Fanning friction factor, equation defining

Where ij. is defined as the kinematic viscosity (centistokes), and is a constant with a value of 2,213.8 in USCS units and 353.68 in SI units. An empirical relation for the Fanning friction factor is the Colebrook-White equation ... 

The model for turbulent drag reduction developed by Darby and Chang (1984) and later modified by Darby and Pivsa-Art (1991) shows that for smooth tubes the friction factor versus Reynolds number relationship for Newtonian fluids (e.g., the Colebrook or Churchill equation) may also be used for drag-reducing flows, provided (1) the Reynolds number is defined with respect to the properties (e.g., viscosity) of the Newtonian solvent and (3) the Fanning friction factor is modified as follows ... 

The term rj pu2) in equation 2.9 defines a quantity known as the Fanning friction factor /, thus... 

Fanning friction factor, which is defined by equation 2.10, equation 2.9 may be written as... 

Equation 2.73 is another way of writing equation 2.13 where, in this case, the pressure drop is expressed in height of fluid instead of in force per unit area. In equation 2.73, de is the equivalent diameter defined as four times the cross-sectional flow area divided by the appropriate flow perimeter,/is the Fanning friction factor for flow in an open channel and u is the mean velocity. Combining equations 2.72 and 2.73, and solving for u gives... 

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) ... 

In turbulent flow the frictional pressure drop down the drill pipe must be calculated from equations that have been determined empirically. The commonest method in drilling fluid hydraulics (91-93) is to use a friction factor/, the so-called Fanning friction factor, defined by the ratio of the wall shear stress rw to the kinetic energy per unit volume of the flowing fluid 0.5 pvm2 (94)... 

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. 

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