Moody diagram

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

The formulas are represented in the Moody diagram, which allows a quick solution. 

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 /. 

All the relevant variables and parameters are uniquely related through the three dimensionless variables / /VRe, and e/D by the Moody diagram or the Churchill equation. Furthermore, the unknown (DF = ef) appears in only one of these groups (/). The procedure is thus straightforward ... 

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. 

First, assume / = 0.005 and use this to get NRe from Nc=fN 9. From NRe we find Z)ec, and thus s/Dtc. Then, using the Churchill equation or Moody diagram, we find a valyue for / and compare it with the assumed value. This is repeated until convergence is achieved ... 

The driving force (DF) is given by Eq. (7-45), in which the K- s are related to the other variables by the Moody diagram (or Churchill equation) for each pipe segment (Kpipe), and by the 3-K method for each valve and fitting (Kfit), as a function of the Reynolds number ... 

For each pipe segment of diameter Z) , get f from the Churchill equation or Moody diagram using NRei and i/Dh and calculate plpe = 4 (fL/D. ... 

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. 

Calculate, VRe = DG//i and use this to find f from the Moody diagram or the Churchill 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 ... 

Moody diagram - [HEAT-EXCHANGE TECHNOLOGY- HEAT TRANSFER] (Vol 12)... 

FIGURE 3A Moody diagram for Newtonian pipe flow. [Adapted from Moody, L. F. (1944). Trans. ASME 66, 671-684.]... 

For rough pipes, approximate values of NuD are obtained if/is estimated by tne Moody diagram of Sec. 6. Equation (5-48) is corrected for entrance effects per (5-53) and Table 5-3. Sieder and Tate [Ind. Eng. Chem., 28, 1429 (1936)] recommend a simpler but less accurate equation for fully developed turbulent flow... 

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... 

At high Reynolds numbers, friction losses become practically constant. If the Moody diagram for flow in pipes is inspected, this statement will be found to be true. Agitators are not an exception. If vortices and swirls are prevented, at high Reynolds numbers greater than or equal to 10,000, power dissipation is independent of Re and the relationship simply becomes... 

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. 

The Colebrook equation is convenient for determining the flow rate from the allowable friction loss (e.g., driving force), tube size, and fluid properties. Published plots of/vs. and e/D (i.e., the Moody diagram) are usually generated from the Colebrook equation. 

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