Equation Colebrook

The Colebrook equation [6, 58] is considered a reliable approach to determining the friction factor, f (Moody factor)... 

If the Reynolds number is greater than 4,000, the flow will generally be turbulent and the friction factor can be calculated from the Colebrook equation ... 

In the fully turbulent region, / is independent of /VRe, so the Colebrook equation reduces to... 

A reasonable guess might be based on the assumption that the flow conditions are turbulent, for which the Colebrook equation, Eq. (6-38), applies. 

Project I Introduce a counter into our m file colebrookplotsolve. m, which finds the number of function evaluations performed in the first 10 lines of the code when trying to find an inclusion interval for the solution / of the Colebrook equation. 

Several equations have been developed using this Reynolds calculation that have proven accurate for calculating the f factor. The first equation proven was the Colebrook equation [4] (also called the Cole-brook-White equation) ... 

Professor L. F. Moody took the Reynolds work and, combining it with the Colebrook equation (6.3), made a series of curves by plotting constant curve values of e/D on a plot of f vs. Re [5]. The resulting curves perfectly matched f experimentally. Both the curves and the Colebrook equation revealed excellent findings for f. 

The problem regarding the Colebrook equation, however, is the fact that it must be solved by trial and error. Thus, a computer program could easily solve it, such as by applying the Newton convergence method of trial and error. Later in time, however, other well-founded... 

Chen, His-Jen, Extract Solution to the Colebrook Equation, Chem. Eng., February 16, 1987. 

The reader will note that both the Karman-Nikuradse and the Colebrook equations are implicit in the friction factor and require a trial and error solution. For hand calculations, it is often simpler to use the friction factor chart. 

Fouling factors, heat transfer, 180 data, 183, 184, 186 Fourier equation, 169 Fractionation. See Distillation Fractionator conntrol lower ends, 49,50 upper ends, 51,52 Freeze drying, 639 cvcle lengths. 639 products 646 Friction, 93 Friction factor, 92 Colebrook equation, 94 granular beds, 117 non-Newtonian fluids, 109 Rounds equation, 94... 

Chemical engineers are familiar with the Fanning (or Darcy) friction factor,/, the Moody chart of/vs. Reynolds number, Rg, and how all of this fits together to calculate pressure drop for a given fluid flow in a given sized pipe. The friction factor is calculated from the Colebrook equation ... 

Serghides compared nine explicit approximation formulas. Various formulas gave good results but none exactly compatible with the Colebrook equation. Here is a new strategy to solve this equation. The method uses direct substitution repeatedly the results are quite accurate. 

The results In all cases, the accuracy agi ees within at least six decimal places with the Colebrook equation. Thus, Eq. (5) is valid for all values of Rg and e/D. In fact, the convergence is so good that any degi ee of precision can be obtained simply by increasing the number of the iteration. 

The experimental results obtained are presented in tabular, graphical, and functional forms oblaincd by curve-fitting experimental data. In 1939, Cyril F. Colebrook (1910-1997) combined the available data for transition and turbulent flow ill smooth as well as rough pipes into the following implicit relation known as the Colebrook equation ... 

For smooth pipes, the agreement between the Petukhov and Colebrook equations is very good. The friction factor is minimum for a smooth pipe (but still not zero because of the no-slip condition), and increase,s with roughness (Fig. 8-25). 

The Colebrook equation is implicit inf, and thus the determination of the friction factor requires some iteration unless an equation solver such as EES is used. All approximate explicit relation for/was given by S. E. Haaland in 1983 as... 

The results obtained from this relation are within 2 percent of those obtained from the Colebrook equation. If more accurate results are desired, Etp 8-V5 can be used as a good first guess in a Newton iteration when using a programmable calculator or a spreadsheet to solve for/with Eq. 8-74. 

In turbulent flow, wall roughness increases the heat transfer coefficient h by a factor of 2 or more [Dipprey and Saber.sky (1963)]. The convection heat transfer coefficient for rough tubes can be calculated approximately from the Nusselt number relations such as Eq. 8-71 by using the friction factor determined from the Moody chart or the Colebrook equation. However, this approach is not very accurate since there is no further increase in h with/for /> 4/sn,ooih [Norris (1970)1 and correlations developed specifically for rough tubes should be used when more accuracy is desired. 

The friction factor corresponding to this relative roughness and the Reynolds number can simply be determined from the Moody chart. To avoid the reading error, we determine it from the Colebrook equation ... 

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