Dimensional Analysis Made Easy
DESN 100
Christine GriffithSpring 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
milefthour
hourmiles
15280
sec60min1
min60160
Notice that the original units of miles per hour are multiplied by fractions that are equal to 1. 1 hour = 60 minutes5280ft=1mile1 minute = 60 seconds
Cancelling on the diagonal
milefthour
hourmiles
15280
sec60min1
min60160
Hour on top cancels with hour on the bottomMinute on top cancels with minute on the bottomMiles on top cancels with mile on the bottom
Finish the problem…
fpsft
ftft
88sec
88sec60
52801
5280sec601
601
160
Now notice that the cancelled units turned into 1’sThe 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
2
2
304801
10154.2
112100
smm
cmmm
incm
ftin
sft
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
2
2
2
2
0689.040.251
40.251
1448.410
40.251
1448.410
mmN
mmin
mmin
lbN
inlb
mmin
lbN
inlb