Empirical Colebrook equation implicit in unknown flow friction factor (λ) is an accepted standard forcalculation of hydraulic resistance in hydraulically smooth and rough pipes. The Colebrook equation givesfriction factor (λ) implicitly as a function of the Reynolds number (Re) and relative roughness (ε/D) of innerpipe surface; i.e. λ0=f(λ0, Re, ε/D). The paper presents a problem that requires iterative methods for thesolution. In particular, the implicit method used for calculating the friction factor λ0is an application of fixed-point iterations. The type of problem discussed in this "in the classroom paper" is commonly encountered influid dynamics, and this paper provides readers with the tools necessary to solve similar problems. Students’task is to solve the equation using Excel where the procedure for that is explained in this “in the classroom”paper. Also, up to date numerous explicit approximations of the Colebrook equation are available where as an additional task for students can be evaluation of the error introduced by these explicit approximations λ≈f(Re,ε/D) compared with the iterative solution of implicit equation which can be treated as accurate.

Abstract

Empirical Colebrook equation implicit in unknown flow friction factor (λ) is an accepted standard forcalculation of hydraulic resistance in hydraulically smooth and rough pipes. The Colebrook equation givesfriction factor (λ) implicitly as a function of the Reynolds [...]

Separate flow friction formulations for laminar and turbulent regimes of flow through pipes are in common use in engineering practice. However, variation of different parameters in a system of conduits during conveying of fluids can cause changes in flow pattern from laminar to fully turbulent and vice versa. Because of that, it is useful to unify formulations for laminar and turbulent hydraulic regimes in one single coherent equation. In addition to a physical interpretation of hydraulic friction, this communication gives a short overview of already available Darcy’s flow friction formulations for both laminar and turbulent flow and additionally includes two simple completely new approximations based on symbolic regression.

Abstract

Separate flow friction formulations for laminar and turbulent regimes of flow through pipes are in common use in engineering practice. However, variation of different parameters in a system of conduits during conveying of fluids can cause changes in flow pattern from laminar to [...]