Estimate Water Usage for Local Town of 30000

[PhysicsCCR]

Homework Statement

An average family of four uses roughly 1600 liters of water per day. How much depth would a lake lose per year if it uniformly covered an area of 90 square kilometers and supplied a local town with a population of 30000 people? Consider only population uses, and neglect evaporation and so on.

I don't even know where to begin.

 

[Simon Bridge]

how much water does the town use per day?
relate the volume of the lake to it's area and depthcontext ... longest dry spell is 90 days where I live, during that time I have 6000gal ~22700L ... a top-up costs NZ$150 for 1200gal to be trucked in, so water conservation is a big deal here. Two of us would use almost all of the 6000gal in that 90 days.

That makes it 130Lpp per day or about 500L per day for four adults. So, to me, 400Lpp-pd is a shocking waste.

IIRC: The Apollo missions carried less than 100L of water for 3 adults for 12days (Apollo 17).
But they didn't take showers, wash clothes, flush toilets, or water lawns.

 

[PhysicsCCR]

Here's what I did. I converted 1600 liters t cm^3 and then converted that to m^3, and got 1.6E8 m^3. Then, I multiplied that with the population of 30000 and 365 (days in a year). Then I converted 90 km^2 into m^2 and got 9E7 m^2. To calculate depth, I divided volume over area and got 1.95E7 m. I entered this into the computer, and it was incorrect. What did I do wrong?

 

[PeterO]

Homework Statement

An average family of four uses roughly 1600 liters of water per day. How much depth would a lake lose per year if it uniformly covered an area of 90 square kilometers and supplied a local town with a population of 30000 people? Consider only population uses, and neglect evaporation and so on.

I don't even know where to begin.

How many litres of water does the town use each day [hint: how many "families of for" make up 30000 people]

How many litres per year does that make [hint: there are 365 days per year - or 366 this year]

How many cubic metres does that make? ... and so on

 

[PeterO]

Here's what I did. I converted 1600 liters t cm^3 and then converted that to m^3, and got 1.6E8 m^3. Then, I multiplied that with the population of 30000 and 365 (days in a year). Then I converted 90 km^2 into m^2 and got 9E7 m^2. To calculate depth, I divided volume over area and got 1.95E7 m. I entered this into the computer, and it was incorrect. What did I do wrong?

Th population in 30000, but the consumption figure was per 4 people

 

[PhysicsCCR]

[Delete]

 

[PhysicsCCR]

Th population in 30000, but the consumption figure was per 4 people

So do I divide 30000 by 4?

 

[PeterO]

So do I divide 30000 by 4?

You seem to have calculated a figure 4 times too big [I have not checked any of your arithmetic] so you need to divide by 4 at some stage.
Given that you have done all the work, perhaps you could just divide your final answer by 4 and check that it is correct.

 

[Simon Bridge]

Here's what I did. I converted 1600 liters t cm^3 and then converted that to m^3, and got 1.6E8 m^3.

Does this seem real to you?
1liter is a cubic decimeter: a cube 10cm on each side.
so 10x10x10=1000 of them fit in a cubic meter.
so 1600L = 1.6m³

Then, I multiplied that with the population of 30000 and 365 (days in a year).

But the 1600L/day figure was for how many people?

Then I converted 90 km^2 into m^2 and got 9E7 m^2. To calculate depth, I divided volume over area and got 1.95E7 m.

That's 19500km ... which is greater than the diameter of the Earth! (12800km) - That's some lake!
No wonder the climates in trouble with Americans using up water like that ;) that rate lowers all the Earths oceans by 5m. Think of the erosion!

I entered this into the computer, and it was incorrect. What did I do wrong?

see above.

 

[PhysicsCCR]

How many litres of water does the town use each day [hint: how many "families of for" make up 30000 people]

How many litres per year does that make [hint: there are 365 days per year - or 366 this year]

How many cubic metres does that make? ... and so on

Oh, I think I get it.

 

[PeterO]

Oh, I think I get it.

Don't overlook the problems "Simon Bridge" pointed out.

 

[PhysicsCCR]

Thanks to you, too, Simon!

 

[Simon Bridge]

You seem to have calculated a figure 4 times too big [I have not checked any of your arithmetic] so you need to divide by 4 at some stage.
Given that you have done all the work, perhaps you could just divide your final answer by 4 and check that it is correct.

