-
ffm50___.pdfffm100__.pdfffm200__.pdfffm300__.pdfffm400__.pdfffm500__.pdfffm600__.pdfffm800__.pdfffm900__.pdfffm1000_.pdfffm1100_.pdfffmappa_.pdfffmappb_.pdfffmappc_.pdfffmappd_.pdfffmappe_.pdfffmappf_.pdfffmappg_.pdfffmapph_.pdfffmappi_.pdf
-
50 Using This Manual
AbstractThis section summarizes the contents and explains the
organization of the Fluid Flow Manual. This manual is in one volume
that includes engineering guidelines with accompanying appendices.
The manual has a table of contents and a complete index to aid you
in finding specific subjects.Chevron Corporation 50-1 March
1997
-
50 Using This Manual Fluid Flow ManualScope and ApplicationThe
Fluid Flow Manual provides basic fluid flow theory, calculational
methods, and physical data for use in piping design. It is directed
both to entry-level personnel and nonspecialists regardless of
experience. This manual should not be used as a substitute for
sound engineering judgment.The intent is to provide practical,
useful information based on Company experi-ence. Therefore, forms
have been included in the front of the manual for your convenience
in suggesting changes. Your input and experience are important for
improving subsequent printings and keeping this manual up to
date.
OrganizationThis manual comprises Engineering Guidelines and
appendices that address such concerns as: (1) designing piping to
efficiently carry fluids, (2) determining open channel flow, (3)
calculating surge pressures, (4) handling special pipeline
prob-lems, (5) fluid and pipe properties, (6) available computer
programs.
TabsThe colored tabs in the manual will help you find
information quickly.
White tabs are for table of contents, introduction, appendices,
PC disks, index, and general purpose topics
Blue tabs denote Engineering Guidelines
Red tab marks a place for you to keep documents that are
developed at your facilityMarch 1997 50-2 Chevron Corporation
-
Fluid Flow Manual 50 Using This ManualOther Company ManualsThe
text sometimes refers to documents in other Company manuals. These
docu-ments carry the prefix of that manual. The prefixes are
defined here:
Prefix Company ManualCIV Civil and StructuralCMP CompressorCOM
CoatingsCPM Corrosion PreventionDRI DriverELC ElectricalEXH Heat
Exchanger and Cooling
TowerFFM Fluid FlowFPM Fire ProtectionHTR Fired Heater and Waste
Heat
RecoveryICM Instrumentation and ControlIRM Insulation and
RefractoryMAC General MachineryNCM Noise Control in DesignsPIM
PipingPMP PumpPPL PipelinePVM Pressure VesselTAM TankUTL
UtilitiesWEM WeldingChevron Corporation 50-3 March 1997
-
50 Using This Manual Fluid Flow ManualFig. 50-1 Fluid Flow
Manual Quick-Reference Guide
Task Fluid Flow Manual Sections
Learning Background Information
Pressure drop calculations 100, 200, 300, 400, 500
Pipeline friction heating 900
Surge 800
Open channel flow 700
Computer programs 1100, Appendices D, E, F, G, H, I
Selecting the Best Computer Program
Selection guide 1100
Detailed operation Appendices D, E, F, G, H, I
Calculating Flow Rates
By PCFLOW program 1100, Appendix D
With flow charts 400
With sophisticated programs 1100, Appendices D, E, F, G, H,
I
Finding Engineering Data
Pipe dimensions Appendix C
Fluid properties 1000
Heat transfer properties 900March 1997 50-4 Chevron
Corporation
-
100 Introduction
AbstractThis section describes the scope of the Fluid Flow
Manual and discusses its basic approach to fluid flow problems.
Contents Page
110 Scope of the Fluid Flow Manual 100-2120 Basic Elements of
Pressure Drop 100-2130 Importance of the Darcy-Weisbach Equation
100-2140 Nomenclature 100-3150 References 100-3Chevron Corporation
100-1 January 1990
-
100 Introduction Fluid Flow Manual110 Scope of the Fluid Flow
ManualThe Fluid Flow Manual presents the equations that model basic
fluid flow phenomena. Most of the equations and discussions are
oriented toward solving for pressure drop given well defined
fluids, flow rates, and geometry in simple hydraulic systems. In
general the manual treats isothermal flow. The exception to this is
that some of the computer programs referenced in Section 1100
perform heat transfer calculations and appropriately adjust fluid
properties and pressure drop along the flow path.
120 Basic Elements of Pressure DropThe total pressure drop in a
fluid flow system can be accurately defined if all of the following
components of that pressure drop are found:
Pressure change due to elevation change Pressure drop due to
acceleration losses Pressure drop due to frictional losses
The relationship between the three components of pressure drop
may be expressed as follows:
Psystem = Pelevation + Pacceleration + Pfriction(Eq. 100-1)
These components of total system pressure drop are treated in
Sections 200, 300, and 400, respectively, for simple cases. Special
considerations are treated in the remaining sections. For example,
Section 500 presents a method for approximating the combination of
both acceleration and friction losses that occurs in valves,
fittings, and pipe entrances.
130 Importance of the Darcy-Weisbach EquationThe dominant effect
in most fluid flow systems is friction pressure drop. The
Darcy-Weisbach equation solves for friction pressure drop for any
fluid, in any pipe, over any length for which the fluid properties
remain relatively constant. This equation is presented here because
of its importance. It is discussed more fully in Section 410:
(Eq. 100-2)where:
h = head loss, ft
f = friction factor
L = pipe length, ft
h fLD------V2
2g-------=January 1990 100-2 Chevron Corporation
-
Fluid Flow Manual 100 IntroductionD = pipe internal diameter,
ft
V = fluid velocity, ft/sec
g = gravitational constant (32.17 ft/sec2)The Darcy-Weisbach
equation defines the friction factor, f. Whenever possible the
reader is encouraged to use this equation instead of the flow
charts in Section 400. This equation is automated in the
Incompressible Flow section of the PCFLOW program, which is
provided on disk at the end of this manual.
140 NomenclatureThis manual does not contain a master list of
nomenclature. Equation variables are defined following each
equation.
150 ReferencesThe following selection of general references is
supplemented by specific refer-ences in the applicable sections of
the manual.
1. Fox, R. W., A. T. McDonald. Introduction to Fluid Mechanics.
John Wiley & Sons, New York: 1978.
2. Perry, R. H., C. H. Chilton. Chemical Engineers Handbook,
Section 5. McGraw-Hill, New York: 1973.
3. Streeter, V. L., E. B. Wylie. Fluid Mechanics. McGraw-Hill,
New York.
4. Engineering Data Book, Section 17. Gas Processors
Association, Tulsa: 1987.
5. Cameron Hydraulic Data. Ingersoll-Rand, Woodcliff Lake, N.J.:
1979.Chevron Corporation 100-3 January 1990
-
200 Static Pressure
AbstractThis section discusses the equations for calculating
static pressure and head.
Contents Page
210 Definition of Static Pressure 200-2220 Equations for Static
Pressure and Head 200-2Chevron Corporation 200-1 January 1990
-
200 Static Pressure Fluid Flow Manual210 Definition of Static
PressureThe pressure generated by the height of a column of liquid
(see Figure 200-1) is expressed as static pressure, or,
alternatively, static head or elevation head. Pres-sures other than
static pressure are often expressed in terms of the column of
liquid required to generate an equivalent static pressure, such as
feet of water or inches of mercury. Similarly head (H), expressed
in feet, often describes pressures that are not static. Units of
static pressure and head can be converted to one another using the
following equations.
220 Equations for Static Pressure and HeadEquation 200-1
expresses the static pressure in psi generated by a column of
liquid:
(Eq. 200-1)
where:Ps = static pressure, psi
h = height of liquid column, ft
= fluid density, lbm/cu ft
Fig. 200-1 Static Pressure
Psh144---------=January 1990 200-2 Chevron Corporation
-
Fluid Flow Manual 200 Static PressureEquation 200-2 expresses
head, in feet, equivalent to an arbitrary pressure, in psi:
(Eq. 200-2)
where:H = head, ft
P = pressure, psi
= fluid density, lbm/cu ft
The conversion of head in feet to pressure in pounds per square
inch for water at 60F is as follows:
Ps = 0.433 h
h = 2.31 Ps
H P144---------=Chevron Corporation 200-3 January 1990
-
300 Acceleration Pressure Drop
AbstractThis section presents the equations for calculating
pressure drop due to fluid accel-eration and discusses the
phenomenon in terms of changes in pipe geometry and change of
phase.
Contents Page
310 Definition of Acceleration Pressure Drop 300-2320 Equations
for Acceleration Pressure Drop 300-2330 Discussion 300-2Chevron
Corporation 300-1 October 1992
-
300 Acceleration Pressure Drop Fluid Flow Manual310 Definition
of Acceleration Pressure DropAn increase in velocity (i.e.,
acceleration) of a fluid is accompanied by a decrease in its static
pressure. This decrease is called acceleration pressure drop. It
occurs at pipe entrances and reducers, and where a phase change
from liquid to gas occurs, to give two common examples.
Acceleration pressure drop is usually expressed in pounds per
square inch (psi) or in units of velocity head (in feet). One
velocity head is the acceleration head loss of a fluid accelerated
from rest in a reservoir to a specific velocity in a pipe.
320 Equations for Acceleration Pressure DropVelocity head is
calculated using the following equation:
(Eq. 300-1)where:
h = velocity head in feet of liquid, ft
V = fluid velocity, ft/sec
g = gravitational constant (32.17 ft/sec2)Acceleration pressure
drop across an entrance or reducer, expressed in terms of static
pressure drop (in psi), is:
(Eq. 300-2)where:
P = static pressure drop, psi
= fluid density, lbm/cu ft
V1 = upstream fluid velocity, ft/sec
V2 = downstream fluid velocity, ft/sec
Determination of acceleration pressure drop is particularly
important when calcu-lating the NPSHA of reciprocating pumps, to
avoid cavitation. See Section 100 of the Pump Manual.
