Friction factor effect

Reinius (R4), 1961 Studies of water flows in open channels at small slopes, Nr, = 50-13,000. Data on film thicknesses, film friction factors, effects of wall roughness. 

The segmental friction factor introduced in the derivation of the Debye viscosity equation is an important quantity. It will continue to play a role in the discussion of entanglement effects in the theory of viscoelasticity in the next chapter, and again in Chap. 9 in connection with solution viscosity. Now that we have an idea of the magnitude of this parameter, let us examine the range of values it takes on. 

Whether the beads representing subchains are imbedded in an array of small molecules or one of other polymer chains changes the friction factor in Eq. (2.47), but otherwise makes no difference in the model. This excludes chain entanglement effects and limits applicability to M < M., the threshold molecular weight for entanglements. 

The following analysis enables one to calculate the diameter of a pipeline transporting any compressible fluid. The required inputs are volumetric flow rate, the specific gravity of the gas relative to air, flow conditions, compressibility factor Z where Z is defined by nZRT = PV, the pressure at the point of origin and the destination, the pipe length, and pipe constants such as effective roughness. The working equations have been obtained from the literature. Since the friction factor... 

The value of C3 is 0.011454 in USCS units and 20.178 x 10 in SI units. The inputs for the calculation are Q (bbl/hr or mVhr) and pipeline length (miles or km), viscosity U (Centistokes), pipe diameter D (inches or meters), effective pipe roughness e, and pipeline lengths (miles or km). The Fanning friction factor is... 

To allow for the effect of roughness one can use the results of empirical tests in ducts that have been artificially roughened with particles glued on the surface. This approach allows roughness levels to be determined as a function of the particle diameter k. The following friction factor equation has been derived for large Reynolds numbers ... 

The empirical frictional factor (T fric) is independent of shear rate but increases in poor solvent this permits to account for the dependence of the scission rate constant on solvent quality. The entanglement part (r enl), as given by Graessley s theory which considers the effect of entanglement and disentanglement processes, is a complex function of shear rate ... 

Experiments were conducted with air through micro-channel A = 319 (friction factor. The relative surface roughness was low k /H = 0.001) and Kn < 0.001, thus the experiments were effectively isolated from the influence of surface roughness and rarefaction. The local friction factor is plotted versus Ma in Fig. 2.25 for air. The experimental A increases about 8% above the theoretical A as Ma increases to 0.35. 

The influence of compressibility was assessed by varying the Mach number in the range 0 < Ma < 0.38, while Kn and ks/H were kept low. Friction factor data were reported only with Ma < 1 at the exit, to ensure the flow rate was controlled by viscous forces alone. A mild increase in the friction factor (8%) was observed as Ma approached 0.38. This effect was verified independently by numerical analysis for the same conditions as in the experiment. The range of relative surface roughness tested was 0.001 < ka/H < 0.06, yet there was no significant influence on the friction factor for laminar gas flow. 

Basically, there may be three reasons for the inconsistency between the theoretical and experimental friction factors (1) discrepancy between the actual conditions of a given experiment and the assumptions used in deriving the theoretical value, (2) error in measurements, and (3) effects due to decreasing the characteristic scale of the problem, which leads to changing correlation between the mass and surface forces (Ho and Tai 1998). 

Several investigators obtained friction factors in micro-channels with rough walls that were greater than those in smooth wall channels. These observations should be considered taking into account the entrance effects, losses from change in channel size, etc. 

The results obtained by Brutin and Tadrist (2003) showed a clear effect of the fluid on the Poiseuille number. Figure 3.14 shows results of experiments that were done in the same experimental set-up for hydraulic diameters of 152 and 262 pm, using distilled water and tap water. The ion interactions with the surface can perhaps explain such differences. Tap water contains more ions such as Ca +, Mg +, which are 100 to 1,000 times more concentrated than H3O+ or OH . In distilled water only H30 and OH exist in equal low concentrations. The anion and cation interactions with the polarized surface could modify the friction factor. This is valid only in the case of a non-conducting surface. 

Celata et al. (2005) evaluated the effect of viscous heating on friction factor for flow of an incompressible fluid in a micro-channel. By integrating the energy equation over the micro-channel length, a criterion that determines conditions when viscous dissipation effect is signiflcant was obtained ... 

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 number of tube rows has little effect on the friction factor and is ignored. 

For a diabatic flow case, as in the high heat flux, boiling water system typical of reactor cores, Tarasova et al. (1966) proposed the following correlation for the effect of wall heat flux on friction factors by a correction factor ... 

The Moody diagram illustrates the effect of roughness on the friction factor in turbulent flow but indicates no effect of roughness in laminar flow. Explain why this is so. Are there any restrictions or limitations that should be placed on this conclusion Explain. 

---