Are you a genius?

Loco-Deer-Slayer

Loco-Deer-Slayer

Active member
I hate making these Math Help threads but I have no idea what to do with this one. If you can help me out I will love you forever and karma/cookies will be given. If you live in SLC I'll buy you some beer.

This is for a groundwater geo class that is heavily based on Calculus.

Here is problem: 25,000 acre feet of water/year is being diverted into a basin. Water seeps out of the bottom at a rate of .16ft/day and evaporation rate is 40 inches/year. The basin of these inputs and outputs is circular.

The question: What is the diameter of the reservoir when the inflow exactly matches the outflow?

(I'm assuming this is a partial derivative word problem but I hate these motherfuckers. Correct me if I wrong.)

Help NS??
 
so, by your thread title, anyone that passes highschool calculus is a genius??

genius, such a loosely thrown around word.

same with love.
 
you have a yearly IN-flux of 25 000 acre feet of water, since i hate working with imperial measurements, this is 3.084 x 10^10 L or 3.084 x 10^7 m³ of water /year

your out-flux is split into two, one being - 0.16ft/day (bottom seep) and the second being -40 inches / year (evaporation)

let's set both to yearly fluxes and SI units, making it

-0.0488m/day -> -17.8m/year (bottom seep)

and

-1.016m/year (evaporation)

both totaling for an out-flux of -18.816m/year of dissipating water ....

so what is asked is a surface area of the basin we're looking at, if we multiply our out-flux velocity with this area we get the total discharge of the basin (this is volume X/year)

in this situation we want this discharge to equal the yearly in-flux of 3.084 x 10^7 m³ /year

so let's call this area or surface (A)

this gives us the equation:

(IN-Flux) + (Out flux) = 0

(3.084 x 10^7 m³ /year) + ( -18.816m/year * (A) ) = 0

=> 18.816m/year * (A) = 3.084 x 10^7 m³ /year

=> (A) = (3.084 x 10^7 m³ /year) / (18.816m/year)

=> (A) = 1.639 x 10^6 m²

or

=> (A) = 405 acres

since we assume a circular reservoir we know that R²*PI = Area

so => R² * PI = 1.639 x 10^6 m²

=> R = +Sqrt (1.639 x 10^6 m² / PI)

R = 722m or 2370 ft or 789.9 yards





 
recalculating might be a good idea, i did this quickly and it will give you an idea how to do it on your own ...
 
Thank you! That's exactly what I was looking for. I appreciate that, even if it's not right... the layout was what I was looking for.

+ Mother effin K...wish I could go to 20
 
For what's it's worth, I'm a fan of Utah's Unita Brewery. Especially the Cutthroat IPA. it's a pretty good beer.

Drinkc_100422.jpg


the answer to your problem is elevendy
 
I worded the title that way for the sole purpose of attracting clicks on this thread. If I titled it "Calculus question" not as many people would of clicked on it.

Know what I mean?
 
Shit...now that I look at it this doesn't even really have calc in it. The problem is set up in differential form but since outputs and inputs are linear there is no differentiating.

Correct? Just trying to understand a little.
 
Although his method may be correct - that's not utilizing calculus. If your required to base this of calculus work you'll have to rewrite his equation as a differential equation in the form of a mixing problem.

You know your rate of change, you know your input, and you know your output. Calculating the diameter/whatever the size was would leave you one unknown in a single equation - thus very solvable and would properly utilize your newly found calculus skills.
 
Yeah I get what your saying (My post two up).

Differential equations were something my calc teachers glossed over as most people found them difficult, me included. Go figure. The hard part is translating the word problem into the correct differential equation, once you get that set up the math isn't too bad.

Appreciate the advice though +k
 
My hint to you for this problem, would be to think of it implicitly.

Try and utilize dy/dx
 
Breweries are a huge part of the economy here. I drank a 8.7 IPA from epic yesterday, it was fucking amazing.

You should come drink utah beer.
 
My buddy works at Epic off of State, names Ty. He works the food counter in the back. You guys should all go in and say what's up. Throw him some tips and he'll hook you up.
 
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