Optimal Pipe Diameter

by Glen Flores

Submitted : Fall 2008

The calculus based engineering project involved a goal of finding the optimal pipe diameter which would minimize the total cost per year. In order to achieve my goal, it was needed to discover the least expensive total cost, which included the cost of the pipe added to the cost of the pump power requirement, by finding the most efficient diameter. Therefore, one equation was accumulated for the total cost per year using the equations and information given. Next, the first derivative of the total cost per year equation with respect to the diameter was founded and set it equal to zero in order to find the minimum point values. In conclusion, a piping diameter of less than 3 centimeters was established for 0.001 m^3/s of water to flow through 50 meters of straight pipe to minimize the total cost.

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