Moody correlation, turbulent

All models for turbulent flows are semiempirical in nature, so it is necessary to rely upon empirical observations (e.g., data) for a quantitative description of friction loss in such flows. For Newtonian fluids in long tubes, we have shown from dimensional analysis that the friction factor should be a unique function of the Reynolds number and the relative roughness of the tube wall. This result has been used to correlate a wide range of measurements for a range of tube sizes, with a variety of fluids, and for a wide range of flow rates in terms of a generalized plot of/ versus /VRe- with e/D as a parameter. This correlation, shown in Fig. 6-4, is called a Moody diagram. 

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. 

There are a number of correlations for pipe friction factors [14]. Here we only use the relationship by Moody, which applies to turbulent flow in hydraulically rough pipes. It is... 

For turbulent flows, the friction factor is a function of both the Reynolds number and the relative roughness, where s is the root-mean-square roughness of the pipe or channel walls. For turbulent flows, the friction factor is found experimentally. The experimentally measured values for friction factor as a function of Re and are compiled in the Moody chart [1]. Whether the macroscale correlations for friction factor compiled in the Moody chart apply to microchannel flows has also been a point of contention, as numerous researchers have suggested that the behavior of flows in microchannels may deviate from these well-established results. However, a close reexamination of previous experimental studies as well as the results of recent experimental investigations suggests that microchannel flows do, indeed, exhibit frictional behavior similar to that observed at the macroscale. This assertion will be addressed in greater detail later in this chapter. 

For turbulent flow, numerous correlations exist for both smooth and rough-walled pipes. A number of charts have been prepared such as those by Moody, and by Stanton and Pannell, in which friction factor is correlated against Reynolds number for differing pipe surface roughness. Itisimportantto note thatthisFanningfrictionfactorhasavalueof one-quarter of the Darcy friction factor. 

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