1. Liquid Flow in Pipes

2. Basic
Principles

3. Reynolds Number
The Reynolds number is a dimensionless parameter
that relates the ratio of inertia forces to viscous
forces.
'
Re
µ
ρ VD
=

4. Where Re = Reynolds number
ρ = density, lb/ft3
D = pipe ID, ft
V = flow velocity, ft/sec
µ’ = viscosity, lb/ft-sec
'
Re
µ
ρ VD
=

5. Flow Regimes
Flow regimes describe the natural of fluid flow.
There are two basic flow regimes for flow of a single-
phase fluid: laminar flow and turbulent flow.
Laminer flow is characterized by little mixing of the
flowing fluid parabolic profile and Re < 2,000.
Turbulent flow involves complete mixing of the fluid, a
more uniform velocity profile and Re > 4,000.
Reynolds numbers between 2,000 and 4,000 are in a
transition zone, and thus the flow may be either laminar
or turbulent.

6. Darcy’s Equation
gD
fLV
H L
2
2
=
Where L = length of pipe, ft
D = pipe diameter, ft
f = factor of proportionality

7. Table 1. Pipe Roughness
Type of Pipe Roughness Roughness
(New, clean
condition)
(ft) (in).
Unlined Concrete 0.001 - 0.01 0.012 - 0.12
Cast Iron – Uncoated 0.00085 0.01
Galvanized Iron 0.0005 0.006
Carbon Steel 0.00015 0.0018
Fiberglass Epoxy 0.000025 0.0003
Drawn Tubing 0.000005 0.00006

8. Liquid Flow
5
2
16- .).(
)x10(11.5
d
GSQLf
P =∆
where ∆P = pressure drop, psi
f = Moody friction factor, dimensionless
L = length of pipe, ft
Q1
= liquid flow rate, bpd
S.G. = specific gravity of liquid relative to
water
d = pipe ID, in.

9. PRESSURE LOSS DUE FRICTION IN
HORIZONTAL PIPELINES
( Darcy Equation )
Dimana : P = Pressure, psi
L = Length, miles
d = Inside Diameter, in
ρ = Density, lbm/cuft
Q = Flowrate, B/D
(∆P) = 9.7 x 10
f Q L
df
- 4
2
5
ρ

10. PRESSURE LOSS DUE FRICTION IN
HORIZONTAL PIPELINES
( Darcy Equation )
(∆P) = 9.7 x 10
f Q L
df
- 4
2
5
ρ
1 2 3 4 5 6 7
Suatu pipa minyak dengan panjang total sebesar 56 km dengan diameter dalam sebesar 6
inches mengalirkan minyak dari A ke B. Untuk perhitungan, pipa tersebut dibagi dalam 7
segmen. Dari hasil pengukuran dilapangan , distribusi temperatur fluida sepanjang pipa dapat
dilihat spt gambar diatas. Laju alir minyak sebesar 10,000 BBL/D, densitas minyak 62
lbm/cuft, Jika tekanan yang diharapkan tiba di B adalah 60 psia, berapa tekanan pompa di A
(psia) ang diperlukan?
Vis,
cp
5 8 9 80 60 30 10
BA

11. PRESSURE LOSS DUE FRICTION IN
HORIZONTAL PIPELINES
( Darcy Equation )
(∆P) = 9.7 x 10
f Q L
df
- 4
2
5
ρ
1 2 3 4 5 6 7
Suatu pipa minyak dengan panjang total sebesar 56 km dengan diameter dalam sebesar 6
inches mengalirkan minyak dari A ke B. Untuk perhitungan, pipa tersebut dibagi dalam 7
segmen. Dari hasil pengukuran dilapangan , distribusi temperatur fluida sepanjang pipa dapat
dilihat spt gambar diatas. Laju alir minyak sebesar 10,000 BBL/D, densitas minyak 62
lbm/cuft, Jika tekanan yang diharapkan tiba di B adalah 60 psia, berapa tekanan pompa di A
(psia) ang diperlukan?
Vis,
cp
5 7 8 40 20 15 10
BA

12. PRESSURE LOSS DUE FRICTION IN
HORIZONTAL PIPELINES
( Darcy Equation )
(∆P) = 9.7 x 10
f Q L
df
- 4
2
5
ρ
1 2 3 4 5 6 7
Suatu pipa minyak dengan panjang total sebesar 56 km dengan diameter dalam sebesar 6
inches mengalirkan minyak dari A ke B. Untuk perhitungan, pipa tersebut dibagi dalam 7
segmen. Dari hasil pengukuran dilapangan , distribusi temperatur fluida sepanjang pipa dapat
dilihat spt gambar diatas. Laju alir minyak sebesar 10,000 BBL/D, densitas minyak 62
lbm/cuft, Jika tekanan yang diharapkan tiba di B adalah 60 psia, berapa tekanan pompa di A
(psia) ang diperlukan?
Vis,
cp
5 8 9 11 20 40 80
BA

13. In an effort to avoid an iterative calculation, several
empirical formulas have been developed. The most
common of these is the Hazen-Williams formula, which
can be expressed as follows:
L
d
gpm
C
85.1
87.4
85.1
L
100
0.00208H 











=
85.187.4
85.1
1
LH
Cd
LQ
=

14. Where HL = head loss due to friction, ft
L = length, ft
C = 140 for new steel pipe
= 130 for new cast iron pipe
= 100 for riveted pipe
d = pipe ID, in.
gpm = liquid flow rate, gallons/minute
Q1 = liquid flow rate, bpd
85.187.4
85.1
1
LH
Cd
LQ
=
L
d
gpm
C
85.1
87.4
85.1
L
100
0.00208H 











=

15. •The Hazen-Williams equation is frequently used for
calculating pressure losses and line capacities in water
service.
•The discharge coefficient “C” must be carefully
chosen to reflect both fluid viscosity and pipe roughness
in a used condition. It ranges between 80 and 140.
•A “C” factor of 90 to 100 in steel pipe is common for
most produced liquid problems.
•Hazen-Williams factor “C” must not be confused with
the Moody friction factor “f,” as these two factors are
not directly related to each other.

16. fL
2
2
2c
2
2
1
1c
1 Z
g2
)v(
g
Pg
Z
g2
)v(
g
Pg
Z 21
++
ρ
+=+
ρ
+
ENERGY BALANCE EQUATION IN HEAD
UNIT (ELEVATION)
z
( 1 ) ( 2 )
P1 , v1 , Z1 , ρ1
P2 , v2 , Z2 , ρ2
Where P = pressure, Z = height / elevation , v = velocity , ρ = density

17. dg
Lf
Z v
fL
2
2
=
ZfL
= head loss, ft
f = faktor gesekan
L = panjang pipa, ft
v = kecepatan laju alir, ft/detik
d = diameter dalam pipa
g = percepatan gravitasi, ft/detik2
d
Lf
P v
2
2
ρ
=∆ d
Lf v
2
Zg
2
fL
ρ
ρ =
HEAD LOSS DUE TO FRICTION
DARCY EQUATION

18. Untuk aliran dari wellhead (kepala sumur) ke
dasar sumur melalui tubing seperti terlihat
dibawah ini, tekanan fluida pada dasar sumur
dapat ditentukan dengan persamaan :
2
1
12221
2
144
)(
P ρ
ρ
ρρ
fLZ
PZZ
−+
−
=
PWH = P1
PWF = P2
wfL
w ZPwh
144
H
Pwf ρ−+
ρ
=
H
)(
85.187.4
1.85
Lq
015.0
144
HWi Cd
ww H
Pwh
H
Pwf
ρρ
−+=