Moody diagram, friction factor

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

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 /. 

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 ... 

As mentioned before, the power given to the fluid is actually equal to the power dissipated as friction. In any friction loss relationships with Re, such as the Moody diagram, the friction factor has an inverse linear relationship with Re in the laminar range (Re < 10). The power number is actually a friction factor in mixing. Thus, this inverse relationship for % and Re, is... 

In the above equation, L is the length over which the pressure drop p — p2 is to be calculated pi is the absolute pressure of the flow at an upstream point 1, and p2 is the absolute pressure of the flow at a downstream point 2 / is the Darcy-Weisbach friction factor that can be determined from the Moody Diagram y is the adiabatic exponent (equal to 1.4 for air) and Mi is the Mach number of the flow at the upstream point 1. In addition to the pressure equations, the following equation of state of ideal gas is also needed ... 

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.

FIGURE 5.9 Moody s [58] friction factor diagram for fully developed flow in a rough circular duct [45]. 

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. 

In Equation 5, f, appears on both sides of the equation, and the solution can only be obtained by the use of iterative procedure. Friction factor can also be determined from a graph commonly known as Moody s diagram (Moody [47]). Barr [48] proposed the following equation... 

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). 

---