Menon E.S. Liquid Pipeline Hydraulics
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Appendix B 243
Chapter 11
Problem 11.6.1: Potential surge=903 ft. Wave speed=3913 ft/s.
Problem 11.6.3:
Thin wall: 3967 ft/s 3926 ft/s 3868 ft/s
Thick wall: 3942 ft/s 3903 ft/s 3847 ft/s
Copyright © 2004 by Marcel Dekker, Inc.
244
Appendix C
Summary of Formulas
Chapter 2
API Gravity/Specific Gravity
Specific gravity (Sg)=141.5/(131.5+API) (2.1)
API=141.5/Sg-131.5 (2.2)
Specific Gravity Versus Temperature
S
T
=S
60
-a(T-60) (2.3)
where
S
T
=Specific gravity at temperature T
S
60
=Specific gravity at 60° F
T=Temperature, °F
a=A constant that depends on the liquid
Specific Gravity Blending
(2.4)
Copyright © 2004 by Marcel Dekker, Inc.
Appendix C 245
where
S
b
=Specific gravity of the blended liquid
Q
1
, Q
2
, Q
3
, etc.=Volume of each component
S
1
, S
2
, S
3
, etc.=Specific gravity of each component
Viscosity Conversion
Centistokes=0.226(SSU)-195/(SSU) for 32≤SSU≤100 (2.8)
Centistokes=0.220(SSU)-135/(SSU) for SSU>100 (2.9)
Centistokes=2.24(SSF)-184/(SSF) for 25<SSF=40 (2.10)
Centistokes=2.16(SSF)-60/(SSF) for SSF>40 (2.11)
Viscosity Versus Temperature
Log Log(Z)=A-B Log(T) (2.15)
where
Log=logarithm to base 10
Z depends on the viscosity of the liquid
v=viscosity of liquid, cSt
T=Absolute temperature, °R or K
A and B are constants that depend on the specific liquid. The variable Z is
defined as follows:
Z=(v+0.7+C-D) (2.16)
C=exp[-1.14883-2.65868(v)] (2.17)
D=exp[-0.0038138-12.5645(v)] (2.18)
Viscosity Blending
(2.21)
where
V
b
=Viscosity of blend, SSU
Q
1
, Q
2
, Q
3
, etc.=Volumes of each component
V
1
, V
2
, V
3
, etc.=Viscosity of each component, SSU
H=40.073-46.414 Log
10
Log
10
(V+B) (2.22)
B=0.931(1.72)
v
for 0.2<V<1.5 (2.23)
B=0.6 forV≥1.5 (2.24)
Hm=[H1(pct1)+H2(pct2)+H3(pct3)+…]/100 (2.25)
Copyright © 2004 by Marcel Dekker, Inc.
Appendix C246
where
H, H1, H2, etc.=Blending Index of liquids
Hm=Blending Index of mixture
B=Constant in Blending Index equation
V=Viscosity, cSt
pct1, pct2, etc.=Percentage of liquids 1, 2, etc., in blended mixture
Bulk Modulus
Adiabatic bulk modulus:
Ka=A+B(P)-C(T)
1/2
-D(API)-E(API)
2
+F(T)(API) (2.27)
where
A=1.286×10
6
B=13.55
C=4.122×10
4
D=4.53×10
3
E=10.59
F=3.228
P=Pressure, psig
T=Temperature, °R
API=API gravity of liquid
Isothermal Bulk Modulus:
Ki=A+B(P)-C(T)
1/2
+D(T)
3/2
-E(API)
3/2
(2.28)
where
A=2.619×10
6
B=9.203
C=1.417×10
5
D=73.05
E=341.0
P=Pressure, psig
T=Temperature, °R
API=API gravity of liquid
Bernoulli’s Equation
(2.37)
where
Z
A
, P
A
and V
A
=Elevation, pressure, and liquid velocity at point A
Z
B
, P
B
and V
B
=Elevation, pressure, and liquid velocity at point B
γ=Specific weight of the liquid
Copyright © 2004 by Marcel Dekker, Inc.
