Estimation of friction factor

A correct value of friction factor is required for the estimation of pressure drop. The value of the friction factor depends upon the flow characteristics. For laminar flow less than 2100), the friction factor varies inversely with the Re5molds number, whereas for turbulent flow, the friction factor has a complex relationship with the pipe diameter, roughness of the pipe, and the Reynolds number. 

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Hence the condition that the Reynolds number be greater than 100000 is easily satisfied, and we may regard our estimate of friction factor as reasonable. 

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. 

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,... 

To predict the pressure drop for this flow regime, an empirical correlation for estimating the friction factor was obtained from experimental data in the range of 0.008 < uq -H l) < 1 ms ... 

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). 

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 /. 

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. 

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