Problem 5:
To an order of magnitude, how much water do Americans use each year watering their lawns? Keep in mind that much of this water is potable, and that grass is not edible or otherwise useful to humans. How does this amount of water compare to the amount of water Americans drink each year?
At first this problem seems daunting; we're being asked to come up with a figure for how many gallons of an entire country uses watering lawns without any concrete numbers to go off of. It could be anything from a few billion gallons to a few quadrillion. There's now way to know without statistical data. So we decided to approach this problem by first collecting our own data in a survey of some of our classmates. We asked 16 people if they had lawns and if so did they water it. 4 (25%) responded that they had no lawn, 6 (37.5%) said that they had a lawn but did not water it, and 6 (37.5%) said that they had a lawn that they watered. We then had to apply this data to some estimates about population, households, lawn size, and water usage.
Calculating the number of gallons used watering lawns
We estimated that there were about 320 million people in the United States. With an average family size of around 4 people, that would mean there were 80 million households. Now, according to our survey, 25%, or 20 million, of those household do not have lawns. An additional 30 million have lawns but do not water them. That left 30 million, or \(3\:\times\:10^{7}\) households with lawns that are regularly watered. We then came up with an estimate, based on our intuition and experience, that the size of the average lawn, or at least the average size of the watered portion of each lawn, was about .5 acres. Then using a guess of how many sprinklers were used to water our own lawns, we decided that it would take about 10 small sprinklers to water a half acre. We further estimated that each of these sprinklers used 1 gallon of water per minute and were in use for 30 minutes each session, 25 times a year. That left us with some calculations to do.
\[3\:\times\:10^{7}\: lawns\:times\:\frac{.5\:acres}{lawn}\:times\:\frac{10\:sprinklers}{.5 acres}\:\times\:\frac{1\:gallon}{min}\:\times\:\frac{30\: min}{session}\:\times\:\frac{25\:sessions}{year}\]
This comes out to about 300,000,000,000 (\(3\:\times\:10^{11}\)) gallons of water used watering lawns each year. The EPA estimates that 9 billion gallons of water are used for landscape irrigation each day. That works out to about 3.3 trillion (\(3\:\times\:10^{12}\)) gallons annually. That is roughly 10 times (1 order of magnitude) higher than our estimate.
Calculating the number of gallons consumed each year by drinking
The last part of the problem asked us to perform a similar estimate but this time on how many gallons Americans drank each year. We estimated that each person drank the recommended 8 8-ounce cups of water a day. We then converted that number into gallons, multiplied by roughly the number of days in a year, and then multiplied by the number of people in America. \[\frac{8\:cups}{day}\:\times\:\frac{1\:pint}{2\:cups}\:\times\:\frac{1\:quart}{2\:pints}\:\times\:\frac{1\:gallon}{4\:quarts}\:times\:\frac{3.6\:times\:10^{2}\:days}{year}\:\times\:3.2\:\times\:10^{8} Americans\]
This comes out to about \(6\:\times\:10^{10}\) gallons per year.
To an order of magnitude, how much water do Americans use each year watering their lawns? Keep in mind that much of this water is potable, and that grass is not edible or otherwise useful to humans. How does this amount of water compare to the amount of water Americans drink each year?
At first this problem seems daunting; we're being asked to come up with a figure for how many gallons of an entire country uses watering lawns without any concrete numbers to go off of. It could be anything from a few billion gallons to a few quadrillion. There's now way to know without statistical data. So we decided to approach this problem by first collecting our own data in a survey of some of our classmates. We asked 16 people if they had lawns and if so did they water it. 4 (25%) responded that they had no lawn, 6 (37.5%) said that they had a lawn but did not water it, and 6 (37.5%) said that they had a lawn that they watered. We then had to apply this data to some estimates about population, households, lawn size, and water usage.
Calculating the number of gallons used watering lawns
We estimated that there were about 320 million people in the United States. With an average family size of around 4 people, that would mean there were 80 million households. Now, according to our survey, 25%, or 20 million, of those household do not have lawns. An additional 30 million have lawns but do not water them. That left 30 million, or \(3\:\times\:10^{7}\) households with lawns that are regularly watered. We then came up with an estimate, based on our intuition and experience, that the size of the average lawn, or at least the average size of the watered portion of each lawn, was about .5 acres. Then using a guess of how many sprinklers were used to water our own lawns, we decided that it would take about 10 small sprinklers to water a half acre. We further estimated that each of these sprinklers used 1 gallon of water per minute and were in use for 30 minutes each session, 25 times a year. That left us with some calculations to do.
\[3\:\times\:10^{7}\: lawns\:times\:\frac{.5\:acres}{lawn}\:times\:\frac{10\:sprinklers}{.5 acres}\:\times\:\frac{1\:gallon}{min}\:\times\:\frac{30\: min}{session}\:\times\:\frac{25\:sessions}{year}\]
This comes out to about 300,000,000,000 (\(3\:\times\:10^{11}\)) gallons of water used watering lawns each year. The EPA estimates that 9 billion gallons of water are used for landscape irrigation each day. That works out to about 3.3 trillion (\(3\:\times\:10^{12}\)) gallons annually. That is roughly 10 times (1 order of magnitude) higher than our estimate.
Calculating the number of gallons consumed each year by drinking
The last part of the problem asked us to perform a similar estimate but this time on how many gallons Americans drank each year. We estimated that each person drank the recommended 8 8-ounce cups of water a day. We then converted that number into gallons, multiplied by roughly the number of days in a year, and then multiplied by the number of people in America. \[\frac{8\:cups}{day}\:\times\:\frac{1\:pint}{2\:cups}\:\times\:\frac{1\:quart}{2\:pints}\:\times\:\frac{1\:gallon}{4\:quarts}\:times\:\frac{3.6\:times\:10^{2}\:days}{year}\:\times\:3.2\:\times\:10^{8} Americans\]
This comes out to about \(6\:\times\:10^{10}\) gallons per year.
Excellent! I really like the survey method.
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