Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre of land to a depth of 1 ft. A severe thunderstorm dumped 2.0 in. of rain in 30 min on a town of area 26 km2. What volume of water, in acre-feet, fell on the town?
Whenever we convert units, the first step is to figure out what our starting and ending units are. We'll place the starting units on the left, an equals sign and ending units on the right, and some conversion factors in between.
Also, remember that if one of the starting units has an exponent (like m3 or s2), the conversion factors for that unit also need to have the same exponent. For example:
The conversion factors must cancel out the starting unit and leave the ending unit. So to cancel out the starting unit in the numerator, the first conversion factor must have that same unit in the denominator.
The exact opposite happens with the starting unit in the denominator. To cancel it, the second conversion factor must have that same unit in the numerator. Other conversion factors may be necessary. Once all the units have canceled and you’re left with the ending units (both numerator and denominator), multiply and divide all the numbers through.
We want to express the volume in acre-feet (acre•ft), but we're given square kilometers and inches. So what we'll do here is convert km2 to acres and inches to, then multiply those results together to get the final answer. (You can also do the whole conversion on one line.)
(You might notice that the problem also gives us a time measurement of 30 minutes, but we don't need that information to answer the question. Real-life data often works that way, and some physics problems try to do the same thing so students get used to the idea.)