330 DiscussionEquations 300-1 and 300-2 describe acceleration
loss at pipe entrances and reducers. Frictional losses (see Section
500) must be added to get the total loss for
h V2
2g-------=
P V2
2 V12
( )2g 144---------------------------------=October 1992 300-2
Chevron Corporation
-
Fluid Flow Manual 300 Acceleration Pressure Dropthis geometry.
The fitting loss coefficients given in Section 500 for other types
of valves and fittings (besides pipe entrances and reducers) take
into account both acceleration and friction effects.
During changes of phase (evaporation, flashing, and boiling),
the velocity of a fluid must increase as the gas phase increases
its mass flow rate. The pressure required to produce that
acceleration is accurately described by Equations 300-1 and 300-2.
The total pressure drop is the sum of the acceleration pressure
drop and the flowing friction pressure drop. This friction loss can
be difficult to calculate because the flow rates of the two phases
are changing and, therefore, the friction pressure drop is changing
as the fluid moves downstream.
The static pressure that is converted to kinetic energy through
the acceleration of a flowing fluid is theoretically recoverable as
static pressure when the flow deceler-ates. However, since even
carefully designed diffusers can recover only a fraction of the
original static pressure, this recovery is not attempted in normal
piping situa-tions. In standard piping systems the kinetic energy
of a flowing fluid is dissipated as turbulence at pipe exits and
enlargements. Confusion on this point can arise because some
authors attribute acceleration pressure loss not to the pipe
entrance or reducer, but to the pipe exit or enlargement, where the
potentially recoverable energy is finally lost. This gives some
readers the false impression that there is a static pressure drop
across pipe exits and enlargements. Static pressure dropproduced by
acceleration and friction effectsoccurs across pipe entrances and
reducers, not their exits and enlargements.Chevron Corporation
300-3 October 1992
-
400 Friction Pressure Drop
AbstractThis section presents equations for calculating the
relationship between flow rate and pressure drop for incompressible
flow, two-phase flow, compressible flow, and gas flow at high
pressure drop (choked flow).
Contents Page
410 Incompressible Flow 400-2411 Fitting Loss Coefficients
412 Pipe and Tube Friction Losses
420 Two-phase Flow 400-7421 Pressure Drop Calculations
422 Friction Pressure Drop Correlations
423 Fitting and Bend Losses
424 Acceleration Pressure Loss
425 Elevation Losses426 Accuracy of Friction Pressure Drop
Calculation427 Liquid Holdup Correlation
430 Compressible Flow 400-17440 Gas Flow At High Pressure Drop
(Choked Flow) 400-19441 Assumptions
442 Use of Design Charts
443 Sonic Flow
444 Choked Flow
445 Temperature Variations446 Effects of Valves and
FittingsChevron Corporation 400-1 March 2001
447 Deviation from Assumptions
450 References 400-24
-
400 Friction Pressure Drop Fluid Flow Manual410 Incompressible
FlowThe Darcy-Weisbach Equation (Equation 400-1) expresses the
relationship between flow rate and friction pressure drop for
incompressible flow in pipes and tubes. It is accurate for both
liquids and gases, and for any length of pipe over which fluid
properties are relatively constant.
(Eq. 400-1)where:
h = head loss, ft
f = Darcy friction factor
L = pipe length, ft
D = pipe inside diameter, ft
V = fluid velocity, ft/sec
g = gravitational constant (32.17 ft/sec2)The Darcy-Weisbach
Equation can be rewritten in terms of pressure drop in psi, flow
rate in pounds per hour, and a constant that combines all the unit
conversions, as in Equation 400-2.
(Eq. 400-2)where:
P = pressure drop, psi
W = mass flow rate, lbm/hr
= fluid density, lbm/ft3
411 Fitting Loss CoefficientsFitting loss coefficients (see
Section 500) are dimensionally equivalent to the term fL/D and can
be added to pipe friction losses using Equation 400-3. Fitting loss
coefficients include both friction and acceleration effects.
(Eq. 400-3)
h fLD------
V2
2g-------=
P fLD------
W2
D4 7.4 1010( )---------------------------------------=
P K fLD------+ W
2
D4 7.4 1010( )---------------------------------------=March 2001
400-2 Chevron Corporation
-
Fluid Flow Manual 400 Friction Pressure Dropwhere:K = fitting
loss coefficient (from Section 500)
412 Pipe and Tube Friction LossesFor pipe and tube flow, the
friction factor is a function of the Reynolds number and the flow
regime. In the turbulent flow regime it is also a function of pipe
roughness. Reynolds number can be written using units consistent
with Equation 400-3, as follows:
(Eq. 400-4)where:
Re = Reynolds number
= absolute viscosity, cp
There are no sharp divisions between the laminar, transition,
and turbulent flow regimes. For design purposes, the recommended
boundary between laminar and transition flow is Re = 1600. The
recommended boundary between transition and turbulent flow is Re =
3400. These values provide relatively smooth transitions between
regimes for calculated friction factors, and produce conservative
results (tend to overpredict pressure drop) around the
laminar-to-transition flow boundary. The friction factor for
laminar flow (Re < 1600) can be derived analytically (without
experimental components) to give:
f = 64/Re(Eq. 400-5)
The friction factor for transition flow (1600 < Re < 3400)
cannot be predicted accu-rately. The following conservative value
(overprediction) is recommended for most cases:
f = 0.04(Eq. 400-6)
The Moody Diagram (Figure 400-1) presents experimentally derived
friction factors for turbulent flow (Re 3400). In turbulent flow
the friction factor is a func-tion of pipe roughness as well as the
Reynolds number. At high Reynolds numbers the friction factor is a
function of only relative roughness (absolute roughness/diam-eter).
Figure 400-2 gives the relative roughness for various diameters and
types of pipe.
Re 0.526WD-------------------=Chevron Corporation 400-3 March
2001
-
400 Friction Pressure Drop Fluid Flow ManualFig. 400-1 Moody
Diagram Crane Technical Paper 410-C, 1984, Flow of Fluids. Courtesy
of Crane ValvesMarch 2001 400-4 Chevron Corporation
-
Fluid Flow Manual 400 Friction Pressure DropFig. 400-2 Relative
Pipe Roughness (/D) and Friction Factors (f) for Complete
Turbulence Crane Technical Paper 410-C, 1984, Flow of Fluids.
Courtesy of Crane ValvesChevron Corporation 400-5 March 2001
-
400 Friction Pressure Drop Fluid Flow ManualMany equations have
been proposed to approximate the Moody Diagram friction factors.
One of these is the Chen Equation (Equation 400-7), which is
simple, accu-rate, and stable when used on small computers:
(Eq. 400-7)where:
= absolute pipe roughness, ft
D = pipe diameter, ft
= relative roughness
Typical values of roughness, , are as follows:
f 24 log10
(A1-A2)-------------------------------------------
2=
A1
D----
3.7065----------------=
A2 5.0452Re---------------- log10 A3( )=
A3
D----
1.1098
2.8257-----------------------
7.149Re
------------- 0.8981
+=
D----
Pipe Absolute Roughness,
Plastic 0.000005 ftSmooth Steel, New 0.00015 ftGalvanized Steel
0.00042 ft
Cast Iron, Asphalted 0.00042 ft
Transite 0.00042 ft
Cast Iron, Uncoated, New 0.00083 ft
Steel, Concrete Lined 0.00083 ft
Concrete 0.0083 ft
Riveted Steel 0.025 ftMarch 2001 400-6 Chevron Corporation
-
Fluid Flow Manual 400 Friction Pressure DropWhere accurate
performance data are required, pressure losses should be
deter-mined by test. If test measurements are not possible, the
friction factor can be found with the Moody Diagram or calculated
with the Chen Equation (Equation 400-7).
420 Two-phase FlowThis section presents a method for calculating
gas-liquid two-phase flow pressure drop. Lines carrying flashing
mixtures, solid-liquid mixtures, or gas-solid mixtures must be
analyzed more thoroughly than this method allows. The special cases
of (1) mixture flow in column and furnace transfer lines, and (2)
flashing water are covered in the Fired Heater and Waste Heat
Recovery Manual and Utilities Manual, respectively.
LimitationsThe method described here applies to isothermal
gas-liquid flow, not to situations in which a phase change occurs;
that is, constant gas-liquid ratios (by weight) are assumed.
This method has not been verified for very long vertical piping
(such as in oil wells) nor has the accuracy been established for
horizontal piping more than 5-1/2 inches in diameter. In these
cases the method should be used with caution, for vertical piping,
PIPEPHASE will yield better results. In addition, the limited
experimental data available indicate that when the mixture velocity
is less than 3 ft/sec the accu-racy of the friction pressure drop
calculations is very poor.
This method is not fully applicable to flow of water-oil-gas
(WOG) mixtures (so-called three-phase flow). This case requires the
more powerful calculation methods of PIPEPHASE.
General ReferencesReference 1 (see Section 450) contains a more
detailed discussion of two-phase flow. Reference 2 contains an
extensive bibliography of two-phase literature.
421 Pressure Drop CalculationsAs in single-phase flow, pressure
drop in two-phase flow consists of several compo-nents, as shown in
Equation 400-8.
Ptotal = Pfriction + Pfittings + Pacceleration + Pelevation(Eq.
400-8)
The components of this equation, Pfriction, Pfittings,
Pacceleration, and Pelevation are discussed in the following
sections. The total pressure drop is calculated by evaluating each
component individually and summing.Chevron Corporation 400-7 March
2001
-
400 Friction Pressure Drop Fluid Flow Manual422 Friction
Pressure Drop CorrelationsMore than 25 correlations for two-phase
friction pressure drop have appeared in print. Because these
correlations contain empirical factors obtained from limited
experimental data, they cannot be applied with confidence beyond
their particular experimental bases.
The five most widely used correlations are compared in Reference
3 using experi-mental data from a number of investigators. The data
were carefully screened to eliminate unreliable measurements. The
screened data, about 2600 points in all, cover pipe diameters from
1 to 5-1/2 inches and liquid viscosities from 1 to 20 centipoise.
