Dimensional Analysis and Using Units

Ali, the plumber, has discovered a leaky pipe in his house. He calculates that the pipe is leaking at a rate of

8

fluid ounces per minute. How fast is the pipe leaking in gallons per hour?

Given Quantity	Conversion	Result
$3$ $pounds$	$3 pounds \cdot \frac{1 6 ounces}{1 pound}$	$48$ $ounces$
$160$ $ounces$	$160 ounces \cdot \frac{1 pound}{1 6 ounces}$	$10$ $pounds$
$1$ $mile$	$1 mile \cdot \frac{1 7 6 0 yards}{1 mile}$	$1760$ $yards$

Quantity (Symbol)	Expression	Base Units	Unit Symbol (Name)
Area $(A)$	length $\times$ width	$m^{2}$	$m^{2}$
Volume $(V)$	area $\times$ height	$m^{3}$	$m^{3}$
Speed $(r)$	$\frac{distance}{time}$	$m / s$	$m / s$
Acceleration $(a)$	$\frac{speed}{time}$	$m / s^{2}$	$m / s^{2}$
Density $(ρ)$	$\frac{mass}{length ^{3}}$	$kg / m^{3}$	$kg / m^{3}$
Force $(F)$	mass $\times$ acceleration	$kg \cdot m / s^{2}$	N (newton)
Pressure $(P)$	$\frac{force}{area}$	$N / m^{2}$	Pa (pascal)
Energy $(E)$	force $\times$ distance	$N \cdot m$	J (joule)
Power $(P)$	$\frac{force \times distance}{time}$	$J / s$	W (watt)
Frequency $(F)$	$\frac{1}{time}$	$1 / s$	Hz (hertz)

Start Time	End Time	Time Interval (minutes)	Distance Covered (meters)
$10 : 00 A . M .$	$10 : 10 A . M .$	$10$	$1500$
$10 : 10 A . M .$	$10 : 15 A . M .$	$5$	$500$
$10 : 15 A . M .$	$10 : 22 A . M .$	$7$	$1120$

Measure	Conversion Factor
1gallon equals 128 ounces	1gal/128 oz
60 minutes equals 1 hour	60 min/1 h

Combining Base Units

	13 Theory slides
	12 Exercises - Grade E - A
	Each lesson is meant to take 1-2 classroom sessions

Measure	Conversion Factor
1000 meters equals 1 kilometer	1000m/1 km
1 hour equals 3600 seconds	1h/3600 s