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40 Part I Liquid Drilling Systems

and

μ
ρ 0:75 1:75 0:25
v
Δp f = ΔL (2.57)
1:25
1,396ðd 2 − d 1 Þ
These two equations are valid in U.S. field units. When expressed
in SI units, the constant 1,800 becomes 631.8 and the constant 1,396
becomes 490.

Bingham Plastic Fluids
For Bingham plastic fluids, the pressure loss under laminar flow inside the
drill string and in the annulus can be estimated using the following equa-
tions respectively:

μ v τ y

p
Δp f = + ΔL (2.58)
1,500d 2 225d
and

" #
μ v τ y
p
Δp f = + ΔL (2.59)
2
200ðd 2 − d 1 Þ
1,000ðd 2 − d 1 Þ
These two equations are valid in U.S. field units. When expressed in SI
units, the constants 1,500, 225, 1,000, and 200 become 31.33, 187.5,
20.88, and 166.7, respectively.
The pressure loss under turbulent flow inside the drill string and in
the annulus can be estimated using the following equations respectively:

ρ 0:75 1:75 0:25
μ
v
Δp f = p ΔL (2.60)
1,800d 1:25
and

μ
ρ 0:75 1:75 0:25
v
Δp f = p ΔL (2.61)
1:25
1,396ðd 2 − d 1 Þ
These two equations are valid in U.S. field units. When expressed in
SI units, the constant 1,800 becomes 6,320, and 1,396 becomes 4,901.