Of the five the most reliable correlation over this range of
experimental conditions was the Lockhart-Martinelli correlation
(see Reference 4).Another somewhat better correlation with the
screened experimental data was achieved using similarity analysis
(see Reference 5). This method is based on calcu-lating a two-phase
density, tp, and viscosity, tp, evaluated at the pipe entrance
pressure and temperature and assumed constant for the friction and
fitting pressure drop calculation, as follows:
tp = l () + g (1.0 - )(Eq. 400-9)
tp = l () + g (1.0 - )(Eq. 400-10)
where: = fluid density, lbm/ft3
= absolute viscosity, cp
tp = two-phase
l = liquid phase
g = gas phase
= liquid volume fraction at pipe entrance
Equations 400-9 and 400-10 assume that both phases flow at the
same velocity.
The two-phase Reynolds number Retp is expressed as follows:
(Eq. 400-11)where:
Vm = velocity of mixture, ft/sec
D = pipe inside diameter, ft
RetpVmDtp
tp1490------------
---------------------
0.527WtDtp
---------------------= =March 2001 400-8 Chevron Corporation
-
Fluid Flow Manual 400 Friction Pressure DropWt = mass flow rate
of total fluid, lbm/hr
For new steel pipe, two-phase Reynolds numbers should be used
with the Moody diagram (Figure 400-1) to determine the friction
factor f. If different pipe condi-tions exist or a more accurate
determination is desired, the Colebrook formula (Equation 400-12)
may be used.
(Eq. 400-12)where:
= absolute pipe wall roughness, ft
The need to proceed by trial and error is an inconvenience when
using this equation for hand calculation, but a computer or Moody
chart eliminates this problem. The equation reduces to the smooth
tube equation when the wall roughness (left term in bracket)
approaches zero or to Nikuradses Formula at high Reynolds numbers
(when the right term in bracket approaches zero). The same absolute
wall rough-ness, , should be used for both single-phase and
two-phase flow calculations. The pressure drop due to friction may
then be calculated as follows:
(Eq. 400-13)where:
P = pressure drop, psi
f = friction factor
L = pipe length, ft
go = gravitational constant (32.174 lbm ft/lbf sec2)Wl = flow
rate of liquid, lbm/hr
Wg = flow rate of gas, lbm/hr
Wt = Wl + WgThis method of calculating friction pressure drop
has the following characteristics:
It reduces to the single-phase flow equations if the flow rate
of either phase is zero.
1f
------ 2 log10
3.7D------------
2.51Retp f-----------------+
=
Pfriction fLD----
tp144---------
Vm2
2go-----------=
1.35 10 11 f LD5-------
Wt2
tp---------=Chevron Corporation 400-9 March 2001
-
400 Friction Pressure Drop Fluid Flow Manual Except for the
assumptions concerning two-phase density and viscosity (Equa-tions
400-9 and 400-10), no empirical factors from two-phase flow data
have been used.
It is reasonably accurate for all flow patterns (see Section
426).
423 Fitting and Bend LossesFor two-phase flow, as for
single-phase flow, pressure drop due to bends and fittings can be
expressed in terms of velocity head loss. However, for two-phase
flow, the velocity head is based on the pipe inlet mixture density,
rtp, from Equation 400-9, as follows:
(Eq. 400-14)where:
K = single phase velocity head loss
424 Acceleration Pressure LossAcceleration losses also
contribute to the total pressure drop. In most cases this loss is
relatively small, and may be neglected if only a rough estimate is
required. However, when the total pressure drop along the line is
large, the acceleration losses can be significant and should be
calculated. In this case, the gas expands and the mixture occupies
a larger volume at a lower pressure. This causes the mixture to be
accelerated to a higher velocity in order to maintain the same mass
flow. The expression for acceleration pressure drop, as given in
Reference 5, is as follows:
(Eq. 400-15)where:
Z = compressibility factor
T = temperature, R
R = gas constant
P1 = upstream pressure, psi
P2 = downstream pressure, psi
D = pipe inside diameter, ft
PfittingsKtp144
------------
Vm2
2go----------- 1.35 10 11
KW t2
D4tp--------------- = =
Pacceleration1.87 10 13 WtWgZRT
D4P1P2---------------------------------------------------------
Ptp=March 2001 400-10 Chevron Corporation
-
Fluid Flow Manual 400 Friction Pressure Drop425 Elevation
LossesThe calculation of two-phase density using Equation 400-9 is
an approximation that assumes the velocities of the liquid and gas
phases are equal. However, the actual density of the gas-liquid
mixture is needed to calculate the elevation pressure drop for
upwards flow. One cannot assume that the velocities of the two
phases are equal.
The actual flow density depends on how the liquid and gas are
distributed in the pipe. The flow density in a short section of
pipe of length L is given by Equation 400-16:
(Eq. 400-16)where:
= actual density in pipe section
Ag = area gas
Al = area liquid
Rg = gas volume fraction
Rl = liquid holdup
Rg is the fractional volume of the pipe filled with gas and Rl
is the fractional volume of the pipe filled with liquid. Rl is
called liquid holdup (see Equation 400-22). Because of the
difference in velocity of the two phases, liquid holdup is greater
downstream than at the entrance. Therefore, to calculate the actual
flow density, the liquid holdup Rl has to be known along the pipe.
The available correlations for liquid holdup were checked against
experimental data from Reference 3. The corre-lation developed by
Hughmark (see Reference 7, and below in this section, Liquid Holdup
Correlation) was the best.The effects of bends and fittings on
liquid holdup and, therefore, the flow density cannot be predicted
at this time. Therefore, it is assumed that the same holdup
corre-lation can be used even if the pipe contains bends and
fittings.
In two-phase flow, as in single-phase flow, the elevation head
loss is expressed as follows:
(Eq. 400-17)where:
h = static elevation, ft
tpLAgg LA11+
LA----------------------------------------- Rgg R11+= =
Pelevationtp144--------- h=Chevron Corporation 400-11 March
2001
-
400 Friction Pressure Drop Fluid Flow ManualThe flow density is
calculated using Equation 400-16, where the gas density is
eval-uated at the average pressure. The elevation pressure drop
term is included only in vertical upward flow.
A conservative evaluation of acceleration pressure loss for
vertical downward flow cannot take credit for the elevation
pressure component in the downward section. Therefore, sections
where the flow is downward should be treated as horizontal piping.
No provisions have been made to handle inclined piping.
426 Accuracy of Friction Pressure Drop CalculationThe friction
pressure drop calculation was checked against carefully screened
exper-imental data from a number of investigators. Partial results
of the comparison are shown in Figure 400-5. A more extensive
discussion of the calculations and a statis-tical analysis of the
errors are available in References 3 and 5.
The values shown in Figure 400-5 represent the percent deviation
between the calculated pressure drop and experimental data, as
shown in Equation 400-18.
(Eq. 400-18)Figure 400-6 can be used to estimate the accuracy of
a calculated friction pressure drop for any flow regime. For
example, the calculated friction pressure drop for horizontal slug
flow is within -18.0 to +12.0 percent of the actual value. Equation
400-18 may be restated as follows:
(Eq. 400-19)Based on the range of deviation for horizontal slug
flow, the actual value of a calcu-lated pressure drop of 10 psi
would be (approximately) between the following values:
(Eq. 400-20)and
(Eq. 400-21)
%devPcalc Pexp
Pexp------------------------------------- 100=
PexpPcalc
1 % dev100---------------+
------------------------=
P 101 0.18( )+--------------------------- 12.2 psi= =
P 101 0.12+------------------- 8.9 psi= =March 2001 400-12
Chevron Corporation
-
Fluid Flow M
anual400 Friction Pressure Drop
Chevron Corporation400-13
March 2001
F of the Oil and Gas Journalig. 400-3 Flow Pattern Map for
Horizontal Two-Phase Flow O. Baker: Multiphase Flow in Pipelines
Nov. 1958. Courtesy
-
400 Friction Pressure DropFluid Flow
Manual
March 2001
400-14Chevron Corporation
Fig. 400-4 Flow Pattern Map for Vertical Two-Phase Flow From Two
Phase Slug Flow by Griffith & Wallis. Journal of Heat Transfer,
Transactions of ASME
Series C83 (Aug., 1961). Courtesy of ASME
-
Fluid Flow Manual 400 Friction Pressure DropA comparison between
calculated and experimental friction pressure drop for vertical
flow is not available.
427 Liquid Holdup CorrelationThe density of two-phase mixtures
at any section in the pipe may be calculated if the liquid
holdupthe fractional volume of the pipe occupied by the liquidis
known. Correlations have been developed to predict the holdup as it
changes along the pipe. That developed by Hughmark (Reference 7) is
the most accurate. This correlation relates the flow parameter Y to
the variable X as shown in Figure 400-6.
The relationship between the flow parameter Y and the gas volume
fraction Rg assumes that Rg is distributed radially across the
pipe, with the largest value at the center. The relationship is
expressed in terms of the gas volume fraction Rg and liquid holdup
Rl, as follows:
(Eq. 400-22)The variable X in Equation 400-22 is defined as
follows:
(Eq. 400-23)where:
Fr = Froude number = V2/Dg
Fig. 400-5 Calculated vs. Experimental Frictional Pressure
DropHorizontal Flow Dukler, Wicks and Cleveland, Frictional
Pressure Drop in Two-Phase Flow: A Compar-ison of Existing
Correlations for Pressure Loss and Hold-up. From AlChE Journal Vol.
10, #1m 1964. Used by permission.
Flow Regime Range of Deviation (%)
Plug -22.3 to -2.3
Stratified -25.3 to +24.7
Wave -21.0 to +39.0
Slug -17.9 to +12.1
Annular -59.2 to +15.8
Dispersed -24.4 to +30.6
Bubble not given
Rg 1 R1Y
g1-----
1X---- 1 1+
-----------------------------------= =
X Re16---
Fr18---
14---
----------------------=Chevron Corporation 400-15 March 2001
-
400 Friction Pressure Drop Fluid Flow Manual = liquid volume
fraction at pipe entrance
D = diameter, ft
g = gravitational constant (32.174 ft/sec2)The dimensionless
numbers used in the variable X are shown in Equations 400-24 and
400-25.
