which is also known as the Colebrook equation, expresses the Darcy friction factor f as a function of pipe relative roughness ε / D h and Reynolds number. In 1939, Colebrook found an implicit correlation for the friction factor in round pipes by fitting the data of experimental studies of turbulent flow in smooth and rough pipes.

Dec 11, 2005 · Well, I guess for the derivation, it's going to depend on how far back you want to go. Ultimately, the derivation for friction factor starts at equating Newton's 2nd law and the definition for a Newtonian fluid. I definitely could not remember all of this so I had to go back to my fluids book (Munson, Young and Okiishi). Dec 11, 2017 · The earliest analytical solution of Colebrook equation that uses Wright Omega is a paper by Clamond in 2008 [4], this paper actually discussed the iterative solution in depth and compared different speed using different derivations. In order of rapidness, from the most to the least is a shifted Wright Omega,...

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solution of the Colebrook Equation, in both its Implicit forms and Explicit forms, without using the graphical approach. These are much more useful when working with electronic spreadsheets as will be done in this series. The series will examine: Implicit Forms of Colebrook: We will look at the three common forms of the Colebrook Equation. The We will look at the three common forms of the Colebrook Equation. The differences between these three equations will be examined and the deviations in the results that they produce will be explored. User Defined Functions (UDF) for the Implicit Forms of Colebrook: We will look at UDFs that solve the three Implicit forms of Colebrook. It is shown that the Colebrook–White equation 1 / λ = − 2 lg [2.51 / Re λ + ϵ / 3.71 D] can be solved analytically for the friction factor λ. The solution contains two infinite sums. For given Reynolds numbers Re and relative roughnesses ϵ / D, one can create an own approximation with the required accuracy by adding a finite number of ...