Friction factor equations

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 ... 

These equations can readily be solved by iteration, as follows. Assuming a value of / allows, VRe to be determined from Eq. (7-31). This is then used with Eq. (7-32) to find, Ylle. The friction factor is then calculated using these values of, VRe and AHe and the Bingham plastic pipe friction factor equation [Eq. (6-62)]. The result is compared with the assumed value, and the process is repeated until agreement is attained. 

Using A Repi and n, calculate / (and the corresponding Kpipe) for each pipe section from the power law friction factor equation [Eq. (6-44)], and calculate Kt for each valve and fitting using the 3-K method [Eq. (7-38)]. 

Dividing equation 3.57 by equation 3.56 and using the definition of the Fanning friction factor (equation 2.10) gives... 

Churchill, S.W. "Friction-factor Equation Spans All Fluid-flow Regimes." Chan. Engg, (1977), Nov. 7, pp 91-92. 

These IF statements are really a form of discrete decision making embedded within the model. One possible approach to remove the difficulties it caused is to move the discrete decisions to the outside of the model and the continuous variable optimizer. For example, the friction factor equation can be selected to be the laminar one irrespective of the Reynolds number that is computed later. Constraints can be added to forbid movement outside the laminar region or to forbid movement too far outside the laminar region. If the solution to the well-behaved continuous variable optimization problem (it is solved with few iterations) is on such a constraint boundary, tests can be made to see if crossing the constraint boundary can improve the objective function. If so, the boundary is crossed—i.e., a new value is given to the discrete decision, etc. 

Any other appropriate friction factor equation for smooth tubes may be used. 

Garcia, E. J. and Steffe, J. F. 1987. Comparison of friction factor equations for non-Newtonian fluids in pipe flow. J. Food Process Eng. 9 93-120. 

Churchill, S. W. (1977) Friction-Factor Equation Spans All Fluid-Flow Regimes, Chemical Engineering Progress, Vol. 84(24), pp. 91-92. 

Transfer properties, the heat and mass transfer coefficient and friction factor, depend not only on transport and thermodynamic properties but also on the hydro-dynamic behavior of a fluid. The geometry of the system will influence the hydro-dynamic behavior. By reducing the parameters by arranging them into dimensionless groups, we can reduce the number of parameters that have to be varied to correlate any of the transfer properties. For example, the friction factor equation,... 

For individually finned tubes as shown in Fig. 17.14a, flow expansion and contraction take place along each tube row, and the magnitude is of the same order as that at the entrance and exit. Hence, the entrance and exit losses are generally lumped into the core friction factor. Equation 17.65 for individually finned tubes then reduces to... 

Turbulent flow in many kinds of noncircular conduits can be estimated by substituting 4j times the hydraulic radius for the diameter in the friction factor plot and the friction factor equation. 

The friction loss in long straight channels or conduits of noncircular cross section can be estimated by using the same equations employed for circular pipes if the diameter in the Reynolds number and in the friction factor equation (2.10-6) is taken as the equivalent diameter. The equivalent diameter D is defined as four times the hydraulic radius r . The... 

S. W. Churchill. Friction-Factor Equation Spans all Fluid Flow Regimes. Chem. Eng., pages... 

Churchill, S. W. 1977. Friction factor equation spans all fluid flow regimes. Chemical Engineering 84, no. 7 91-92. 

An alternative method for estimating the wall friction factor is to use a standard pipe friction factor equation, such as the explicit formula of Swamee and Jain, using the equivalent diameter of the film in Rei. Thus,... 

The constant 2gq/p is called the resistance coefficient and is denoted by / (called friction factor). Equation 2.34 can be modified as... 

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