(Eq. 400-24)where:
Gm = tpVm
= mass velocity mixture (lbm/ft2-sec)
Fig. 400-6 Correlation for the Flow Pattern Y From Holdup in
Gas-Liquid Flow by G.A. Hughmark, Chemical Engi-neering Progress,
Vol. 58, April, 1962, p. 62
Re
D GmR11 Rgg+( )
-------------------------------------
1490-------------------------------------=March 2001 400-16
Chevron Corporation
-
Fluid Flow Manual 400 Friction Pressure DropRe Retp (from
Equation 400-11)
(Eq. 400-25)
(Eq. 400-26)where:
= specific volume
The calculation procedure is to evaluate Re, Fr, and using
Equations 400-24, 400-25, and 400-26. The variable X is then
evaluated using Equation 400-23, and the flow parameter Y is
determined from Figure 400-5. Using the flow parameter Y, the
liquid holdup is found from Equation 400-22. An iterative
calculation is required since the gas density used in Equation
400-22 is evaluated at the average pressure. The gas volume flow
rate Qg used in Equations 400-25 and 400-26 is the inlet value
evaluated using the inlet density.
The actual flow density calculated using Equation 400-16 is then
used to determine the elevation pressure drop in upwards vertical
flow.
The deviation between the calculated (Figure 400-6) and
experimental (Reference 3) values of the liquid holdup varies by
25%. For vertical flow not as much exper-imental data are
available. For the available data the deviation between
experi-mental and calculated liquid holdup does not exceed 10
percent (see Section 450, Reference 7).
430 Compressible FlowPressure drop in gas transmission lines can
be calculated in four ways, as follows:
Using the PIPEPHASE program, discussed in Section 1100
Applying the widely used Weymouth and Panhandle fundamental flow
equa-tions (see Figure 400-7 on page 400-19)
Using the PCFLOW program, discussed in Section 1100
Using COMFLOW, a computer program developed for Chevron Pipeline
Company by CRTC. COMFLOW solves for pressure drop in branched gas
pipeline systems. See Section 1100 for further discussion.
Of these options only COMFLOW and PIPEPHASE consider heat
transfer, and only PIPEPHASE considers condensation. Condensation
due to heat transfer is common in hot gas transmission and can
significantly affect the friction pressure drop. Section 420
discusses two-phase flow pressure drop.
FrVm
2
gD-----------
Q1 Qg+( ) A( )2
gD-----------------------------------------= =
W11
W11 Wgg+------------------------------------
Q1Q1 Qg+--------------------= =Chevron Corporation 400-17 March
2001
-
400 Friction Pressure Drop Fluid Flow ManualWeymouth and
Panhandle EquationsThe general formula for compressible flow has
the following form:
(Eq. 400-27)where:
Q = flow rate, SCFDTo = standard absolute temperature, R
Po = standard pressure, psia
D = pipe ID, in.
P1 = upstream pressure, psia
P2 = downstream pressure, psia
S = fluid specific gravity (air = 1)T = fluid absolute
temperature, R
L = length of pipeline, miles
C1 through C7 = constants as shown in Figure 400-7
This equation can be derived from basic pressure drop relations,
but in the literature it is often presented in simplified form with
certain empirical components. The two most widely accepted forms
are the Weymouth Equation and the Panhandle Equa-tion.
The Weymouth Equation, in which friction is a function of the
diameter, applies at high Reynolds numbers. The Panhandle Equation,
in which friction is a function of the Reynolds number, applies at
lower Reynolds numbers. The break point is defined as follows:
Re = 9031D2.449(Eq. 400-28)
where:D = inside diameter, in.
The constants (C1 through C7) for the Weymouth and Panhandle
equations are shown in Figure 400-7 both as presented in the
literature and as derived without empirical components.March 2001
400-18 Chevron Corporation
-
Fluid Flow Manual 400 Friction Pressure Drop440 Gas Flow At High
Pressure Drop (Choked Flow)A compressible fluid flowing through a
pipe at high pressure drop approaches maximum velocity at a
critical value of downstream pressure. Reduction of pres-sure below
this value will not increase velocity. This maximum gas velocityin
a pipe of constant cross-sectional areais limited to the velocity
of pressure wave propagation in the fluid (the speed of sound).This
section presents a method for determining pressure drop and flow
rate in such situations. Some applications for this method include
design of gas pipelines, pres-sure reduction lines, and relief
lines.
Theoretical methods for calculating high pressure drop are
available, but are usually long and complex. However, C. E. Lapple
(Section 450, Reference 15) has devel-oped a graphical solution,
which is the basis for Figure 400-10.
Fig. 400-7 Weymouth and Panhandle Equation Constant
Equation C1 C2 C3 C4 C5 C6 C7 Source
Weymouth 433.45 Z 1 2.667 1 1 0.5 1
Weymouth 433.50 1 1 2.667 Z 1 0.5 2
Panhandle 435.87 E 1.0788 2.6182 1 0.8539 0.5394 3
Panhandle 503.30 1 1 2.695 1 0.77 0.565 2
where
E = pipeline efficiency, ranging from 0.94 (new pipe) to 0.88
(old rough pipe)Z = compressibility
= (From Source 4.) Accurate within 10% if Pr1.0
or if Pr>0.8 and Tr>1.1
A = Tr16
Tr = T/TcTc = critical temperature, RT = operating
temperature,RPr = P/PcPc = critical pressure, psiaP = operating
pressure, psiaSources:
1. Natural Gas Processors Suppliers Association, Engineering
Data Book, 1972.
2. Derived by W.A. Ebert, Chevron Engineering Department,
1984.
3. Baumeister and Marks, eds., Standard Handbook for Mechanical
Engineers, McGraw-Hill, 1967.
4. Heat Transfer Research Inc., Computer Program Support Volume,
pg. E1-47, 1976.
10.41Pr
Tr4.04
--------------- 0.29( )APr8
+Chevron Corporation 400-19 March 2001
-
400 Friction Pressure Drop Fluid Flow Manual441 AssumptionsThe
charts in Figure 400-10 (and Lapples analysis) are based on the
following assumptions:
The friction factor (f) is constant along the length of the
pipe. For the entire range of each chart, either the Perfect Gas
Law applies or the
compressibility factor (Z) and the ratio of specific heats (K)
of the gases are constant.
The charts are based on horizontal flow through constant
cross-sectional area.
442 Use of Design ChartsThe design charts in Figure 400-10 are
for gases with values of K (the ratio of specific heats cp/cv)
equal to 1.0 (isothermal flow of any gas) and 1.4 (flow of air and
diatomic gases, H2, O2, N2). For the other gases with K values
between 1.0 and 1.4, a visual interpolation between the charts may
be made. Figure 400-8 gives approximate values of K for various
gases.
The design charts in Figure 400-10 are used when upstream
conditions (usually static conditions within a vessel or reservoir)
are known and either the discharge rate or downstream pressure are
required for a given pipe size. In Figure 400-9, the typical
problem is to determine mass flow rate G or pressure P2, given P0,
T0, P3, L, and D. The velocity at Section 0 is assumed to be
zero.
In Figure 400-29, flow rates are expressed as a ratio of the
actual mass velocity, G, to a hypothetical maximum isothermal mass
velocity through a nozzle, Gmax. Thus, it is first necessary to
calculate Gmax from known conditions:
(Eq. 400-29)
Fig. 400-8 Ratios of Specific Heats (cp/cv)
Low Pressure Gas K-value
C2H6 1.2
CO2, SO2, H2O, H2S, NH3, Cl2, CH4, C2H2, C2H4 1.3
Air, H2, O2, N2, NO, HCl 1.4March 2001 400-20 Chevron
Corporation
-
Fluid Flow Manual 400 Friction Pressure Dropwhere:G = mass
velocity, lbm/ft2sec
gc = conversion factor (32.17 lbm ft/lbf sec2)MW = molecular
weight, lbm/mole
e = base of natural logarithm (2.718)R = gas constant, 1546
ftlbf/lbmoleR
T = absolute temperature, R, at location designated by
subscript
P = absolute pressure, lbf/ft2, at location designated by
subscript
V = specific volume, ft3/lbm, at location designated by
subscript
The friction factor (f) must also be established (see Section
410) prior to using the charts, although variations in f affect the
answer very little. The initial value of f is usually assumed to be
0.0143 for gas flow.
443 Sonic FlowAfter considering these preliminaries, use of the
charts is generally self-explana-tory. However, caution is advised
concerning the area on each chart below the diag-onal line labeled
critical pressure ratio. This line defines the minimum possible
pressure within the pipe at the exit for a particular fL/D flow
parameter. That is, P2 will remain constant at this minimum despite
further decrease in discharge reser-voir pressure, P3. A sonic flow
condition is said to exist at the pipe exit, since the exit gas
velocity equals the velocity of sound in the fluid. Therefore, any
further
Fig. 400-9 Flow Conditions High Pressure GasChevron Corporation
400-21 March 2001
-
400 Friction Pressure Drop Fluid Flow ManualFig. 400-10 Design
Charts for Gas Flow at High Pressure Drop (1 of 2) Perry and
Chilton, Engineers Handbook, 5th Ed. Used by permission of The
McGraw-Hill Companies.
1. To use design charts in Figure 400-10:
a. Calculate an overall effective length L of straight pipe of
diameter D, including equivalent length for valve and fitting
losses (see Section 500).
b. Assume a friction factor f for gas flow (usually assumed
0.0143) and calculate fL/D parameter.
c. Calculate the hypothetical maximum mass velocity, Gmax,
from
d. Estimate K (ratio of specific heats) from Figure 400-8.
e. Enter appropriate chart to determine P2/P0 or G/Gmax and
solve for pressure P2 or mass flow.
2. Values for P2/P0 are valid only above the critical pressure
ratio line which defines the point of sonic flow and maximum mass
flow. Ratio P3/P0 is, however, valid over the entire range
shown.
Examples:Given: Air within a reservoir at 80F and 200 psig is
discharging to the atmosphere through 20 feet of three-inch,
schedule 40 pipe which includes two standard 90 long radius
elbows.
