🤓 Based on our data, we think this question is relevant for Professor Hatch's class at UMASS.

Solution: 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?

Problem

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?

Solution

This problem is asking us to convert a volume in inches times square kilometers to acre-feet.

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:

(starting unitstarting unit2)×(conversion factor)×(conversion factor)2=(ending unitending unit2)

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.

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