Helmholtz Numbers: Deciphering the Role of Side Branches and Loops in Pipe Systems

A long-standing discussion is whether the existence of branching or looping pipes hinders or improves the transient response of a water conveying pipe system. We show theoretically and numerically that the role of side branches and loops can be gauged by considering their relevant dimensionless Helmholtz numbers. Specifically, we establish the following two regimes in terms of Helmholtz numbers: (1) one in which the role of the side branches and the loops is negligible; and (2) another in which the side branches and the loops are crucial to the transient analysis of the complete pipe system.