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Mud Hydraulics Fundamentals 39

For smooth pipe, Colebrook’s (1938) friction factor function can be
simplified to
f = 0:0791 (2.52)
N 0:25
Re
which was first presented by Blasius (1913).
Chen’s (1979) correlation has an explicit form and gives similar accuracy
to the Colebrook-White equation (Gregory and Fogarasi, 1985) that was
employed for generating the friction factor chart widely used in the petro-
leum industry. Chen’s correlation takes the following form:
−2
( " #) !
0:8981

ε 5:0452 ε 1:1098 7:149

f = −4log − log + (2.53)
3:7065 N Re 2:8257 N Re
δ
where the relative roughness is defined as ε = .
d
Newtonian Fluids
If the friction factor in Eq. (2.48) is replaced by f = 16 , the pressure loss
N Re
under laminar flow inside the drill string and in the annulus can be esti-
mated using the following equations respectively:
Δp f = μv ΔL (2.54)
1,500d 2

Δp f = μv ΔL (2.55)
2
1,000ðd 2 − d 1 Þ
where

Δp f = pressure loss, psi or kPa
ΔL = length of conduit, ft or m

These two equations are valid in U.S. field units. When expressed in SI
units, the constant 1,500 becomes 0.0313 and 1,000 becomes 0.0209.
Using the Chen friction factor correlation allows for accurate predic-
tion of frictional pressure loss in turbulent flow. However, in many cases,
using the Blasius correlation gives a result that is accurate enough for
frictional pressure calculations. Substituting Eq. (2.52) into Eq. (2.48) and
rearranging the latter yield the pressure loss expressions for inside the drill
string and in the annulus as follows respectively:

ρ 0:75 1:75 0:25
μ
v
Δp f = ΔL (2.56)
1,800d 1:25