Moody chart

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 ... 

Resistance factors are taken from the Moody chart, when the Reynolds number and roughness are known. 

To determine the pressure losses, we have to find out whether the flow is laminar or turbulent, because =/(Re, k/d]. In practical dimensioning, Eq. (4.66) and the Moody chart are used. 

For the Reynolds number range typical of drag reduction (Re 105), / is about 0.02 from the Moody chart (see Fig. 11.7). The typical turbulent intensity of gas in a pipe flow is about 5 percent. Using the Hinze-Tchen model (see 5.3.4.1), the ratio of the velocity fluctuation of the particles to that of the gas may be given by Eq. (5.196) as... 

Figure 11.7. Moody chart for pipe friction with smooth and rough walls (from Moody, 1944).

Equation (95) is the source of the laminar flow line on the Moody chart (Fig. 3). 

Figure 6 was created in this manner for a series of decade values of He. It may be used in place of the Moody chart for standard pipeline design problems. Because of the manner in which the empirical correlation for B was determined, no correction for pipe relative roughness is needed when one is dealing with commercial grade-steel line pipe. 

Charts and equations describing the variation of the friction factor, /, with the Reynolds number, Rep, and wall roughness ratio, elD, where e is a measure of the roughness of the walls, are available [18],[19], [20]. A Moody chart that gives the friction factor variation is shown in Fig. 7.4. 

Chemical engineers are familiar with the Fanning (or Darcy) friction factor,/, the Moody chart of/vs. Reynolds number, Rg, and how all of this fits together to calculate pressure drop for a given fluid flow in a given sized pipe. The friction factor is calculated from the Colebrook equation ... 

The Moody chart for the friction factor for fully developed flow in circular pipes 867... 

Commercially available pipes differ from those used in the experiments in that the roughness of pipes in the market is not uniform and it is difficult to give a precise description of it. Equivalent roughness values for some commercial pipes are given in Table 8-3 as well as on the Moody chart. But it should be kept in mind that these values are for new pipes, and the relative roughness of pipes may increase with use as a result of corrosion, scale... 

In turbulent flow, wall roughness increases the heat transfer coefficient h by a factor of 2 or more [Dipprey and Saber.sky (1963)]. The convection heat transfer coefficient for rough tubes can be calculated approximately from the Nusselt number relations such as Eq. 8-71 by using the friction factor determined from the Moody chart or the Colebrook equation. However, this approach is not very accurate since there is no further increase in h with/for /> 4/sn,ooih [Norris (1970)1 and correlations developed specifically for rough tubes should be used when more accuracy is desired. 

The friction factor corresponding to this relative roughness and the Reynolds number can simply be determined from the Moody chart. To avoid the reading error, we determine it from the Colebrook equation ... 

Table A-2 Boiling and freezing point properties 843 Table A-3 Properties of solid metals 844 846 Table A-4 Properties of solid nonmetals 847 Table A-5 Properties of building materials 848-849 Table A-6 Properties of insulating materials 850 Table A-] Properties of common foods 851-852 Table A-8 Properties of miscellaneous materials 853 TableA-9 Properties of saturated water 854 Table A 10 Properties of saturated refrigerant-134a 855 Table A-11 Properties of saturated ammonia 856 Table A-12 "Properties of saturated propane 857 Table A-13 Properties of liquids 858 Table A-14 Properties of liquid metals 859 Table A- 5 Properties of air at 1 atm pressure 860 TableA-16 Properties of gases at 1 atm pressure 861-862 Table A-17 Properties of the atmosphere at high altitude 863 Table A-18 Emissivities of surfaces 864-865 Table A-19 Solar radiative properties of materials 866 Figure A-20 The Moody chart for friction factor for fully developed flow in circular pipes 867...

The Moody chart for the friction factor for fully developed flow in circular pipes for use in the head loss relation -----. Friction factors in tlie turbulent flow... 

For turbulent flows, the friction factor is a function of both the Reynolds number and the relative roughness, where s is the root-mean-square roughness of the pipe or channel walls. For turbulent flows, the friction factor is found experimentally. The experimentally measured values for friction factor as a function of Re and are compiled in the Moody chart [1]. Whether the macroscale correlations for friction factor compiled in the Moody chart apply to microchannel flows has also been a point of contention, as numerous researchers have suggested that the behavior of flows in microchannels may deviate from these well-established results. However, a close reexamination of previous experimental studies as well as the results of recent experimental investigations suggests that microchannel flows do, indeed, exhibit frictional behavior similar to that observed at the macroscale. This assertion will be addressed in greater detail later in this chapter. 

Method for calculation of major losses of liquids. First determine fluid properties such as the density, and dynamic viscosity at the operating temperature. Determine the inner diameter of the pipe, and evaluate its absolute roughness based on Table 20.3. Then calculate the Reynolds number for average velocity of the liquid. Afterwards, either use the Moody chart to evaluate the Fanning friction factor based on the Reynolds number and relative roughness, or compute the Colebrook equation by successive iterations. Finally, use the Darcy-Weisbach equation to determine the friction head loss. 

This relationship holds up to a Reynolds (Re) number of 2100. Beyond that and for turbulent flow and for design purposes, Moody chart, shown in Figure 5.4, is used to predict the value of f and, hence, the frictional pressure drop of round pipes. 

The friction factor, f, can be determined from the Moody chart (Figure 2.2) or Swamee and Jain alternative equation. 

Since Reynolds number is greater than 4000 and the flow is turbulent, from the Moody chart... 

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