2023 Volume 29 Issue 1 Pages 9-18
The Darcy–Weisbach equation describes the flow in a pipe, and the coefficient of friction loss, f, depends on the Reynolds number, Re. The authors proposed using f=aRe-b for pipes in the near-hydraulically smooth transition zone for practical flows of the order, 105<Re<106. For coefficients a and b, we collected data from hydraulic experiments on various types of inner coatings and resin pipes. However, hydraulic experiments are complex, and data collection is challenging. Takakuwa (1972) derived a new discharge equation by combining the coefficient of friction loss from the Colebrook equation with the Hazen–Williams equation. The power number of hydraulic gradient I, in the new equation is obtained from the equivalent roughness k, inner diameter D, and Reynolds number Re. The authors obtained coefficient b from the power number, verified the relationship between Re ~ b, Re ~ a, and b ~ a, and expressed a as a function of b. Furthermore, we propose a process for determining the hydraulic gradient I, friction loss head hf, and discharge Q using the average discharge equation incorporating f=aRe-b based on pipe inner surface conditions of k, a, b and hydraulic design conditions of D.
