Turbulent flow Colebrook equation

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 ... 

For rough tubes in turbulent flow (7VRc > 4000), the von Karman equation was modified empirically by Colebrook to include the effect of wall roughness, as follows ... 

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

Churchill also provided a single equation that may be used for Reynolds numbers in laminar, transitional, and turbulent flow, closely fitting/= 16/Re in the laminar regime, and the Colebrook formula, Eq. (6-38), in the turbulent regime. It also gives unique, reasonable values in the transition regime, where the friction factor is uncertain. 

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 ... 

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. 

Solving problems in chemical engineering and science often requires finding the real root of a single nonlinear equation. Examples of such computations are in fluid flow, where pressure loss of an incompressible turbulent fluid is evaluated. The Colebrook [8] implicit equation for the Darcy friction factor, f, for turbulent flow is expressed... 

The Colebrook implicit equation for the Darcy friction factor, f, for turbulent flow is ... 

The Darcy friction factor is four times the Fanning friction factor, fp, i.e., fp = 4fp. For fully developed turbulent flow regime in smooth and rough pipes, the Colebrook [5] equation or the Chen [6] equation can be used. 

Values of k and k for various polymer/tube systems are given in Table 5.10. (Values of k and ki can be determined for a given polymer solution from laboratory measurements of pressure drop in smooth tubes at two flow rates in the turbulent range.) These values can be used with the model to predict friction loss for that solution at any Reynolds number in any size pipe. If the Colebrook equation for smooth tubes is used, the appropriate generalized expression for the friction factor is... 

For laminar flow that is very simple because (as we discussed before) the laminar-flow part of the friction factor plot is simply /= 16/. For turbulent and transition flow, it is more difficult. The common friction factor plot (Fig. 6.10) is based bn the Colebrook equation [5]... 

The Co/efarook equation combines experimental results of studies of laminar and turbulent flow in pipes. It was developed in 1939 by the British physicist Cyril Frank Colebrook (1910-1997). 

For turbulent flow, appropriate values for the friction factor can be determined using the Swamme and Jain Equation, which provides values within 1 percent of the Colebrook Equation over most of the useful ranges ... 

The friction factor/for turbulent flow of an incompressible fluid in a pipe is given by the nonlinear Colebrook equation... 

For turbulent flow, the friction factor is estimated by using the well-known Moody diagram. This can also be calculated by using the Colebrook equation, which is the basis of the Moody diagram [3] ... 

The model for turbulent drag reduction developed by Darby and Chang (1984) and later modified by Darby and Pivsa-Art (1991) shows that for smooth tubes the friction factor versus Reynolds number relationship for Newtonian fluids (e.g., the Colebrook or Churchill equation) may also be used for drag-reducing flows, provided (1) the Reynolds number is defined with respect to the properties (e.g., viscosity) of the Newtonian solvent and (3) the Fanning friction factor is modified as follows ... 

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