# Using Dimensional Analysis to Understand the World

Dimensional analysis is a way to use the units of different quantities to determine how those quantities are related. The simplest example is that distance has units of meters, time has units of seconds, so if you need to calculate a speed (in meters/second), you divide a distance by a time. Everything in the physical world has units, and we can use these units to make all sorts of useful calculations. Please review this useful Dimensional Analysis web page, developed here at NCSU, then attempt the warmup exercises.

## Warm Up Exercises

Exercise 1: How fast is 60 miles/hour in kilometers/hour? in meters/second?

Exercise 2: My car gets 25 miles /gallon, and my daily commute is 10 miles round trip. How much fuel do I use each day? Is it more or less than a gallon?

## Water Use in America

According to the EPA, about 400 Billion gallons of water are withdrawn from our reservoirs and groundwater each day. Not all of this goes down the drain; about half is used for cooling power plants and eventually re-enters the water supply. Only about a quarter of the water withdrawn is consumed and goes down the drain (USGS website). About 45 Billion gallons of water are consumed each day for public supply, including your house (if you don't have a well), public swimming pools, water for city gardens and the like. What fraction of this goes down the toilets?

Exercise 1: Convert the water consumed for public supply to liters per day. Hint: 1 Billion = 1,000,000,000 = 109, and 1 gallon = about 4 liters.

Exercise 2: A bathtub holds about 15 gallons of water, and there are 300 Million (300,000,000) people in the United States. How many liters would it take for everyone to take a bath?

Exercise 3: Divide your answer to exercise 2 by your answer to exercise 1. What fraction of public supply is used for baths?

Exercise 4: If we all saved water, we could reduce American household consumption by 100 gallons/person/day. Convert that to liters/person/year.

Exercise 5: People in sub-saharan Africa use about 25,000 liters/person/year. How many Africans could be supported by the water one American wastes?