Colebrook correlation, friction

Since the Colebrook correlation is awkward to use, an approximate explicit relation for the friction factor was published by Haaland ... 

The fully developed turbulent friction factor seems to be in disagreement with the Blasius equation for smooth microcharmels and with the Colebrook correlation for rough microchannels. 

The problan formulation consists of applying the Bernoulli equation to the three different pipes, with diameters dl, d2, and d3, and a global mass balance at the splitter. The fanning factor for the friction loss is calculated using the Colebrook correlation [5] ... 

In rough microtubes, like metallic microtubes, the effect of the inner roughness e on the friction factor cannot be neglected and the friction factor can be calculated by using the Colebrook correlation ... 

The familiar Moody Diagram is a log-log plot of the Colebrook correlation on an axis of the friction factor and the Reynolds number, combined with the/ = 64/Re result for laminar flow. 

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. 

In the turbulent flow region, it is not possible to obtain an analytical solution for the friction factor as we do for laminar flow. Most of the data available for evaluating the friction factor in turbulent flow have been derived from experiments. For turbulent flow (Reynolds number above 4(X)0), the friction factor is dependent upon the pipe wall roughness as well as the Reynolds number. For turbulent flow, Colebrook (1939) found an implicit correlation for the friction factor in round pipes. This correlation converges well in a few iterations. 

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