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28 Part I Liquid Drilling Systems

and
v = q (2.16)
0:7854d 2
where
v = average flow velocity, m/s
3
q = flow rate, m /s
For annular flow, the Reynolds number becomes

N Re = 0:816 × ρvðd 2 − d 1 Þ (2.17)
μ

where
d 2 = hole or casing diameter, m
d 1 = outside diameter of pipe, m

and
q
v = (2.18)
2 2
2 1
0:7854ðd − d Þ
The term 0.816(d 2 – d 1 ) in Eq. (2.17) is the equivalent circular diameter of
a slot representation of the annulus (Bourgoyne et al., 1986).
In U.S. field units (where ρ is given in ppg; v in ft/s; q in gpm; d, d 1 ,and
d 2 in inches; and μ in cp), Eqs. (2.15) through (2.18), respectively, become

N Re = 928 × ρvd (2.19)
μ

q
v = (2.20)
2:448d 2

N Re = 757 × ρvðd 2 − d 1 Þ (2.21)
μ

q
v = (2.22)
2 2
2:448ðd 2 − d 1 Þ
As a general guideline, Reynolds numbers of less than 2,100 indicate laminar
flow, while Reynolds numbers greater than 4,000 indicate turbulent flow.
Between these values, flow is considered transitional.