Friction factor, estimation

Reference 115 gives the diffusion coefficient of DTAB (dodecyltrimethylammo-nium bromide) as 1.07 x 10" cm /sec. Estimate the micelle radius (use the Einstein equation relating diffusion coefficient and friction factor and the Stokes equation for the friction factor of a sphere) and compare with the value given in the reference. Estimate also the number of monomer units in the micelle. Assume 25°C. 

On occasion one will find that heat-transfer-rate data are available for a system in which mass-transfer-rate data are not readily available. The Chilton-Colburn analogy provides a procedure for developing estimates of the mass-transfer rates based on heat-transfer data. Extrapolation of experimental or Jh data obtained with gases to predict hquid systems (and vice versa) should be approached with caution, however. When pressure-drop or friction-factor data are available, one may be able to place an upper bound on the rates of heat and mass transfer, according to Eq. (5-308). 

For condensing vapor in vertical downflow, in which the hquid flows as a thin annular film, the frictional contribution to the pressure drop may be estimated based on the gas flow alone, using the friction factor plotted in Fig. 6-31, where Re is the Reynolds number for the gas flowing alone (Bergelin, et al., Proc. Heat Transfer Fluid Mech. Inst., ASME, June 22-24, 1949, pp. 19-28). 

If the friction factor

[Pg.370]

Determine the value of the Reynolds number for SAE 10 lube oil at 100°F flowing at a rate of 2000 gpm through a 10 in. Schedule 40 pipe. The oil SG is 0.92, and its viscosity can be found in Appendix A. If the pipe is made of commercial steel (e = 0.0018 in.), use the Moody diagram (see Fig. 6-4) to determine the friction factor / for this system. Estimate the precision of your answer, based upon the information and procedure you used to determine it (i.e., tell what the reasonable upper and lower bounds, or the corresponding percentage variation, should be for the value of / based on the information you used). 

Equation (6-41) adequately represents the Fanning friction factor over the entire range of Reynolds numbers within the accuracy of the data used to construct the Moody diagram, including a reasonable estimate for the intermediate or transition region between laminar and turbulent flow. Note that it is explicit in /. 

A first estimate for the pipe friction factor and the AT/s can be made by assuming that the flow is fully turbulent (and the a s = 1). Thus,... 

Using the Ergun (1952) equation for the interfacial friction factor, Wen and Yu (1966) derived the following general equation to estimate the minimum fluidization superficial velocity Umf for spherical particles ... 

All quantities in equation 7.64 can be readily evaluated with the exception of the friction factor. There are several approaches to estimating the friction factor for two-phase flow. 

The total number of openings N affects the flow rate, velocity, and Ret) in the region of the last opening, which is determined to (1/AO of the opening at the entrance of the distributor. So, ReD at die first and the last opening of the distributor can be calculated, and in turn, the corresponding values of the fanning friction factors can be estimated. The mean value of these two factors should be used in the calculations in diis procedure. 

From Eqs. (4)-(10) of Example 6.6, any combination of seven quantities Qn and/or Ltj and/or D can be found. Assuming that the g,y are to be found, estimates of all seven are made to start, and the corresponding Reynolds numbers and friction factors are found from Eqs. (2) and (3). Improved values of the Qtj then are found... 

Correlations for friction factors and heat transfer coefficients are rated in HEDH. Some overall coefficients based on external bare tube surfaces are in Tables 8.11 and 8.12. For single passes in cross flow, temperature correction factors are represented by Figure 8.5(c) for example charts for multipass flow on the tube side are given in HEDH and by Kays and London (1984), for example. Preliminary estimates of air cooler surface requirements ram be made with the aid of Figures 8.9 and 8.10, which are applied in Example 8.9. 

Alternatively, the friction loss can be estimated using the formula and friction factor (Fp) chart presented in Ref. P3 (p. 143). In this case the friction factor is a function of Reynolds number (NRe). Friction loss per metre = 4 FDp u2/D... 

The friction loss can also be estimated using the formula and friction factor chart given in Ref. P3 (p.143) ... 

S based on experiments with water in turbulent flow, in channels icient roughness that there is no Reynolds number effect. The hydraulic radius approach may be used to estimate a friction factor with which to compute friction losses. Under conditions of uniform flow where liquid depth and cross-sectional area do not vary significantly with position in the flow direction, there is a balance between gravitational forces and wall stress, or equivalently between frictional fosses and potential energy change. The mechanical energy balance reduces to tv = g(zx — z2). In terms of the friction factor and hydraulic diameter or hydraulic radius,... 

F or turbulent pipe flow, the friction velocity u = Vx ,/p used earlier in describing the universal turbulent velocity profile may be used as an estimate for V Together with the Blasius equation for the friction factor from which e may be obtained (Eq. 6-214), this provides an estimate for the energy-containing eddy size in turbulent pipe flow ... 

For Newtonian fluids flowing in smooth pipes, the friction losses can be estimated for laminar flow (Re < 2100) using the Fanning friction factor, f. The Reynolds number, Re, is given by ... 

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