Need help for math/science problem

Rbert

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Aug 21, 2019
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Hi everyone,

I've never been good in math and help would be appreciated.
A friend of mine showed me a math problem he received in class the other day and we had no idea how to solve it.

I do not have the math problem but I think I remember everything.

The goal of the problem is to calculate how much time a certain pool heater will take to rise the pools' temperature from 75 to Fahrenheit to 85 Fahrenheits.
know if it's worth it. He wants

The heat energy source comes from a metal box. In the center of the box are 4 flames, each pointing on one side of the cube. The top and the bottom are not heated. The box is under water level, in the center of the pool and it's fixed. (I know it needs oxygen and the problem didn't made sens because of this but the teacher said : let's just assume it would have fluid air flow, even under water).

Here are the rest of the information:

Metal box dimensions : 30cm x 30cm x 30cm
Combustible : Liquid ethanol going through 4 nozzles. I'm sorry I cannot remember the informations given about ethanols' combustion rate equation.
Pool : Contains 25 000 gallons of water
Pool temperature : Starts at 75 Fahrenheit, stops at 85 Fahrenheits.

With the liquid ethanol combustion rate equation we also needed to find the fuel tank capacity.




There was also a bonus question : I know it's not directly math related, but what kind of metal should be used for the metal box (Heat source) and why...
 
The problem is basically a physics problem. Even as a physics problem, there does not seem to be enough data to answer the question, and the math involved seems to involve integral calculus.
 
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