Determine: Discharge rate to the atmosphere
Solution:1. Calculate fL/D parameter (use consistent units)
f = 0.0143; assumed D=3.068 in. = 0.256 ftL = 20 + L = 20 +
(2)(0.256)(23) = 31.8 ft (see Section 500)
2. Calculate maximum mass velocity, GmaxTo = 460 + 80 = 540RPo =
(200 + 14.7)(144) = 30,900 lbf/ft
2
MW = 29 lbm/mole
3. Find Flow RateP3 = (14.7)(144) = 2120 lbf/ft
2
P3/Po = 2120/30,900 = 0.0685G/Gmax = 0.76 (K=1.4)G = (627)(0.76)
= 476 lbm/(sec)(ft)
2
A = (0.256)2/4 = 0.0515 ft2
Flow Rate = (G)(A) = (476)(0.515) = 24.6 lbm/sec
Gmax
gcPoevo
-------------0.5
Po
gcMW
eRTo-----------------
0.5 lbm
ft2
sec-------------------= =
Gmax 30 90032.17( ) 29( )
2.718( ) 1546( ) 540(
)---------------------------------------------0.5
, 627lbm
sec( ) ft( )2-------------------------= =March 2001 400-22
Chevron Corporation
-
Fluid Flow Manual 400 Friction Pressure DropFig. 400-10 Design
Charts for Gas Flow at High Pressure Drop (2 of 2) Perry and
Chilton, Engineers Handbook, 5th Ed. Used by permission of The
McGraw-Hill Companies.Chevron Corporation 400-23 March 2001
-
400 Friction Pressure Drop Fluid Flow Manualreduction in P3
cannot be transmitted back to the pipe exit to result in further
pres-sure reduction within the pipe. The excess pressure energy in
such a case (P2 - P3) is dissipated in turbulence from the rapid
lateral expansion of gases leaving the pipe.
444 Choked FlowFor the same reasons, the flow rate is at its
maximum under critical pressure ratio conditions and will remain so
regardless of any further decrease in P3. This limiting phenomenon
can result in choking of a vent relief or pressure reduction line.
A relief valve might be sized to handle the required flow only to
have an inadequate vent line choke or limit the discharge rate at
the critical pressure ratio.
445 Temperature VariationsIn the case of adiabatic flow, a drop
in gas temperature from T0 to T2 may also be estimated from the
design chart (for K = 1.4). Temperature ratios T2/T0 are shown as
diagonal lines intersecting the fL/D parameter curves. For known
reservoir temperature T0 and flow rate or pressure drop, the gas
temperature T2 at the pipe exit may easily be calculated.
446 Effects of Valves and FittingsThe increased pressure drop
through valves and fittings should be taken into account by the
equivalent length method of Section 500. The equivalent length L,
of the valve or fitting is added to the actual length of straight
pipe to yield the effec-tive overall length used to calculate the
fL/D parameter.
447 Deviation from AssumptionsVarious deviations from the
assumptions in Lapples analysis (listed previously) will affect the
accuracy of the design charts. One such deviation is the variation
from the perfect gas laws under high pressure. Allowance for such
variation may be made by multiplying the gas constant R by the
compressibility factor Z (a measure of varia-tion from perfect gas
properties) before calculating the hypothetical maximum discharge
mass velocity, Gmax. Since the compressibility factor Z will vary
along the length of the pipe, calculations should be made at
stepped intervals and the results added together. Further
discussion and techniques for handling such devia-tions are
included in the references.
450 References1. Scott, D. S. Properties of Concurrent
Gas-Liquid Flow. Advances in Chemical
Engineering, Vol. 4, p.199. New York: Academic Press, 1963.
2. Gouse, W. S., Jr. An Index to the Two-Phase Gas-Liquid Flow
Literature. MIT Report No. 9. MIT Press, 1966.March 2001 400-24
Chevron Corporation
-
Fluid Flow Manual 400 Friction Pressure Drop3. Dukler, A. E., M.
Wicks III, and R. G. Cleveland. Frictional Pressure Drop in
Two-Phase Flow: A. A Comparison of Existing Correlations for
Pressure Loss and Holdup. AIChE Journal 10 (1964), p. 38.
4. Lockhart, R. W., and R. C. Martinelli. Proposed Correlation
of Data for Isothermal Two-Phase, Two-Component Flow in Pipes.
Chemical Engineering Progress, 45 (1949), p. 39.
5. Dukler, A. E., M. Wicks III, and R. G. Cleveland. Frictional
Pressure Drop in Two-Phase Flow: B. An Approach Through Similarity
Analysis. AIChE Journal 10 (1964), p. 44.
6. Streeter, V. L. Fluid Mechanics. 2nd Edition. New York:
McGraw-Hill, 1958.
7. Hughmark, G. A. Holdup in Gas-Liquid Flow. Chemical
Engineering Progress Vol. 58 (April 1962), p. 62.
8. Baker, O. Multiphase Flow in Pipelines. Oil and Gas Journal,
10 (Nov, 1958).9. Griffith, P., and G. B. Wallis. Two-Phase Slug
Flow. Journal of Heat Transfer,
Transactions of ASME Series C 83 (Aug 1961), p. 307.10.
California Research Corporation Standard Technical Books.
California
Research Corporation, Richmond, California, 1960.
11. Marks Mechanical Engineers Handbook. 6th Edition. New York:
McGraw-Hill, 1958.
12. Perrys Chemical Engineers Handbook. 4th Edition. New York:
McGraw-Hill, 1963.
13. Technical Data Book - Petroleum Refining. New York: American
Petroleum Institute, Division of Refining, 1966.
14. S I Engineering Data Book. Tulsa: Gas Processors Suppliers
Association, 1987.
15. Lapple, C.E. Isothermal and Adiabatic Flow of Compressible
Fluids. Transac-tions of AIChE, Vol. 39 (1943), pp. 385-432.
16. Loeb, M. B. Graphical Solution of Compressible Fluid Flow
Problems. NASA/Kennedy Space Center Document TR-256D, 1965.
17. Loeb, M. B. New Graphics for Solving Compressible Flow
Problems. Chem-ical Engineering, Vol. 76, No. 11 (May 19,
1969).
18. Shapiro, A. H. The Dynamics and Thermodynamics of
Compressible Fluid Flow, Vol. I. New York: The Ronald Press
Company, 1953.Chevron Corporation 400-25 March 2001
-
500 Fitting Pressure Drop
AbstractThis section discusses energy loss at changes in pipe
section. Two methods for calculating pressure drop in fittings are
presented, the velocity head loss method and equivalent length
method, and example calculations are given.
Contents Page
510 Introduction 500-2520 Velocity Head Loss Method 500-2530
Equivalent Length Method 500-5540 Transition and Laminar Flow
Conditions 500-7550 Examples 500-7551 Example 1Velocity Head Loss
Method552 Example 2Equivalent Length Method560 References
500-10Chevron Corporation 500-1 March 1997
-
500 Fitting Pressure Drop Fluid Flow Manual510
IntroductionValves and fittings cause more energy loss than pipe of
equal axial length. This loss may be relatively insignificant in
long lines but, within process plants, it can be a major
contributor to system losses.Losses at a change in section take two
distinct forms, pressure loss and energy loss. At a well-rounded
pipe entrance, there is a pressure loss due to the increase in
velocity, but a negligible energy loss. At a pipe exit, pressure
change is usually nominal and velocity energy is dissipated as
turbulence.
Head loss through a valve or fitting can be expressed in two
ways:
As the number of velocity heads lost
As a length of straight pipe with a diameter and pressure drop
equal to those of the valve or fitting
520 Velocity Head Loss MethodIn the turbulent flow range, the
resistance to flow through a fitting is roughly a constant times
the square of the average line velocity at the fitting. This can be
expressed as follows:
(Eq. 500-1)where:
hf = head loss through the fitting, ft
V = average velocity in the line, ft/sec
K = constant for the fitting type
g = gravitational constant (32.2 ft/sec2)Since V2/2g is the
velocity head of the fluid, K is the number of velocity heads lost
through the fitting. The average values of K for various valves and
fittings are shown in Figure 500-2. K values for various entrance
losses are given in Figure 500-1.
hf KV2
2g------- =March 1997 500-2 Chevron Corporation
-
Fluid Flow Manual 500 Fitting Pressure DropFig. 500-1 Losses
Through Entrances and Changes in Section Courtesy of Tube Turns
TechnologiesChevron Corporation 500-3 March 1997
-
500 Fitting Pressure DropFluid Flow
Manual
March 1997
500-4Chevron Corporation
Fig. 500-2 Valve and Fitting Loss Data Crane Technical Paper
410-C, 1984, Flow of Fluids. Courtesy of Crane Valves
-
Fluid Flow Manual 500 Fitting Pressure Drop530 Equivalent Length
MethodThe equivalent length method is a convenient but less
accurate way to estimate pres-sure drop through valves and
fittings. This method may be understood by looking at the
Darcy-Weisbach equation for friction head loss, which can be
expressed as follows:
(Eq. 500-2)where:
h = friction head loss, ft
f = friction factor
L = length of fitting, ft
D = diameter of fitting, ft
Thus K equals f(L/D). By expressing this relation in terms of L,
the loss through the fitting may be expressed as an equivalent
length (L) of straight pipe (of the same diameter as the fitting).
That is,
(Eq. 500-3)Figure 500-3 gives equivalent length of various sizes
of valves and fittings.
The L/D ratio provides equivalent length values in terms of
diameters of straight pipe, so that one value can be applied to
varying diameters of a valve or fitting. The equivalent length
ratios shown in Figure 500-2 were calculated from the fittings K
values (assumed constant for each type fitting) and a friction
factor of 0.025 for liquids and 0.0143 for gases. Because the
actual friction factor may differ appre-ciably, the equivalent
length method should be used only for rough estimates or when the
total equivalent length for valves and fittings is small compared
to the length of straight pipe.
h f LD----V2
2g------- =
L DKf---- or
L
D-----Kf----= =Chevron Corporation 500-5 March 1997
-
500 Fitting Pressure DropFluid Flow
Manual
March 1997
500-6Chevron Corporation
Fig. 500-3 Equivalent Length of Valves and Fittings in Feet From
Engineering Data Book, 9th Ed. 1972. Courtesy of GPSA.
