Convert 100 ft/s² to mm/s²

A last “tricky” problem Sometimes the units we need to change are raised to a power… Example: Convert 10 psi (1b/in²) into N/mm² N stands for Newtons, the unit of force in SI units

Recall: (a/b)²=a/b * a/b