Fanning friction factor, definition

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. 

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. 

Dividing equation 3.57 by equation 3.56 and using the definition of the Fanning friction factor (equation 2.10) gives... 

It is useful to regroup the usual definition of the Fanning friction factor, Eq. (10), as follows ... 

Since Equation 10.50 rigorously portrays the laminar flow behavior of the fluid (provided n and K are evaluated at the correct shear stress), it may be used to define a Reynolds number applicable to all purely viscous fluids under laminar flow conditions. This dimensionless group can be derived simply by the substitution of (DAP/4L) from Equation 10.50 into the usual definition of the fanning friction factor, that is. 

See nomenclature for definition of symbols and units. The units presented are English engineering units, unless a conversion is required. The friction factor is the only experimental variable that must be determined by reference to the above equations and it is represented by Figure 2-3. Note that this may sometimes be referred to as the Fanning formula, and may be modified to )held a fric-... 

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. 

By analogy to single-phase flow, the two-phase frictional pressure-drop can be expressed by the conventional Fanning equation, and thereby a friction factor is defined. These friction factors may be based on liquid properties, gas properties, or on a fictitious single fluid of mean properties obtained by some averaging procedure. Typical definitions, such as those shown in equation (32), have been given and discussed recently by Govier and Omer (G4) ... 

Flow in the laminar regime is often characterized by a friction loss factor, which is 64/Re for the Darcy factor or 16/Re for the Fanning factor (this topic wiU be discussed in more details in Chapter 2). As a result, the losses in the laminar regime appear to be a linear function of speed, whereas in the turbulent regime they are proportional to the square of the speed. As we wiU see in Chapter 5, researchers have struggled with special definitions of a modified Reynolds number for non-Newtonian flows. 

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