Determination of the coefficient of friction in the penstock of a hydro-electric dam: Application of two approaches

Abstract

ABSTRACT Several formulae of the coefficient of friction have emerged after that of Nikuradse such as the Colebrook–White formula adopted for the calculation of the coefficient of friction in penstocks. However, this requires enormous computing resources because it suffers from an implicit nature. Other authors have proposed explicit formulae for this in order to reduce calculation times and make applications easy. Among these authors, the most used are the formulae of Swamee–Jain and Haaland. In this work, we set out to study the evolution of friction on the top, bottom and side walls of a penstock using these two formulas. The objective is to find which one best characterizes the friction and gives results close to the implicit Colebrook–White formula. To carry out this work, the study was made by a numerical approach in FLUENT. It appears that the Swamee–Jain correlation gives values closer to that of Colebrook–White along the walls. On the side walls, Haaland's formula better describes the constancy of friction with a much larger range of values than Swamee–Jain. On the upper and lower walls, the friction has a linear character.