Determining the Optimal Pipe Diameter

by Nicholas Pieri

Submitted : Spring 2011

The purpose of this optimization problem was to determine the optimal diameter of a fifty meter pipe. The pipe was connected to a pump operating at a known cost. The diameter of the pipe affected the total anual cost of pumping a known amount of water thorugh the pipe. Building the pipe too small causes the pumping costs to become too large, build the pipe too large and the cost of the pipe becomes too large. Thus the optimal diameter could be determined using calculus. The first derivative test of the cost function determined the critical number of the function, revealing the optimal diameter.

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