STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

Drilling Mud Hydraulics
83 1
where de = equivalent diameter of a flow channel in in.
v = average flow velocity in ft/s
7 = drilling fluid specific weight in lb/gal
p = drilling fluid dynamic viscosity in cp
The equivalent diameter of the flow channel is defined as
de =
4 (flow cross-sectional area)
wetted perimeter
(4-91)
The flow changes from laminar to turbulent in the range of Reynolds numbers
from 2,100 to 4,000 [60]. In laminar flow, the friction pressure losses are
proportional to the average flow velocity. In turbulent flow, the losses are proportional
to the velocity to a power ranging from 1.7 to 2.0.
The average flow velocity is given by the following equations:
Flow in circular pipe
(4-92)
Flow in an annular space between two circular pipes
v=
q
2.45(d: -di)
(4-93)
where q = mud flow rate in gpm
d = inside diameter of the pipe in in.
d, = larger diameter of the annulus in in.
d, = smaller diameter of the annulus in in.
For non-Newtonian drilling fluids, the concept of an effective viscosity' can
be used to replace the dynamic viscosity in Equation 4-89.
For a Bingham plastic fluid flow in a circular pipe and annular space, the
effective viscosities are given as [61].
Pipe flow
zd
pe = pp + 6.651
V
(4-94)
Annular flow
(4-95)
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'Also called equivalent or apparent viscosity in some published works.