Revised Friction Groups for Evaluating Hydraulic Parameters: Pressure Drop, Flow, and Diameter Estimation

Abstract

Suitable friction groups are provided for solving three typical hydraulic problems. While the friction group based on viscous forces is used for calculating the pressure drop or head loss in pipes and open channels, commonly referred to as the Type 1 problem in hydraulic engineering, additional friction groups with similar behaviors are introduced for calculating steady flow discharge as the Type 2 problem and, for estimating hydraulic diameter as the Type 3 problem. Contrary to the viscous friction group, the traditional Darcy–Weisbach friction factor demonstrates a negative correlation with the Reynolds number. This results in curves that slope downward from small to large Reynolds numbers on the well-known Moody chart. In contrast, the friction group used here, based on viscous forces, establishes a more appropriate relationship. In this case, the friction and Reynolds number are positively correlated, meaning that both increase or decrease simultaneously. Here, rearranged diagrams for all three mentioned problems show similar behaviors. This paper compares the Moody diagram with the diagram for the viscous force friction group. The turbulent parts of both diagrams are based on the Colebrook equation, with the newly reformulated version using the viscous force friction group. As the Colebrook equation is implicit with respect to friction, requiring an iterative solution, an explicit solution using the Lambert W-function for the reformulated version is offered. Examples are provided for both pipes and open channel flow.