Moody friction factor

Fig. 5. Moody diagram for Darcy friction factor (13) (-----), smooth flow (----), whoUy turbulent flow ( ), laminar flow.

For smooth pipe, the friction factor is a function only of the Reynolds number. In rough pipe, the relative roughness /D also affects the friction factor. Figure 6-9 plots/as a function of Re and /D. Values of for various materials are given in Table 6-1. The Fanning friction factor should not be confused with the Darcy friction fac tor used by Moody Trans. ASME, 66, 671 [1944]), which is four times greater. Using the momentum equation, the stress at the wall of the pipe may be expressed in terms of the friction factor ... 

FIG. 6-9 Fanning Friction Factors. Reynolds niimher Re = DVp/ i, where D = pipe diameter, V = velocity, p = fluid density, and i = fluid viscosity. (Based on Moody, Trans. ASME, 66, 671 [1.944].)... 

AP = Pressure drop, Ib/fr / = Friction factor (Fanning = Moody s/4)... 

D = Header diameter, ft f = Moody friction factor L = Header equivalent length, ft M2 == Mach number at the header outlet Pi,P2 = Inlet and outlet header pressures, psia... 

Determination of friction factors for some fluid flow applications can involves a trial-and-error procedure because the friction factor is not a simple function of the Reynolds number. Process engineers, therefore, refer to a Moody chart that has been developed using the following relationships ... 

In practice the friction factors are calculated either by integration of Eq. (4.51) or by reference to a Moody chart. This is based on Eq. (4.51) by using equivalent roughness values representing the sand particle roughness (see Table 4.3). 

Figure 4.4 shows the Moody chart for tubes when k = 0.03 mm, which is the case for steel tubes. Friction factors for other values of k can be attained by using the following ratio ... 

Figure 2-3. Moody or regular Fanning friction factors for any kind and size of pipe. Note the friction factor read from this chart is four times the value of the f factor read from Perry s Handbook, 6th Ed. [5]. Reprinted by permission, Pipe Friction Manual, 1954 by The Hydraulic Institute. Also see Engineering DataBook, 1st Ed., The Hydraulic Institute, 1979 [2]. Data from L. F, Moody, Friction Factors for Pipe Flow by ASME [1].

Important Note The Moody [1] friction factors reproduced in this text (Figure 2-3) are consistent with the pub-... 

The Colebrook equation [6, 58] is considered a reliable approach to determining the friction factor, f (Moody factor)... 

Determine friction factor, f, from Moody Friction Factor Charts, Figure 2-3. 

Equations 2-60 and 2-61 are illustrated graphically in Figure 2-21. This chart is called a Moody diagram, and it may be used to find the friction factor, given the Reynolds number and the surface roughness. 

Equation 3.11 is due to Blasius(6) and the others are derived from considerations of velocity profile. In addition to the Moody friction factor / = 8R/pu2, the Fanning or Darcy friction factor / = 2R/pu2 is often used. It is extremely important therefore to be clear about the exact definition of the friction factor when using this term in calculating head losses due to friction. 

With the friction factors used by Moody and Fanning, / and / respectively, the head loss due to friction is obtained from the following equations ... 

Moody, L.F. Trans. Am. Soc. Mech. Engrs. 66 (1944) 671. Friction factors for pipe flow. 

Friction factor correlations, smooth pipes 67 - — Darcy and Fanning 67, 68 -- — Moody 65... 

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). 

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. 

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 Moody diagram illustrates the effect of roughness on the friction factor in turbulent flow but indicates no effect of roughness in laminar flow. Explain why this is so. Are there any restrictions or limitations that should be placed on this conclusion Explain. 

Equation (7-25) is implicit for Dec, because the friction factor (/) depends upon Dec through the Reynolds number and the relative roughness of the pipe. It can be solved by iteration in a straightforward manner, however, by the procedure used for the unknown diameter problem in Chapter 6. That is, first assume a value for/ (say, 0.005), calculate Z>ec from Eq. (7-25), and use this diameter to compute the Reynolds number and relative roughness then use these values to find / (from the Moody diagram or Churchill equation). If this value is not the same as the originally assumed value, used it in place of the assumed value and repeat the process until the values of / agree. 

Using this Reynolds number, determine the revised pipe friction factor (and hence ATpipe = AfL/D) from the Moody diagram (or Churchill equation), and the Kfit values from the 3-K equation. 

Evaluation of each term in Eq. (15-51) is straightforward, except for the friction factor. One approach is to treat the two-phase mixture as a pseudo-single phase fluid, with appropriate properties. The friction factor is then found from the usual Newtonian methods (Moody diagram, Churchill equation, etc.) using an appropriate Reynolds number ... 

Care must be taken when comparing the pressure drop in motionless mixers, because three definitions exist. In this chapter, Moody s friction factor is adopted,... 

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