BAKER HUGHES - Drilling Fluids Reference Manual

HYDRAULICS
μ ep
=
effective viscosity inside pipe, cp
K p = power law constant, poise
V p = bulk fluid velocity in pipe, ft/sec
D = inside diameter of the pipe, in.
n p = power law constant for pipe
The equation for effective viscosity in the annulus is:
where:
144V
μ e 100K a
a ------------------ n a – 1
=
a
D 2 – D 1
µ ea = the annular effective viscosity, cp
K a = power law constant, poise
V a = annular fluid velocity, ft/sec
D 2 = hole diameter, in.
D 1 = outside pipe diameter, in.
n a = power law constant for annulus
Reynolds Number
After calculating the effective viscosity, μ e , as a function of fluid velocity and power law constants,
the Reynolds Number is calculated to determine the flow regime of the fluid (i.e., laminar,
transitional, or turbulent flow).
The equation for Reynolds Number inside the pipe is:
where:
928( V p )(
D p )ρ
Re p = -------------------------------------
3n
μ ep
----------------- p + 1 n p
4n p
Re p = Reynolds Number inside the pipe
V p = fluid velocity inside the pipe, ft/sec
D p = inside diameter of the pipe, in.
ρ = fluid density, lb m /gal
μe p
= effective viscosity inside pipe, cp
n p = power law constant for pipe
To obtain the Reynolds Number in the annulus:
928V
Re a ( D 2 – D 1 )ρ
a = ------------------------------------------
2n a + 1
μ e
----------------- n a
a 3n a
where:
Re a = Reynolds Number in the annulus
V a = fluid velocity in the annulus, ft/sec
BAKER HUGHES DRILLING FLUIDS
REFERENCE MANUAL
REVISION 2006 9-12