His final answer is bigger than the diameter of the Earth, dividing by four puts the lake bottom in the mantle. Steamy :)
This is terribly unprofessional of me - I shouldn't really laugh but the image of drilling a hole through the Earth to supply a town with water just grabbed hold of me.

The amount the lake actually lowers is still pretty shocking though... you'd notice it.
You can see how a town can quickly run dry in a drought.

I think the important, take-away, lesson here is about reality-checking your numbers.

IRL you are bombarded with statistics and asked to worry or not worry about them ... you need to be able to figure out how these numbers are important and in what way in order to know what they actually mean.

Automatically asking these questions is part of being a scientist.

 

[PhysicsCCR]

lol I messed up my arithmetic. Thanks for pointing that out, Simon. It is 1.6 m^3. I accidentally multiply instead of divide.

 

[PhysicsCCR]

Lmao! It's all good, man. I see what I did wrong there.

 

[PhysicsCCR]

Finally got the right answer, which is 4.87E-2 m. Thanks for your help!

 

[Simon Bridge]

about 5cm per annum if nothing is done.

part of what obscures these figures from reality-checks is leaving them in calculator notation. 4.87E-2 doesn't resonate with your intuition the way 4.87cm does. That's about 2-3 fingers.

get used to comparing figures to things aye.

 

[PhysicsCCR]

Well, in real life, of course, I'll say 4.87 cm, or about 5 cm. But since the online physics homework system uses scientific notation, I thought I might just stick with that.

 

[Simon Bridge]

Yeah I realized - it is one of the problems with these computer-based learning systems.
You should not let the machine tell you what units etc to use - use what you are comfy with then convert into something the machine understands at the end.

1.95e7m does not parse as well as 19500km ... I suspect you'd have been more intuitively worried about the second form. It's also good for when you ask for help - since you are talking to humans here :) or when you are answering written exam papers.

If you find yourself doing things for the benefit of a machine you are doing it wrong.
The machine is there for your benefit, not the other way around.

Above all - have fun.
Cheers.

 

[PeterO]

Yeah I realized - it is one of the problems with these computer-based learning systems.
You should not let the machine tell you what units etc to use - use what you are comfy with then convert into something the machine understands at the end.

1.95e7m does not parse as well as 19500km ... I suspect you'd have been more intuitively worried about the second form. It's also good for when you ask for help - since you are talking to humans here :) or when you are answering written exam papers.

If you find yourself doing things for the benefit of a machine you are doing it wrong.
The machine is there for your benefit, not the other way around.

Above all - have fun.
Cheers.

Interesting to note than an answer like 1.95e7 is instantly marked wrong in exams/test in my state [of Australia]. It is a rubbish value. Number values do not have an e in them.
Converted to 1.95 x 10⁷ it would be looked at - and then marked wrong; but only because it is the wrong value.
Some calculators present that answer as 1.95⁷ - and that is wrong too.

 

[Simon Bridge]

Gudduy from across the Tasman ;)
It's just notation that is easy for machines...

1.95 x 10⁷ has an "x" in it :P and no units 1.95\times10^7\text{m} is better typesetting aye?

technically, "e" is the exponential number, so 1.95e7 = 1.95 \times e \times 7 = 37.1045469584660
... which is to say: still wrong. Like you said.

I tell you, this machine learning is a disease!

 

[PeterO]

Gudduy from across the Tasman ;)
It's just notation that is easy for machines...

1.95 x 10⁷ has an "x" in it :P and no units 1.95\times10^7\text{m} is better typesetting aye?

technically, "e" is the exponential number, so 1.95e7 = 1.95 \times e \times 7 = 37.1045469584660
... which is to say: still wrong. Like you said.

I tell you, this machine learning is a disease!

We all know what the e means on a calculator, and the importance of units, it is just that most answers copied down from a calculator will be wrong - either too many or too few figures, or including the "calculator speak" e. Copying such an expression from a calculator does not bring with it any suggestion of understanding and as such earns no marks.

 

[Simon Bridge]

Which is why you get better graduates if humans set and mark the papers.

 

[PhysicsCCR]

I agree with what you're saying. I much prefer using standard notation, rather than scientific notation. And I agree with what you said about machines benefiting us, not the other way around. I used to always submit my answers in standard notation, but the homework system always convert it to scientific notation, regardless how big or small the number is. Nonetheless, on written exams, I would use standard notation, unless maybe if there are so many zeros.