Appendix C 247
H
p
=Pump head input at point A
h
L
=Head lost in friction between point A and point B
Chapter 3
Pressure and Head
Head=2.31(psig)/Spgr ft(English units) (3.7)
Head=0.102(kPa)/Spgr m(SI units) (3.8)
where
Spgr=Liquid specific gravity
Velocity of Flow
V=0.0119(bbl/day)/D
2
(3.10)
V=0.4085(gal/min)/D
2
(3.11)
V=0.2859(bbl/hr)/D
2
(3.12)
where
V=Velocity, ft/s
D=Inside diameter, in.
V=353.6777(m
3
/hr)/D
2
(3.13)
where
V=Velocity, m/s
D=Inside diameter, mm
Reynolds Number
R=VDρ/µ (3.14)
R=VD/v (3.15)
where
V=Average velocity, ft/s
D=Pipe internal diameter, ft
ρ=Liquid density, slugs/ft
3
µ=Absolute viscosity, lb-s/ft
2
R=Reynolds number, dimensionless
v=Kinematic viscosity, ft
2
/s
R=92.24 Q/(vD) (3.16)
Copyright © 2004 by Marcel Dekker, Inc.
Appendix C248
where
Q=Flow rate, bbl/day
D=Internal diameter, in.
v=Kinematic viscosity, cSt
R=3160Q/(vD) (3.17)
where
Q=Flow rate, gal/min
D=Internal diameter, in.
v=Kinematic viscosity, cSt
R=353,678 Q/(vD) (3.18)
where
Q=Flow rate, m
3
/h
D=Internal diameter, mm
v=Kinematic viscosity, cSt
Darcy-Weisbach Equation for Head Loss
h=f(L/D)(V
2
/2g) (3.19)
where
h=head loss, ft of liquid
f=Darcy friction factor, dimensionless
L=Pipe length, ft
D=Pipe internal diameter, ft
V=Average liquid velocity, ft/s
g=Acceleration due to gravity, 32.2 ft/s
2
in English units
Darcy Friction Factor
For laminar flow, with Reynolds number R<2000
f=64/R (3.20)
For turbulent flow, with Reynolds number R>4000 (Colebrook-White
equation)
(3.21)
where
f=Darcy friction factor, dimensionless
D=Pipe internal diameter, in.
e=Absolute pipe roughness, in.
Copyright © 2004 by Marcel Dekker, Inc.
Appendix C 249
R=Reynolds number of flow, dimensionless
f
f
=f
d
/4 (3.25)
where
f
f
=Fanning friction factor
f
d
=Darcy friction factor
Pressure Drop due to Friction
P
m
=0.0605fQ
2
(Sg/D
5
) (3.27)
P
m
=0.2421(Q/F)
2
(Sg/D
5
) (3.28)
where
P
m
=Pressure drop due to friction, psi per mile
Q=Liquid flow rate, bbl/day
f=Darcy friction factor, dimensionless
F=Transmission factor, dimensionless
Sg=Liquid specific gravity
D=Pipe internal diameter, in.
(3.29)
where
F=Transmission factor
f=Darcy friction factor
F=-4Log
10
[(e/3.7D)+1.255(F/R)] 3.30
for turbulent flow R>4000
In SI units
P
km
=6.2475×10
10
fQ
2
(Sg/D
5
) (3.31)
P
km
=24.99×10
10
(Q/F)
2
(Sg/D
5
) (3.32)
where
P
km
=Pressure drop due to friction, kPa/km
Q=Liquid flow rate, m
3
/hr
f=Darcy friction factor, dimensionless
F=Transmission factor, dimensionless
Sg=Liquid specific gravity
D=Pipe internal diameter, mm
Copyright © 2004 by Marcel Dekker, Inc.
Appendix C250
Colebrook-White Equation
Modified Colebrook-White Equation:
F=-4Log
10
[(e/3.7D)+1.4125(F/R)] (3.34)
Hazen-Williams Equation
h=4.73L(Q/C)
1.852
/D
4.87
(3.35)
where
h=Head loss due to friction, ft
L=Length of pipe, ft
D=Internal diameter of pipe, ft
Q=Flow rate, ft
3
/s
C=Hazen-Williams coefficient or C-factor, dimensionless
Q=0.1482(C)(D)
2.63
(P
m
/Sg)
0.54
(3.36)
where
Q=Flow rate, bbl/day
D=Pipe internal diameter, in.
