Reynolds number friction factor diagram

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. 

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 /. 

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 ... 

Fio. 4. Friction factor-Reynolds number diagram for Bingham plastics. 

Weltmann (W4) presented this relationship on a friction factor-Reynolds number diagram similar to Fig. 4 for Bingham-plastic fluids. Excellent agreement between predicted and measured results was found by Salt for two carboxymethylcellulose solutions Weltmann shows no data to support her somewhat more useful rearrangement but cites three literature references for this purpose. Review of these shows that none dealt explicitly with this method of approach, as claimed. 

Fig. 5. Friction factor-Reynolds number diagram for non-Newtonians-low range. Taken from reference (Mil) with permission.

The utility of this generalized Reynolds number has been shown (Mil) by the correlation of all available literature data on flow of non-Newtonian fluids on the conventional friction factor-Reynolds number diagram which is reproduced in Figs. 5, 6, and 7. The curves shown are not drawn through the data points but rather represent the conventional... 

The friction factor for laminar flow in pipes Re < 2300) is given by fo = 4/i = For turbulent flow in rough pipes the friction factors depends on both the Reynolds number and the surface roughness of the tube. Colebrook [35] devised an implicit relation for the Darcy friction factor which reproduce the well known Moody diagram quite well. 

Figure 4.1 Moody diagram Fanning friction factor, f, vs. Reynolds number for the range of commercial pipe relative roughnesses.

Brownell, Dombrowsky, and Dickey [13] correlated the results of several authors on the basis of the /-Re diagram for empty pipes. In order to make the results for packed tubes coincide with those for empty pipes, the characteristic length in / and Re is taken to be the particle diameter. This is not sufficient one has to account for the true fluid velocity and true path length. Brownell et al. introduced two correction factors, one for the Reynolds number. and one for the friction factor, Fj. These were determined as Inunctions of and kji. The results are shown in Figs. 11.5.a-2, 11.5.a-3 and 11.5.a-4. 

In Fig. 3.1-5 the friction factor X for pipes with a siuface roughness k (k is the mean height of protuberances) is plotted against the Reynolds number. The equations presented here in combination with the diagram are general tools to calculate the pressure drop Ap in circular tubes with constant cross-sectional area. 

An interesting behavior is shown in Figure 3.4 and was pointed out by Revellin and Thome [16]. Similarly to the classic Moody diagram in single-phase flow, according to their results, three zones were distinguishable when plotting the variation of the two-phase friction factor versus the two-phase Reynolds number, as follows a laminar zone for < 2000, a transition zone for 2000 < Repp < 8000 and a turbulent zone for Repp >8000. 

The dimensionless pipe friction factor is determined in dependence of the Reynolds number Re (Eq. (17.2)) and the relative pipe roughness kid. The literature [3] shows diagrams. 

FIGURE 2-4 Moody diagram for the friction factor versus the Reynolds number for pipe flow (Reproduced from V. L. Streeter, Fluid Mechanics, McGraw-Hill, 1971. Reproduced by permission of McGraw-Hill, Inc.)... 

Using the Moody diagram determine the ratio of the friction factor for rough to smooth pipe at the value of the Reynolds number (using Rep, ReppQ or 7 e od)-... 

The classic method for determining the friction factor uses the diagram of Moody (22), where the Fanning friction factor / is given as a function of the Reynolds number and the wall roughness e. An explicit formula for this relationship was developed by Haaland (29) ... 

The familiar Moody Diagram is a log-log plot of the Colebrook correlation on an axis of the friction factor and the Reynolds number, combined with the/ = 64/Re result for laminar flow. 

Moody plot, chart, diagram A dimensionless representation of friction factor with Reynolds number tor a fluid flowing in a pipe. Presented on log-log scales, the diagram includes laminar, transition, and turbulent flow regimes. It also includes the effects of pipe relative roughness as a dimensionless ratio of absolute roughness with internal pipe diameter. The plot was developed in 1942 by American engineer and professor of hydraulics at Princeton, Louis Ferry Moody (1880-1953). 

Assume velocity V, and calculate Reynolds number. From Reynolds number, calculate the friction factor from the Moody diagram shown in Figure 2.2, otherwise it can be obtained from the above-mentioned equations. Calculate the pressure drop and then compare the calculated result with the given value of pressure drop which is 118 kPa in the question of the example. Repeat until the desired pressure drop is reached. Polymath software can be used instead (Figure 2.19). The calculated velocity is 5.29 m/s as shown in Figure 2.20. 

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