-
Fluid Flow Manual 500 Fitting Pressure Drop540 Transition and
Laminar Flow ConditionsUnder transition and most laminar flow
conditions, the velocity head loss method, using turbulent range K
values, is accurate enough for normal estimating. However, the K
values increase rapidly for Reynolds numbers below 500. Additional
data and discussion can be found in the references cited in Section
560 (for Re < 500 see Reference 6).
550 ExamplesConsult Figures 500-1 and 500-2 for the K and L/D
values to be used in the following examples. In practice,
manufacturers proprietary fitting loss data should be used whenever
available.
For elbows under three inches in diameter, increase loss by 30
percent. Add appro-priate reducer losses to fitting losses for
total loss through a reducing fitting, such as a tee with a
reducing branch or a venturi pattern valve.
551 Example 1Velocity Head Loss MethodGiven the following,
determine the pressure loss through the fittings:
Flowing liquid: gasoline (gravity = 0.75) with a flow rate of
150,000 lb per hour.
Fittings: 6-inch Schedule 40 size; one globe valve; one check
valve; three 90-degree elbows (R/D = 1.5); one 6-inch to 3-inch
ANSI reducer.
SolutionCalculate the pressure drops separately for each
diameter.
Diameter Ratio: DS/DL = 3.068 in./6.065 in. = 0.51
From Figure 500-1:
Fitting K
Reducer (friction) 0.16
Reducer (acceleration) 0.56
TOTAL 0.72Chevron Corporation 500-7 March 1997
-
500 Fitting Pressure Drop Fluid Flow ManualFrom Figure
500-2:
Pipe Area = A = pir2
= 0.201 ft2
= .051 ft2Flow rate = Q
= 0.89 ft3/sec
= 4.44 ft/sec
=17.45 ft/sec
Fitting K
Globe Valve 10.0
Check Valve 2.3
Elbows (3 x .33) 0.99
TOTAL 13.29
A1 3.146.065
2------------- 2in.2 1ft
2
144 in.2--------------------=
A2 3.143.068
2------------- 2in.2 1ft
3
144 in.2--------------------=
150 000lbhr-----,hr
3600sec--------------------ft3
62.4lb---------------1
.75------- =
Velocity V QA----= =
V1QA1-------
0.89ft3 sec0.201ft2
-----------------------------= =
V2QA2-------
0.89ft3 sec0.051ft2
-----------------------------= =March 1997 500-8 Chevron
Corporation
-
Fluid Flow Manual 500 Fitting Pressure Drop= 0.306 ft
= 4.73 ftTotal pressure drop:
(Eq. 500-4)
552 Example 2Equivalent Length MethodGiven the following,
determine the estimated total equivalent length of straight 6-inch
pipe:
Flowing liquid: gasoline (gravity = 0.75) at a flow rate of
150,000 lb per hour Total line length (including fittings): 800 ft
Pipe and fitting size: 6 inch, schedule 40 = 6.065 in. ID
Fittings: one gate valve (open), six 90 elbows (R/D = 1.5), one
square edged entry, one exit
One Velocity Head V2
2g-------=
V212g---------
4.442ft2 sec22 32.2 ft
sec2--------------------------------------=
V222g---------
17.452sq ft sec22 32.2 ft
sec2------------------------------------------=
P1 13.29( ) 0.306( )62.4 0.75
144--------------------------- 1.322psi= =
P2 0.72( ) 4.73( )62.4 0.75
144--------------------------- 1.107psi= =
Total 2.429 psi=Chevron Corporation 500-9 March 1997
-
500 Fitting Pressure Drop Fluid Flow ManualSolutionFrom Figures
500-1 and 500-2:
Equivalent length L = (L/D) (D) = (146) (6.065)= 855 in. = 71.2
ft
Total equivalent line length 800 + L = 871.2 ft
560 References1. Flow of Fluids Through Valves, Fittings, and
Pipe. Crane Co., Crane Technical
Paper No. 410-C, 1984.
2. King, R.C., and S. Crocker. Piping Handbook, 5th Edition,
McGraw-Hill, pp 167-181, 1967.
3. Piping Engineering - Fluid Flow in Pipe. Tube Turns Bulletin
No. 301, 1951.
4. Simpson, L.L. Process Piping: Functional Design. Chemical
Engineering, Vol. 76, No. 8, 1969.
5. Perrys Chemical Engineers Handbook. 4th Edition, McGraw-Hill,
New York, 1963.
6. Beck, C. Laminar Flow Friction Losses Through Fittings,
Bends, and Valves. Journal American Society Naval Engineers, vol.
56, p. 235-271, 1944.
7. Kittredge, C.P., and D.S. Rowley. Resistance Coefficients for
Laminar and Turbulent Flow Through One-Half-Inch Valves and
Fittings. ASME Transac-tions, Vol. 79, pp 1759-1766, 1957.
Fitting L/D
Gate Valve 8
Elbows (6 x 13) 78
Square Edged Entry (friction) 20
Square Edged Entry (acceleration) 40
TOTAL 146March 1997 500-10 Chevron Corporation
-
600 Noncircular Conduits
AbstractThis section presents methods for approximating pressure
drop for turbulent and laminar flow in noncircular conduits. These
conduits are assumed to be closed and filled with fluid.
Contents Page
610 Introduction 600-2620 Turbulent Flow (Re > 2000) 600-2630
Laminar Flow (Re 2000) 600-3640 References 600-4Chevron Corporation
600-1 January 1990
-
600 Noncircular Conduits Fluid Flow Manual610 IntroductionThe
calculation of pressure drop in noncircular conduits is handled
differently for laminar and turbulent flow. Turbulent flow boundary
layers are thin and relatively unaffected by proximity to the
conduit walls. Laminar boundary layers, however, are thick, and the
boundary layers from opposite walls often interact.
Pressure drop for turbulent flow can be closely approximated
based on the calcula-tion of the conduits hydraulic diameter given
in Section 620. For laminar flow, empirical data is needed to
arrive at a reasonable approximation of the pressure drop for a
specific case. Section 630 provides empirical correlations for the
friction factor for rectangular and concentric annulus geometry.
For this analysis, the transi-tion between laminar and turbulent
flow can be assumed to be at a Reynolds number of 2000.
620 Turbulent Flow (Re > 2000) The hydraulic diameter (Dh) is
derived from the flow area and the wetted perimeter length of the
noncircular conduit. It is used in determining the Reynolds number,
which, in turn, is used to find a friction factor appropriate for
the noncircular conduit flow.
(Eq. 600-1)
(Eq. 600-2)
(Eq. 600-3)where:
f = friction factor from Figure 400-1, Moody Chart
Dh = hydraulic diameter, ft
Ax = cross-sectional flow area, ft2
Pw = wetted perimeter of channel, ft
Re = Reynolds number
= density, lbm/ft3
V = velocity, ft/sec
Dh 4AxPw-------
=
ReVDh
---------------VDh
-----------= =
dh fL V2
Dh 2g-----------------=January 1990 600-2 Chevron
Corporation
-
Fluid Flow Manual 600 Noncircular Conduits = kinematic
viscosity, ft2/sec
= viscosity, lb sec/ft2
f = friction factor
dh = pressure drop in head loss, ft
L = conduit length, ft
g = gravitational constant, 32.17 ft/sec2
630 Laminar Flow (Re 2000)Pressure drop for laminar flow in
noncircular conduits can be calculated using the standard pressure
drop equation (Eq. 600-3) and the hydraulic diameter (Eq.600-1).
The friction factor (f) is a function of the Reynolds number (Eq.
600-2) and the constants as shown in Figure 600-1 and Equations
600-4 and 600-5.
For rectangular conduit geometry choose C1 such that:
a = short side of rectangle
b = long side of rectangle
Calculate the friction factor as follows:
(Eq. 600-4)For concentric tube annulus choose C2 such that:
a = radius of inner tube
b = radius of outer tube
Calculate the friction factor as follows:
(Eq. 600-5)
f C1Re-------=
f C2Re-------=Chevron Corporation 600-3 January 1990
-
600 Noncircular Conduits Fluid Flow Manual640 ReferencesKays and
Crawford, Convective Heat and Mass Transfer, McGraw- Hill,
1980.
Fig. 600-1 Laminar Flow Pressure Drop Constants Kays &
Crawford, Convective Heat and Mass Transfer, 1980. Used by
permission of The McGraw-Hill Companies.
a/b(1) C1(1) C2(1)
0.0 96.0 64.0
0.025 94.0 81.2
0.05 90.0 86.0
0.1 85.2 89.2
0.2 76.8 92.4
0.3 70.4 93.6
0.4 65.6 94.8
0.5 62.8 95.2
0.6 60.0 95.6
0.7 58.8 96.0
0.8 57.6 96.0
0.9 57.2 96.0
1.0 56.8 96.0
Source: See Section 640.
(1) See Eq. 600-4, 600-5January 1990 600-4 Chevron
Corporation
-
800 Surge Pressure
AbstractThis section presents the basic physical principles
involved in surge and a method for approximating surge pressure in
simple cases. In addition, it identifies two computer programs
available within the Company for analysis of complex fluid pressure
transients.
Contents Page
810 Introduction 800-2820 Maximum Surge Pressure in a Simple
Case 800-2830 Surge Computer Programs 800-7840 References
800-7Chevron Corporation 800-1 January 1990
-
800 Surge Pressure Fluid Flow Manual810 IntroductionIf a valve
is closed rapidly in a line containing flowing liquid, the inertia
of the flowing liquid will increase the pressure at the valve. This
effect is called surge, and the increase in pressure is called
surge pressure. Surge can cause extremely rapid changes in
pressurerapid enough to cause the metallic percussions commonly
called water hammer. The surge pressure wave will then propagate
back up the line, and may cause mechanical damage.
Water flowing at 10 ft/sec can generate a surge pressure rise of
about 500 psi. Bulk modulus values for hydrocarbons are generally
lower than for water, but surge pres-sures are still significant
considerations in designing hydrocarbon piping systems. See Figures
800-1 through 800-3.
