Turbulent frictional loss coefficient

Table 8.1 Frictional loss coefficient for turbulent flow. ...

This formula is another variation on the Affinity Laws. Monsieur s Darcy and VVeisbach were hydraulic civil engineers in France in the mid 1850s (some 50 years before Mr. H VV). They based their formulas on friction losses of water moving in open canals. They applied other friction coefficients from some private experimentation, and developed their formulas for friction losses in closed aqueduct tubes. Through the years, their coefficients have evolved to incorporate the concepts of laminar and turbulent flow, variations in viscosity, temperature, and even piping with non uniform (rough) internal. surface finishes. With. so many variables and coefficients, the D/W formula only became practical and popular after the invention of the electronic calculator. The D/W forntula is extensive and eomplicated, compared to the empirieal estimations of Mr. H W. 

Because most applications for micro-channel heat sinks deal with liquids, most of the former studies were focused on micro-channel laminar flows. Several investigators obtained friction factors that were greater than those predicted by the standard theory for conventional size channels, and, as the diameter of the channels decreased, the deviation of the friction factor measurements from theory increased. The early transition to turbulence was also reported. These observations may have been due to the fact that the entrance effects were not appropriately accounted for. Losses from change in tube diameter, bends and tees must be determined and must be considered for any piping between the channel plenums and the pressure transducers. It is necessary to account for the loss coefficients associated with singlephase flow in micro-channels, which are comparable to those for large channels with the same area ratio. 

The loss coefficient is seen to be a function only of the geometry of the system (note that the assumption of plug flow implies that the flow is highly turbulent). For most systems (i.e., flow in valves, fittings, etc.), the loss coefficient cannot be determined accurately from simple theoretical concepts (as in this case) but must be determined empirically. For example, the friction loss in a sudden contraction cannot be calculated by this simple method due to the occurrence of the vena contracta just downstream of the contraction (see Table 7-5 in Chapter 7 and the discussion in Section IV of Chapter 10). For a sharp 90° contraction, the contraction loss coefficient is given by... 

Fig. 8 shows a comparison of the data with the theoretical correlations for laminar and turbulent flow for uniform diameter loops. The experimental data reported by Misale et al. (1991), Bemier-Baliga (1992) and Ho et al. (1997) are well predicted by the theoretical correlation. Most of these data points are from laminar flow region where the total local loss coefficient is negligible compared to Lt/D due to the large value of the friction factor. For the... 

This represents the linear effect of tip speed and the square of impeller size on the flow of a specific impeller. Referring to Figure 12-46, very low flow coefficients for a specific type of centrifugal or axial flow machine cause excessive wall friction or leakage losses, and very high-flow coefficients tend to he subject to turbulence losses due to insufficient flow guiding. ... 

The 0.34 coefficient shown is the conversion of potential energy to acceleration, which includes a reasonable allowance for turbulence and friction. The theoretical coefficient is about 0.18, which only includes acceleration. In my designs, 1 use 0.34 for nozzle exit losses, which my experience has shown represents what 1 actually observe in the field, plus a small safety factor. 

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