P
m
=Frictional pressure drop, psi/mile
Sg=Liquid specific gravity
C=Hazen-Williams C-factor
GPM=6.7547×10
-3
(C)(D)
2.63
(H
L
)
0.54
(3.37)
where
GPM=Flow rate, gal/min
H
L
=Friction loss, ft per 1000 ft of pipe
In SI units
Q=9.0379×10
-8
(C)(D)
2.63
(P
km
/Sg)
0.54
(3.38)
where
Q=Flow rate, m
3
/hr
D=Pipe internal diameter, mm
P
km
=Frictional pressure drop, kPa/km
Sg=Liquid specific gravity
C=Hazen-Williams C-factor
Shell-MIT Equation
R=92.24(Q)/(Dv) (3.39)
Rm=R/(7742) (3.40)
Copyright © 2004 by Marcel Dekker, Inc.
Appendix C 251
where
R=Reynolds number, dimensionless
Rm=Modified Reynolds number, dimensionless
Q=Flow rate, bbl/day
D=Internal diameter, in.
v=Kinematic viscosity, cSt
f=0.00207/Rm (laminar flow) (3.41)
f=0.0018+0.00662(1/Rm)
0.355
(turbulent flow) (3.42)
P
m
=0.241(fSgQ
2
)/D
5
(3.43)
where
P
m
=Frictional pressure drop, psi/mile
f=Friction factor, dimensionless
Sg=Liquid specific gravity
Q=Flow rate, bbl/day
D=Pipe internal diameter, in.
In SI units
P
m
=6.2191×10
10
(f SgQ
2
)/D
5
(3.44)
where
P
m
=Frictional pressure drop, kPa/km
f=Friction factor, dimensionless
Sg=Liquid specific gravity
Q=Flow rate, m
3
/hr
D=Pipe internal diameter, mm
Miller Equation
Q=4.06(M) (D
5
P
m
/Sg)
0.5
(3.45)
where
M=Log
10
(D
3
SgP
m
/cp
2
)+4.35 (3.46)
and
Q=Flow rate, bbl/day
D=Pipe internal diameter, in.
P
m
=Frictional pressure drop, psi/mile
Sg=Liquid specific gravity
cp=Liquid viscosity, centipoise
Copyright © 2004 by Marcel Dekker, Inc.
Appendix C252
In SI Units
Q=3.996×10
-6
(M)(D
5
P
m
/Sg)
0.5
(3.47)
where
M=Log
10
(D
3
SgP
m
/cp
2
)-0.4965 (3.48)
and
Q=Flow rate, m
3
/hr
D=Pipe internal diameter, mm
P
m
=Frictional pressure drop, kPa/km
Sg=Liquid specific gravity
cp=Liquid viscosity, centipoise
P
m
=(Q/4.06M)
2
(Sg/D
5
) (3.49)
T.R.Aude Equation
P
m
=[Q(z
0.104
)(Sg
0.448
)/(0.871(K)(D
2.656
))]
1.812
(3.50)
where
P
m
=Pressure drop due to friction, psi/mile
Q=Flow rate, bbl/hr
D=Pipe internal diameter, in.
Sg=Liquid specific gravity
z=Liquid viscosity, centipoise
K=T.R.Aude K-factor, usually 0.90 to 0.95
In SI Units
P
m
=8.888×10
8
[Q(z
0.104
)(Sg
0.448
)/(K(D
2.656
))]
1.812
(3.51)
where
P
m
=Frictional pressure drop, kPa/km
Sg=Liquid specific gravity
Q=Flow rate, m
3
/hr
D=Pipe internal diameter, mm
z=Liquid viscosity, centipoise
K=T.R.Aude K-factor, usually 0.90 to 0.95
Head Loss in Valves and Fittings
h=KV
2
/2g (3.52)
where
h=Head loss due to valve or fitting, ft
Copyright © 2004 by Marcel Dekker, Inc.