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38 Part I Liquid Drilling Systems

The constant 25.8 in U.S. units is 519 in the SI units.
The Fanning friction factor f is a function of the Reynolds number
N Re and a term called the relative roughness. The relative roughness is
defined as the ratio of the absolute roughness over the pipe diameter,
where the absolute roughness represents the average depth of pipe-wall
irregularities. Table 2.3 shows the absolute roughness of some pipe
surfaces.
For laminar flow, the friction factor is replaced by f = 16 . Several
N Re
empirical correlations for the determination of friction factor for fully
developed turbulent flow in circular pipe have been presented, including
those by Colebrook (1938):

1 ffiffiffi = −4 log 0:269δ/d + 1:255
p p ffiffiffi (2.49)
f N Re f
where the Reynolds number is defined as

928ρ vd
f
N Re = (2.50)
μ
The constant 928 in U.S. units is 1 in SI units.
The δ is the absolute roughness of the pipe surface in inches (in) or
meter (m). The selection of an appropriate absolute roughness for a given
application is often difficult. Fortunately, in rotary drilling applications
involving the use of relatively viscous drilling fluids, for most wellbore
geometries the relative roughness is usually less than 0.0004 in all sec-
tions. For these conditions, the friction factor for smooth pipe can be
applied for most engineering calculations:
1 p ffiffiffi
ffiffiffi = 4 logðN Re f Þ − 0:395 (2.51)
p
f
Table 2.3 Absolute Roughness of Some Pipe Surfaces
Absolute Roughness
Type of Pipe in mm
Riveted steel 0.00025 ~ 0.0025 0.00635 ~ 0.0635
Concrete 0.000083 ~ 0.00083 0.0021 ~ 0.021
Cast iron 0.000071 0.0018034
Galvanized iron 0.000042 0.0010668
Asphalted cast iron 0.000033 0.0008382
Commercial steel 0.000013 0.0003302
Drawn tubing 0.0000004 0.00001016