Friction factors Darcy

Fanning friction factor Darcy friction factor mass flux... 

Figure 7-2 Friction factor (Darcy) versus Reynolds number.

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 ... 

Fluid friction in conduits Darcy friction factor = 4/... 

Figure 2-31 is useful in sohing the usual steam or any vapor flow problem for turbulent flow based on the modified Darcy relation with fixed friction factors. At low vapor velocities the results may be low then use Figure 2-30. For steel pipe the limitations listed in (A) above apply.

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. 

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

This is a form of the Fanning or Darcy formula with friction factor = 0.0055. This friction factor corresponds to approximately the following ... 

Group N6 (or some multiple thereof) is also known as a friction factor (/), because the driving force (AP) is required to overcome friction (i.e., the energy dissipated) in the pipeline (assuming it to be horizontal), and N3 is known as the Reynolds number (N e). There are various definitions of the pipe friction factor, each of which is some multiple of N6 e.g., the Fanning friction factor is N6/2, and the Darcy friction factor is 2N6. The group N4 is also known as the Euler number. 

Fanning (Darcy) friction factor f(f or fD) e, D 2 V2L fo = 4f TW yv2 e, = friction loss (energy/mass) rw = wall stress (Energy dissipated)/ (KE of flow x 4L/D) or (Wall stress)/ (momentum flux) Flow in pipes, channels, fittings, etc. 

Although pV2/2 represents kinetic energy per unit volume, pV2 is also the flux of momentum carried by the fluid along the conduit. The latter interpretation is more logical in Eq. (5-50), because rw is also a flux of momentum from the fluid to the tube wall. However, the conventional definition includes the (arbitrary) factor i. Other definitions of the pipe friction factor are in use that are some multiple of the Fanning friction factor. For example, the Darcy friction factor, which is equal to 4/, is used frequently by mechanical and civil engineers. Thus, it is important to know which definition is implied when data for friction factors are used. 

An incompressible fluid flows in a laminar steady fashion through a long pipe with a linear pressure gradient. Describe the velocity profile and determine the relationship for the Darcy-Weisbach friction factor. 

Now, the Darcy-Weisbach equation for head loss defines the friction factor,/ ... 

Please note the resemblance of Eq. (6.26) to the earlier Darcy equation. Why is the factor 2 installed The answer is that Eq. (6.6) is based on the Moody friction factor f and Eq. (6.26) is based on the Fanning friction factor f. These two friction factors are identical, except that the Moody f is exactly four times larger than the Fanning f. Without a long story as to how these two research scientists came up with the same answer, with the exception of one being four times larger in every case, simply accept the fact that one perhaps wanted to be recognized as an independent developer. Nonetheless, the bottom line is that both Eqs. (6.6) and (6.26) are indeed the same equation. 

Darcy friction factor (fD = 4fF) length of a static mixer (ft, m) fluid velocity (ft/sec, m/sec)... 

At higher Reynolds numbers, the friction factor is affected by the roughness of the surface, measured as the ratio e/D of projections on the surface to the diameter of the pipe. Glass and plastic pipe essentially have = 0. Table 7-11 gives the pipe roughness of various materials. Figure 7-22 shows plots of Darcy friction factor versus Reynolds number for various pipe sizes. Alternatively, an explicit equation for the friction factor is given by [30] ... 

The Darcy friction factor fD is four times the Fanning (fF) friction factor (i.e., fD = 4fF = fc). 

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