This section provides a method for approximating the maximum
surge pressure in a simple system. Because of nonlinear elements in
the analysis, a more thorough calculation of surge pressure can be
a complex problem. See Section 840 for sources providing more
general solution techniques.
820 Maximum Surge Pressure in a Simple CaseThe simplest case is
of flow through a line starting at a vessel and ending at a valve
(see Figure 800-4).When the valve is closed, the kinetic energy of
the flowing liquid is converted to surge pressure as the liquid
compresses and the pipe wall stretches. The conversion of kinetic
energy to surge pressure propagates in a wave upstream to the
vessel at the velocity of sound in the liquid, followed by a return
negative pressure wave back to the valve. This cycle repeats with
diminishing intensity until damped completely.
To a first approximation, the magnitude of the surge pressure is
directly propor-tional to the change in velocity. It follows that
maximum surge pressure occurs when the flow is stopped completely
and quickly. To calculate surge pressure, the velocity of sound in
the liquid must be calculated using Equation 800-1.
January 1990 800-2 Chevron Corporation
-
Fluid Flow Manual 800 Surge PressureFig. 800-1 Average Bulk
Modulus for Crude Oil, Fuel Oil, Gas Oil, and GasolineChevron
Corporation 800-3 January 1990
-
800 Surge Pressure Fluid Flow ManualFig. 800-2 Average Bulk
Modulus for Lubricating OilsJanuary 1990 800-4 Chevron
Corporation
-
Fluid Flow Manual 800 Surge PressureFig. 800-3 Bulk Modulus of
Water
Fig. 800-4 SurgeSimple CaseChevron Corporation 800-5 January
1990
-
800 Surge Pressure Fluid Flow Manual(Eq. 800-1)where:
= speed of sound through liquid in pipe, ft/sec
K = bulk modulus of liquid, psi. For hydrocarbon liquids, see
Figures 800-2 and 800-3; for water, see Figure 800-4.
= density of liquid, lbm/ft3
g = 32.2 ft lbm/sec2 lbfD = inside diameter of pipe, inches
t = wall thickness of pipe, inches
E = modulus of elasticity of pipe material, psi
C = constant which depends on pipe fixity
= 0.91 for line anchored against axial movement
= 0.95 for unrestrained line
A pressure disturbance generated at the valve will propagate
back to the vessel and return to the valve in a propagation time
equal to 2L/ (where L = line length between vessel and valve in
feet). If the valve closing time (T) is less than 2L/, the surge
pressure can be approximated by
(Eq. 800-2)where:
P = surge pressure, psi
V = total change in velocity, ft/sec
T = valve closing time, sec
2L/ = propagation time, sec
This solution is only an approximation tailored to this simple
case. For example, this equation is not valid if the valve closing
time is greater than 2L/. Section 840, references 1, 2, and 3,
presents general techniques for calculating surge pressure
accurately and in more complex situations.
144Kg
1 KDCEt-------------+ -------------------------------=
P V144g---------------- for T2L
-------
-
Fluid Flow Manual 800 Surge Pressure830 Surge Computer
ProgramsThe SURGE computer program available on the VM mainframe
engineering program library (HOVMA) is described in Section 1100
and Appendix H of this manual. This software performs a rigorous
analysis of pressure transients for common applications.
The HYDRESS computer program calculates fluid transients in
small-diameter flex-ible conduits (instrument control and subsea
lines) and is available on VM Houston (OELIB).
840 References1. Symposium on Surges in Pipelines, The
Institution of Mechanical Engineers,
Proceedings 1965-66, Vol. 180, Part 3E.
2. Hydraulic Transients, Rich, G. R., Dover Publications, Inc.,
New York, 1963.
3. Hydraulic Transients, Streeter, V. L., Wylie, E. B.,
McGraw-Hill, 1967.Chevron Corporation 800-7 January 1990
-
900 Pipeline Flow
AbstractThis section discusses the flow effects of increased
temperature and pressure in above-ground, buried, and subsea oil
pipelines. Basic equations are given for calcu-lating friction
heating in viscous flow, pressure correction to viscosity, and
external heat transfer coefficients. Computer programs for
calculating effects of temperature changes on large segments of
pipeline are identified and briefly discussed. Tables for external
heat transfer coefficients and soil conductivities are
included.
Contents Page
910 Introduction 900-2920 Pipeline Temperature Limits 900-2930
Friction Heating In Viscous Flow 900-2940 Pressure Correction to
Viscosity 900-3950 Applicable Computer Programs 900-4960 External
Heat Transfer Coefficients 900-5970 References 900-7Chevron
Corporation 900-1 January 1990
-
900 Pipeline Flow Fluid Flow Manual910 IntroductionSection 900
addresses pipeline flow situations in which large temperature
changes significantly affect fluid properties and flow
characteristics. Other situations, involving typical liquids and
gases at close to ambient temperatures or with small temperature
changes, can be adequately addressed using the methods of Section
400.
For long pipelines carrying fluids that require high pumping
energy, the effects of friction heating should be investigated.
Section 930 defines the relationship of temperature change to
pumping energy for viscous fluids. Similarly, at high pres-sures, a
pressure correction to viscosity may be necessary, as discussed in
Section 940.
Section 960 discusses heat transfer between the pipeline and its
surroundings, including calculation of external heat transfer
coefficients for pipelines in various ambient conditions. Section
950 identifies computer programs available for solving difficult
temperature/flow problems over the length of a pipeline.
920 Pipeline Temperature LimitsThe allowable coating or
insulation temperature normally limits pipeline tempera-ture.
Coating temperature (for buried pipelines) is normally limited to
less than about 150F. Special fusion bonded epoxy coatings of extra
thickness are limited to about 200F. Polyurethane foam insulation
temperature limits are about 200F. Some forms of insulation may
resist higher temperatures, but Chevron has no expe-rience with
them.
930 Friction Heating In Viscous FlowIn a flowing fluid, pressure
dissipated by friction becomes heat. This heat has histor-ically
been ignored in flow calculations because it is often
insignificant. However, with some oils friction heating
significantly decreases the pumping energy required.
The temperature increase from friction heating accumulates over
the length of the pipeline. In a perfectly insulated pipeline, the
outlet temperature would be higher than the inlet temperature. This
change in temperature can be related to the hydraulic horsepower
(friction component) and flow rate by the following
expres-sion:
(Eq. 900-1)where:
T = temperature increase, F
HP = hydraulic (friction) horsepower, hpJanuary 1990 900-2
Chevron Corporation
-
Fluid Flow Manual 900 Pipeline FlowBPD = oil flow rate, BPD
r = oil density, lbm/ft3
Cp = oil specific heat, BTU/lbm F
When Cp = 0.5 and = 58 the expression becomes:
High viscosities increase the ratio of HP to BPD and therefore
increase the tempera-ture change due to friction. How well the
pipeline is insulated determines how much of the added heat will
actually stay in the oil. The following factors determine the
decrease in required pumping power:
How much the viscosity is decreased by the increased
temperature
How sensitive the flow regime is to decreases in viscosity.
Pressure drop in laminar flow is a stronger function of viscosity
than in turbulent flow. Pressure drop in transition flow is not a
function of viscosity
The effect of friction heating generally increases with:
Flow rate Viscosity Insulation Line length
940 Pressure Correction to ViscosityThe viscosity of a liquid
increases with pressure, but, as with friction heating, this effect
is often ignored in pressure drop calculations. At high pressures
and viscosi-ties the average viscosity increase in a pipeline can
be 20% or more. Equation 900-2 gives the increased viscosity due to
pressure for high molecular weight hydrocarbons (source: see
Section 970, reference 1).
V = Vo 10A(Eq. 900-2)
where:
(Eq. 900-3)V = viscosity corrected for pressure, cp
Vo = viscosity at standard pressure, cpChevron Corporation 900-3
January 1990
-
900 Pipeline Flow Fluid Flow ManualP = pressure, psig
As with friction heating, the effect of increased viscosity on
pumping energy requirements depends on the flow regimes sensitivity
to viscosity. Since some pipe-lines have more than one flow regime
(laminar, transition, or turbulent), the change in pumping
requirements can be difficult to calculate without a computer
program.
950 Applicable Computer ProgramsOver the length of a pipeline,
temperature changes and resulting fluid property changes make it
difficult to calculate pipeline hydraulics by hand. Fortunately,
computer programs make hand calculations unnecessary.
Several computer programs are briefly discussed here in terms of
how they handle pipeline considerations. This is not intended to be
a complete description of these programs or to be an exhaustive
list of the programs that could be used for pipeline calculations.
Section 1100 contains more information on fluid flow computer
programs.
HOTOL* calculates pressure drop and heat transfer for
hydrocarbon liquids in pipe-lines where fluid properties change
significantly with temperature. The programs heat transfer routines
assume the fluid is at or above ambient temperature. HOTOL* does
not consider friction heating or pressure correction to viscosity.
The program is available on the mainframe engineering disk. For
details on the use of the program see Appendix G.
HOTPIPE2 is a modification of HOTOL*. It retains the rigorous
fluid property correlations and heat transfer routines of HOTOL*,
and also accepts elevation profiles. It can automatically place
pump stations and heater stations along the pipe-line, and it
considers friction heating and pressure correction of viscosity.
HOTPIPE2 runs on an IBM compatible personal computer. It is
available from the Engineering Analysis Division of Chevron
Research and Technology Company (CRTC).HOTOIL is an IBM compatible
personal computer program that handles both Newtonian and
non-Newtonian flow. As rigorous as HOTOL* in its heat transfer and
Newtonian fluid property correlations, HOTOIL also considers
friction heating, pressure correction to viscosity and elevation
profiles. It is available from the Engineering Analysis Division of
CRTC. For details on the use of the program see Appendix F.
PIPEFLOW-2 is the only program considered here that solves
piping network and multiphase flow problems. It handles elevation
profiles and detects and handles change of phase. Its reference
manual does not mention friction heating. Although it does not
automatically handle pressure correction to viscosity, viscosity
can be entered in tabular form as a function of temperature and
pressure. PIPEFLOW-2 resides on the Houston VM mainframe computer.
