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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.

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dimensional analysis made easy

Dimensional Analysis Made Easy

DESN 100

Christine Griffith

Spring 2009

so what is dimensional analysis
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
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


1 minute = 60 seconds

cancelling on the diagonal
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
Finish the problem…

Now notice that the cancelled units turned into 1’s

The 60’s also cancel

procedure summary
Procedure summary
  • Write the original number with dimensions as a fraction. Example: 60 miles/hour
  • Multiply by fractions with equivalent units in the top and bottom of the fraction. Example: 1 hour/60 minutes.
  • Make sure the units cancel top and bottom until you are left with the units you want
another problem to practice
Another problem to practice
  • Convert 100 ft/s² to mm/s²
a last tricky problem
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