New explicit approximations to the implicitly given Colebrook equation for flow friction factor are given. They are with improved accuracy compared with the one recently published [Shaikh et al.: Int. J. Heat Mass Tran. 88 (2015) 538–543]. The new approximations are highly accurate only in rough pipes under fully developed turbulent cases of flow.
Abstract
New explicit approximations to the implicitly given Colebrook equation for flow friction factor are given. They are with improved accuracy compared with the one recently published [Shaikh et al.: Int. J. Heat Mass Tran. 88 (2015) 538–543]. The new approximations are highly [...]
Darcy’s flow friction factor is expressed in implicit form in some of the relations such as Colebrook’s and have to be solved by iteration procedure because the unknown friction factor appears on both sides of the equation. Lambert W function is implicitly elementary but is not, itself, an elementary function. Implicit form of the Lambert W function allows us to transform other implicit functions in explicit form without any kind of approximations or simplifications involved. But unfortunately, the Lambert W function itself cannot be solved easily without approximation. Two original transformations in explicit form of Colebrook’s relation using Lambert W function will also be shown. Here will be shown efficient procedure for approximate solutions of the transformed relations.
Abstract
Darcy’s flow friction factor is expressed in implicit form in some of the relations such as Colebrook’s and have to be solved by iteration procedure because the unknown friction factor appears on both sides of the equation. Lambert W function is implicitly elementary [...]
A note on explicit approximations to Colebrook’s friction factor in rough pipes under highly turbulent cases 