Dimensional Analysis
Part V.
Combination Units
with Powers
Dimensional Analysis V.
Combination Units with Powers

Typical problem:
The pressure of the atmosphere is
14.7 lbs/in2. Express this pressure
in kg/m2
The pressure of the atmosphere is 14.7
lbs/in2. Express this pressure in kg/m2

Steps to solve





1. Identify starting units
2. Identify ending units
3. Identify unit conversion factors that
connects starting and ending units (you may
need more than one)
4. Arrange conversion factor in an equation so
it cancels the starting unit and changes it to
the final unit. You will have to do a conversion
for every power of a unit
5. Put in the numbers and solve the equation
The pressure of the atmosphere is 14.7
lbs/in2. Express this pressure in kg/m2

Step 1. Identify starting units
Lbs/in2
The pressure of the atmosphere is 14.7
lbs/in2. Express this pressure in kg/m2

Step 2. Identify ending units
Kg/m2
The pressure of the atmosphere is 14.7
lbs/in2. Express this pressure in kg/m2

Step3. Identify unit conversion factor that connects
starting and ending units (you may need more than one)
Start
Lbs/in2
1 lbs = .45359 kg
1 inch = 2.54 cm
1 cm = 1x10-2 m
End
kg/m2
The pressure of the atmosphere is 14.7
lbs/in2. Express this pressure in kg/m2
Step 4: Set up a conversion equation that
cancels the starting units and
leaves only the ending units. You will have to
do a conversion for every power of a unit
Lbs/in2 x (kg/lbs) x (in/cm) x (in/cm) x
(cm/m) x (cm/m) = kg/m2
-orLbs/in2 x (kg/lbs) x (in/cm)2 x (cm/m)2 =
kg/m2
The pressure of the atmosphere is 14.7
lbs/in2. Express this pressure in kg/m2
Step 5: Put in actual numbers and solve the problem
14.7 lbs
in 2
10335
.45359 kg
1 lbs
1 in
2.54 cm
2
g
m2
= 1.03x104 kg/m2 (3 sig fig)
1 cm
1x10 2 m
2
Practice Problems
The next three pages have practice
problems. Go through each step and see
if you are doing them right
The density of water is 1.00g/cm3;
express this density in lbs/ft3
Step 1: Starting Unit
g/cm3
Step 2: Ending Unit
lbs/ft3
Step 3: Unit conversions
1 lbs = 453.59 g
1 cm = 0.39370 in
12 in = 1 ft
Step 4: Equation
g/cm3 x (lbs/g) x (cm/in)3 x (in/ft)3 = lbs/ft 3
Step 5: Solve
100
.
gm
cm3
62.4287 lbs
1 lbs
45359
. g
ft
3
1 cm
0.39370 in
62.4 lbs
ft 3
3
12 in
1 ft
( 3 sig fig)
3
The population density of South
Dakota is 9 people/mi2, what is this in
people/km2
Step 1: Starting Units
people/mi2
Step 2: Ending Units
people/km
2
Step 3: Conversion Factor
1 mi = 1.6093 km
Step 4: Equation
people/mi2 x (mi/km)2 = people/km2
Step 5: Solve
9
people
mi
3
2
people
km2
1 mi
16093
.
km
1 sig fig
2
3.47511
people
km2
The acceleration of gravity at sea level
is 9.80665 m/sec2. Express this
constant in miles/hour2
Step 1: Starting Units
m/sec2
Step 2: Ending Units
miles/hr2
Step 3: Conversion Units
1 km = 0.62137 mi; 1 km = 1x103 m
60 sec = 1 min;
60 min = 1 hr
Step 4: Equation
m/sec2 x(km/m) x(mi/km) x(sec/min)2 x(min/hr)2=mi/hr2
Step 5: Solve
9.80665 m
sec 2
7.89725 10 4 mi
1 km
1x10 3 m
hr 2
0.62137 mi
1 km
60 sec
1 min
2
60 min
1 hr
2