Haves Moody factor

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. 

Gas flow in lagged process pipes will be essentially adiabatic, and some drop in temperature may occur. The drop in temperature will lead to a decrease in viscosity, but the decrease in viscosity will usually be rather small. For example, a drop in temperature of methane from 200°C to 100°C causes the viscosity to drop by 25%, and from equation (4.25), this will lead to an increase of Reynolds number of a similar percentage. This increase in Reynolds number will have no effect on friction factor for Reynolds numbers above 100000 because of the flatness of the Moody curve in this region. We may evaluate the effect for Reynolds numbers below 100000 by differentiating equation (4.28) to give ... 

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. 

Space group determination is based on the observation of the Gjonnes - Moodie lines [173] in certain forbidden diffraction disks. Reflections that are kinematically forbidden may appear as a result of double diffraction under multibeam dynamic diffraction conditions. If such forbidden spots are produced along pairs of different symmetry-related diffraction paths that are equally excited, the interfering beams may be exactly in antiphase for certain angles of incidence if the structure factors have opposite signs. Since the convergent beam disks are formed by beams with con-... 

We now have to thank Stanton and PanneU, and also Moody for their studies of flow using numerous fluids in pipes of various diameters and surface roughness and for the evolution of a very useful chart (see Fig. 48.6). This chart enables us to calculate the frictional pressure loss in a variety of circular cross-section pipes. The chart plots Re)molds numbers (Re), in terms of two more dimensionless groups a friction factor < ), which represents the resistance to flow per unit area of pipe surface with respect to fluid density and velocity and a roughness factor e/ID, which represents the length or height of surface prelections relative to pipe diameter. 

We also have the Fanning friction factor,/, which equals 2(j) and the Moody friction factor/, which equals 8(, just as we saw earlier when discussing frictional pressure loss in rough and smooth pipe for Newtonian fluids. 

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. 

Currently the standard TRACE code heat transfer (Dittus-Boelter) and fluid pressure drop (Churchill and Moody) correlations are applied to the gas cooler. Use of the Churchill correlation and Moody curves, and mathematical representations of the curves, for calculation of the single-phase friction factor in a variety of flow-channel geometries is a common engineering practice. Information on the TRACE default correlations is available in the TRACE theory manual (Reference 12-9). A surface roughness of 2E-6 m is used with the TRACE single phase friction correlations. In order to match the HB24 pressure drop prediction, additional frictional flow factors are included in the hydraulic model. The TRACE model also includes plenums to provide a location to specify form loss factors for the gas cooler. The heat transfer and pressure drop correlations would have been updated as the cooler design was determined and as test data was collected. 

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