Tube flow friction factor

For banks of staggered tubes, the friction factor for isothermal flow is obtained from Fig. (6-42). Each fence (group of parametric curves) represents a particular Reynolds number defined as... 

Any suitable correlation for the cross-flow friction factor can be used for that given in Figure 12.36, the pressure drop across the ideal tube bank is given by ... 

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 ... 

By analogy with laminar flow in a tube, the friction factor in laminar flow would be... 

TABLE 5.9 Fully Developed TUrbulent Flow Friction Factor Correlations for a Rough Circular Duct [48] (a = tube radius)... 

In laminar flow,/is independent of /D. In turbulent flow, the friction factor for rough pipe follows the smooth tube curve for a range of Reynolds numbers (hydrauhcaUy smooth flow). For greater Reynolds numbers,/deviates from the smooth pipe cui ve, eventually becoming independent of Re. This region, often called complete turbulence, is frequently encountered in commercial pipe flows. The Reynolds number above which / becomes essentially independent of Re is (Davies, Turbulence Phenomena, Academic, New York, 1972, p. 37) 20[3.2-2.46ln( /D) ... 

FK . 6-42 Upp er chart Friction factors for staggered tube banks with minimum fluid flow area in transverse openings. Lower chart Friction factors for staggered tube banks with minimum fluid flow area in diagonal openings. (From Gtimison, Trans. ASME, 59,. 5S3 [1.937],)... 

For turbulent flow through shallow tube banks, the average friction factor per row will be somewhat greater than indicated by Figs. 6-42 and 6-43, which are based on 10 or more rows depth. A 30 percent increase per row for 2 rows, 15 percent per row lor 3 rows and 7 percent per row for 4 rows can be taken as the maximum likely to be encountered (Boucher and Lapple, Chem. Eng. Prog., 44, 117—134 [1948]). 

FIG. 6-45 Friction factors for transition region flow across tube hanks, (Pitch is the minimum center-to-center tnhe spacing.) (Prom Bergelin, Btown, and Doherstein, Ti-ans. ASME, 74,. 9.53 [1.9.52],)... 

This equation gives values that are half of those calculated as total gas flow for the shell side by using friction factors from Figure 10-140. (Note that f for plain or bare tubes = f/1.2 (with f from Figure 10-140)). 

Figure 9.30. Friction factor for flow over tube bundles...

Fig. 2.20 (a) Dependence of the friction factor on Reynolds number for tube of diameter 705 pm. Reprinted from Maynes and Webb (2002) with permission, (b) Turbulent flow friction correlations. Reprinted from Sobhan and Garimella (2001) with permission... 

Glass and silicon tubes with diameters of 79.9-166.3 iim, and 100.25-205.3 am, respectively, were employed by Li et al. (2003) to study the characteristics of friction factors for de-ionized water flow in micro-tubes in the Re range of 350 to 2,300. Figure 3.1 shows that for fully developed water flow in smooth glass and silicon micro-tubes, the Poiseuille number remained approximately 64, which is consistent with the results in macro-tubes. The Reynolds number corresponding to the transition from laminar to turbulent flow was Re = 1,700—2,000. 

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. 

Brutin D, Tadiist L (2003) Experimental friction factor of a liquid flow in micro-tubes. Phys Fluids 15 653-661... 

Figure 12.36. Friction factor for cross-flow tube banks...

Malnes, D., 1966, Slip Ratios and Friction Factors in the Bubble Flow Regime in Vertical Tubes, Norwegian Rep. KR-110, Inst, for Atomenergi, Oslo, Norway. (5)... 

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. 

For turbulent flow in smooth tubes, the semiempirical Prandtl-von Karman/Nikuradse or Blasius models represent the friction factor quite well. Whether a tube is hydraulically smooth or rough depends upon... 

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