Water Tank

by Raj Patel

Submitted : Spring 2012

The project deals with water tanks with a certain water consumption rate and using calculus to figure out how long it will take before the tanks need to be refilled. More specifically one of the two equations for the water consumption was recursive. The first step that had to be taken to solve this problem was to find the volume of the cylindrical tank. The next step was to find the pattern that is present for the recursion equation and to then create a general formula that encompasses it in order to find out how long it will take before the tanks need to be refilled. This is accomplished by rearranging the formula so it equals “n” which is the number of hours before the tank needs to be refilled. For the second half of the first question it asked to find another way of arranging the tanks which would make the water supply last longer. The end conclusion that was determined is that arranging the tanks parallel to one another was the best option. For the second half of the problem another water consumption equation was given and again the objective was to find how much water was in the tank at any given point and how long it would take to refill the tank. This required rearranging the given water consumption rate again and taking the integral of it so it equals Q (quantity of water). Afterwards once more the equation needs to be rearranged so it is set equal to t (time) so you can figure out how long before it needs to be refilled.

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