How is it that engineers determine the best pumps to be used for lets say, an arrogation system? Given that you have a system with specific requirements for flow rate and pressure, how is it that one can determine the best pump for the application given just its set of non-dimensional coefficients (Cp, Cq, Ch)? That is, knowing that a pumps efficiency varies with its diameter, operating speed, flow rate, and head how can one determine the best pump that will meet the requirements while operating the most efficiently? I see this problem as a 4 dimensional optimization problem that is going to require some type of method that requires linear algebra in order to solve it. Am I approaching this correctly or there just no systematic way to figure this out?