J friction factor

Once the diameter is known, the Reynolds number. Re can be computed and the friction factor f obtained from Figure 21. Assuming a straight length of pipe for L = 5(X) ft, N (line resistance factor) can be calculated. Next Gj, is calculated based on the downstream pressure and G/G j evaluated. From Figure 20 the ratio Pj/Pfl can be obtained. Since Pj is known, Pq can then be calculated. The pressure at the inlet of the knock-out drum is given by Pq -I- 0.5 psi. Table 6 provides typical values of resistance coefficients for various pipe fittings. 

Khan, A.R and Richardson, J.F., 1990. Pressure gradient and friction factor for sedimentation and fluidisation of uniform spheres in liquids. Chemical Engineering Science, 45, 255-265. 

The correlation studies of heat and mass transfer in pellet beds have been investigated by many, usually in terms of the. /-factors (113-115). According to Chilton and Colburn the two. /-factors are equal in value to one half of the Fannings friction factor / used in the calculation of pressure drop. The. /-factors depend on the Reynolds number raised to a factor varying from —0.36 to —0.68, so that the Nusselt number depends on the Reynolds number raised to a factor varying from 0.64 to 0.32. In the range of the Reynolds number from 10 to 170 in the pellet bed, jd should vary from 0.5 to 0.1, which yields a Nusselt number from 4.4 to 16.1. The heat and mass transfer to wire meshes has received much less attention (110,116). The correlation available shows that the /-factor varies as (Re)-0-41, so that the Nusselt number varies as (Re)0-69. In the range of the Reynolds number from 20 to 420, the j-factor varies from 0.2 to 0.05, so that the Nusselt number varies from 3.6 to 18.6. The Sherwood number for CO is equal to 1.05 Nu, but the Sherwood number for benzene is 1.31 Nu. 

The right-hand side of equation 10.224 gives numerical values which are very close to those obtained from the Blasius equation for the friction factor (j> for the turbulent flow of a fluid through a smooth pipe at Reynolds numbers up to about 106. 

Jones OC (1976) An improvement in the calculation of turbulent friction factor in rectangular ducts. Trans ASME J Eluid Eng 98 173-181... 

Note The friction factor j f is the same as the friction factor for pipes (= (.R/pu2)), defined in Volume 1 Chapter 3. 

Friction-factor chart. (From Unit Operations of Chemical Engineering by W. L. McCabe and J. C. Smith. Copyright (c) 1967. Used with permission of McGraw-Hill Book Company.)... 

Yang, W. C., A Correlation for Solid Friction Factor in Vertical Pneumatic Conveying Lines, AIChE J., 24 548 (1978)... 

The expression for the projection of the /th normal mode onto m of the mth rod is presented elsewhere/17 29) Besides these deformational normal modes, there is also a uniform axial spinning mode in which all of the rods rotate in phase like a speedometer cable. The contribution of that mode to is just 2k Tt/(N+ l)y, as expected for diffusion in one dimension with the friction factor (N + 1)7 of the entire filament. 

Wheeler, J. A. and Whissler, E.H., The friction factor-Reynolds Number Relation for the Steady Flow of Pseudoplastic Fluids through Rectangular Ducts. Part 1. Theory, Am. Inst. Chem. Eng. J., 11, 207 (1965)... 

At very low solvent viscosity, when f is small compared with the internal friction factors, the chain molecules must behave like "frozen molecules. In this case, the initial slope of the extinction angle curve becomes again a linear function of the solvent viscosity. The slope of this straight line, however, is considerably higher than (J eRj2)(M ri jRT). Its intercept with the ordinate axis is equal to zero. This behaviour is schematically shown in Fig. 5.10 (3). 

Figure 6.5. Friction factors in laminar and turbulent flows of power-law and Bingham liquids, (a) For pseudoplastic liquids represented by tw = K [WID) , with K and n constant or dependent on r l/V/ = [4.0/(n )0 75] log10[Re /( "2)] — 0.40/(k )1 2j, [Dodge and Metzner, AIChE J. 5, 159 (7959)]. (b) For Bingham plastics, ReB = DVp/pB, He = 10D2plp% [Hanks and Dadia, AIChE J. 17, 554 (J971)].

Figure 6.8. Friction factors and void fractions in flow of single phase fluids in granular beds, (a) Correlation of the friction factor, Re = DpG/( - e)p and fp = lgcDpe3/Pu2(l - e)](AP/L = 150/Re + 4.2/(Re)1/f [Sa/o et al., J. Chem. Eng. Jpn. 6, 147-152 (1973)]. (b) Void fraction in granular beds as a function of the ratio of particle and tube diameters [Leva, Weintrauh, Crummer, Pollchik, and Storch, U.S. Bur. Mines Bull. 504 (1951)].

An improved correlation is that of Sato (1973) and Tallmadge (AlChE J. 16, 1092 (1970)] shown on Figure 6.8(a). The friction factor is... 

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