An average family of four uses roughly 1200 L (about 300 gallo...

Question

An average family of four uses roughly 1200 L (about 300 gallons) of water per day (1L = 1000 cm³). How much depth would a lake lose per year if it covered an area of 60 km² with uniform depth and supplied a local town with a population of 40,000 people? Consider only population uses, and neglect evaporation, rain, creeks and rivers.

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. If a massive underground reservoir with an area of 100 square kilometers was used to supply water to a city with a population of 100,000 people. Each person used an average of 150 L of water per day. How much would the water level in the underground reservoir drop annually due to the city's water usage? Assuming no factors other than the population use are considered, neglect any replenishment sources and changes in the reservoir's volume for simplicity. OK. So our end goal for this problem, what we're trying to solve for is we're trying to figure out how much would the water level in the underground reservoir drop due to the city's annual water usage? Assuming that no other factors other than the population is being considered in this situation? Awesome. We're also given some multiple choice answers. Let's read them off to see what our final answer might be. A is 5.48 centimeters per year. B is 0.54 m per year. C is 2.43 centimeters per year and D is 0.24 m per year. So first off, let us start to solve this problem by recalling and using dimensional analysis to calculate the volume of the water used by the people per year. So the population is 100,000 people. OK? And we need to note that one person, we'll use 150 L of water per day. So one to keep things simple, I'm just gonna say people, even though that's not proper grammar but oh well. Ok. So one person will use 150 L of water per day. And let's note that there's 365 days in one year. Ok? And let's note that there's 1000 centimeters cubed or cubic centimeters in 1 L. And let's note that and we're running out of room. So I'll write it down here that in one kilometer there is 100 1000 centimeters tubed, the power of three. Ok. So to quickly recap here. So for a population of 100,000 people, they use 150 L of water per day for one person. And there's 365 days in one year and there is 1000 cubic centimeters in 1 L. And in one kilometer, there is 1000 or sorry, 100,000 centimeters to the power of three, so one kilometer divided by 100,000 centimeters cube. So all the units will cancel out but leaving us with kilometers cubed per year, which is the units that we want. So let me plug that into a calculator. We will get 5.475 multiplied by 10 to the power of negative three kilometers cubed per year. Awesome. So to determine the decrease in the water level annually, this can be found by dividing the volume by the area. So D equals V divided by a. So let's plug in our known values and solve. So our volume is 5.475 multiplied by 10 to the power of negative three kilometers cubed year divided by 100 kilometers squared. So that's our area is 100 square kilometers. Awesome. So this is equal to 5.475 multiplied by 10 to the power of negative five kilometers per year. Or let's keep things short and just keep using yr for years multiplied by 100,000 centimeters divided by one kilometer, which is equal to 5.475 centimeters per year. But let us round to two decimal places like our multiple choice answers. So that means that our final answer will be 5.48 centimeters per year and that is our final answer. Hooray, we did it. So as you can see all canceled in blue are kilometers units will cancel out leaving us with centimeters per year, which is what we want our final answer to be in unit. Y So that's a good. So now when we look at our multiple choice answers, the correct answer has to be the letter A which is 5.48 centimeters per year. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Key Concepts

Volume and Depth Relationship

Water Consumption Calculation

Area Conversion

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