For details on the use of the program see Appendix E.January 1990
900-4 Chevron Corporation
-
Fluid Flow Manual 900 Pipeline Flow960 External Heat Transfer
CoefficientsAll the computer programs mentioned in Section 950
require the user to input an external heat transfer coefficient and
the ambient air or water temperature. This value is factored in
with the computer-derived internal heat transfer coefficient to
find the overall heat transfer coefficient.
The external heat transfer coefficient value (ho) should include
all heat transfer resistances between the pipe wall and the ambient
fluid. These include, first, insu-lating pipeline coverings such as
insulation, soil, concrete liners, and pipe coatings of significant
thickness, and, second, the area between the outside of the pipe or
pipe covering and the ambient fluid.
The following sections present equations for calculating
external heat transfer coef-ficients for buried, above-ground, and
subsea pipe.
Buried PipelinesThe appropriate ambient temperature value for a
buried line is the yearly average air temperature. The external
heat transfer coefficient for buried pipe can be calcu-lated as
follows:
(Eq. 900-4)where:
ho = external heat transfer coefficient, Btu/hr ft2 F
k = soil thermal conductivity, Btu/hr ft F
D = pipe outside diameter, inches
d = virtual pipe burial depth, inches
= da + 12 k/hawhere:
da = actual pipe depth to center line, inches
ha = ground to air heat transfer coefficient, Btu/hr ft2 F
Ground-to-air heat transfer coefficients are typically 1 to 3
Btu/hr sq ft F for low to moderate winds.
Soil thermal conductivity is mainly a function of moisture
content. Typical values are between 0.2 and 1 Btu/ hr ft F. Figure
900-2 gives conductivity values for some soil, sand, and rock
types, and other related materials. It also shows the relationship
between soil density and thermal conductivity.Chevron Corporation
900-5 January 1990
-
900 Pipeline Flow Fluid Flow ManualGround moisture tends to
migrate away from heated objects. Therefore, the actual soil
conductivity around a buried hot (or warm) pipeline may vary with
time and with distance from the line.
Above-Ground and Subsea PipelinesThe appropriate ambient
temperature value for above-ground lines is the yearly average air
temperature. The cases for high summer and low winter temperatures
should also be checked. For subsea lines, use the average bottom
water temperature.
The external heat transfer coefficient (ho) for above-ground and
subsea pipelines can be approximated using Equation 900-5. This
equation can accommodate thermal resistance values for an arbitrary
number of coverings on the pipeline (R1, R2, etc.). For an
above-ground pipeline, these coverings might include insulation and
pipe coatings. Subsea lines are likely to have an outside concrete
liner. For bare lines, the layer terms (R1, R2, etc.) equal zero
and are dropped from the equation.
(Eq. 900-5)
where:ho = external heat transfer coefficient, Btu/hr ft2 F
ha = ambient fluid heat transfer coefficient, Btu/hr ft2 F
R1 = thermal resistance of layer 1, hr ft2 F/Btu
R2 = thermal resistance of layer 2, hr ft2 F/Btu
rop = outside radius of outermost layer on pipe, ft
ro1 = outside radius of layer 1, ft
ro2 = outside radius of layer 2, ft
ri1 = inside radius of layer 1, ft
ri2 = inside radius of layer 2, ft
k1 = thermal conductivity of layer 1, Btu/hr ft FJanuary 1990
900-6 Chevron Corporation
-
Fluid Flow Manual 900 Pipeline Flowk2 = thermal conductivity of
layer 2, Btu/hr ft F
ln = natural logarithm
Thermal conductivity for subsea concrete (k1) coatings is about
0.5 Btu/hr ft F. Subsea ambient heat transfer coefficients (ha) are
in the low one-hundreds for moderate currents. Using ha equal to
150 Btu/hr sq ft F should give acceptable accuracy. Figure 900-1
shows approximate ambient heat transfer coefficients for air.
970 References1. Petroleum Refining, Technical Data Book.
Washington, D.C.: American Petro-
leum Institute, 1970, pp 11-47.
Fig. 900-1 Heat Loss from Hot Surfaces to AirChevron Corporation
900-7 January 1990
-
900 Pipeline Flow Fluid Flow ManualFig. 900-2 Soil Conductivity
Chart (1 of 4)
Material Conductivity, Btu/hr ft F Source
(dry density where reported)
Moisture Content
dry 2% 4% 6% 8% 10% 12% 14% 20% 30%
Soil 0.2 1
Soil (80 lb/cu ft) 0.24 0.40 0.50 0.58 2
Soil (90 lb/cu ft) 0.31 0.51 0.59 0.72 2
Soil (100 lb/cu ft) 0.61 0.73 2
Soil (110 lb/cu ft) 0.72 2
Sandy soil 0.16 2
Sand 0.20 0.60 1
White sand, clean 0.14 2
Yellow sand, clean 0.17 0.20 0.28 0.40 0.56 2
Yellow sand and clay 0.16 0.17 0.20 0.26 0.35 0.51 0.79 2
Clay 0.74 3
Fine crushed quartz
(100 lb/cu ft) 1.00 4
(110 lb/cu ft) 1.33 4
Crushed quartz
(100 lb/cu ft) 0.96 4
(110 lb/cu ft) 1.33 4
(120 lb/cu ft) 1.83 4
Graded Ottawa sand
(100 lb/cu ft) 0.83 4
(110 lb/cu ft) 1.17 4
Fairbanks sand
(100 lb/cu ft) 0.71 4
(110 lb/cu ft) 0.87 1.25 4
(120 lb/cu ft) 1.12 4January 1990 900-8 Chevron Corporation
-
Fluid Flow Manual 900 Pipeline FlowLowell sand
(100 lb/cu ft) 0.71 4
(110 lb/cu ft) 0.87 1.12 4
Chena river gravel
(110 lb/cu ft) 0.75 4
(120 lb/cu ft) 1.08 4
Crushed feldspar
(100 lb/cu ft) 0.50 4
(110 lb/cu ft) 0.62 4
(120 lb/cu ft) 0.79 4
Crushed granite
(100 lb/cu ft) 0.46 4
(110 lb/cu ft) 0.62 4
(120 lb/cu ft) 0.79 4
Dakota sandy loam
(110 lb/cu ft) 0.54 4
(120 lb/cu ft) 0.79 1.08 4
Crushed trap rock
(100 lb/cu ft) 0.42 4
(110 lb/cu ft) 0.50 4
(120 lb/cu ft) 0.58 4
Ramsey sandy loam
(100 lb/cu ft) 0.37 4
(110 lb/cu ft) 0.54 0.83 4
Fig. 900-2 Soil Conductivity Chart (2 of 4)
Material Conductivity, Btu/hr ft F Source
(dry density where reported)
Moisture Content
dry 2% 4% 6% 8% 10% 12% 14% 20% 30%Chevron Corporation 900-9
January 1990
-
900 Pipeline Flow Fluid Flow ManualNorthway fine sand
(100 lb/cu ft) 0.37 4
(110 lb/cu ft) 0.46 0.71 4
Northway sand
(100 lb/cu ft) 0.37 4
(110 lb/cu ft) 0.50 0.62 4
Healy clay
(90 lb/cu ft) 0.46 0.67 4
(100 lb/cu ft) 0.33 0.83 4
(110 lb/cu ft) 0.75 4
Fairbanks silt loam
(90 lb/cu ft) 0.42 0.62 4
(100 lb/cu ft) 0.83 4
(110 lb/cu ft) 0.75 4
Fairbanks silty clay loam
(90 lb/cu ft) 0.42 0.62 4
(100 lb/cu ft) 0.79 4
(110 lb/cu ft) 0.75 4
Northway silt loam
(90 lb/cu ft) 0.33 0.50 4
(100 lb/cu ft) 0.58 4
(110 lb/cu ft) 0.58 4
Iraq Desert Steppe 0.27 5
Iraq Desert Sand 0.49 5
Fig. 900-2 Soil Conductivity Chart (3 of 4)
Material Conductivity, Btu/hr ft F Source
(dry density where reported)
Moisture Content
dry 2% 4% 6% 8% 10% 12% 14% 20% 30%January 1990 900-10 Chevron
Corporation
-
Fluid Flow Manual 900 Pipeline FlowAbqaiq sand 1.06 5
(in a limestone trench)
Earth, coarse gravelly 0.30 3
Concrete 0.54 0.70 1
Common red brick 0.36 2
Granite 1.73-3.98 6
Limestone 1.26-1.33 6
Marble 2.07-2.94 6
Sandstone 1.83 6
Material Conductivity, Btu/hr ft F Source
Soil (fairly dry, avg. California summer) 0.25 7
Soil (wet weather, some drainage) 0.35 7
Soil (heavy rains, but ground not flooded) 0.65 7
Soil (marshy or constantly soaked) 1.00 7
Sources
1. Krieth, F. Principles of Heat Transfer. New York: Harper
& Row, 1973.
2. Flow of Hot Oil in Pipelines. Various sources. Chevron:
discontinued.
3. Eckert, E. R. G., and R. M. Drake, Jr. Heat and Mass
Transfer. New York: McGraw-Hill, 1959.
4. McAdams, W. H. Heat Transmission, 3rd ed. New York:
McGraw-Hill, 1954.
5. Journal of the Institute of Petroleum, Vol. 36, No. 321,
September, 1950.
6. Holman, J. P. Heat Transfer, 5th ed. New York: McGraw-Hill,
1981.
7. Flow of Hot Oil in Pipelines. Chevron experience. Chevron:
discontinued.
Fig. 900-2 Soil Conductivity Chart (4 of 4)
Material Conductivity, Btu/hr ft F Source
(dry density where reported)
Moisture Content
dry 2% 4% 6% 8% 10% 12% 14% 20% 30%Chevron Corporation 900-11
January 1990
-
1000 Fluid Properties
AbstractThis section discusses the viscosity and gravity
properties of Newtonian and non-Newtonian fluids as they relate to
the characterization of hydrocarbon liquids and gases. It presents
graphs and equations for estimating or calculating viscosity versus
temperature, gravity versus temperature, viscosity of blends and
brine-in-oil emulsions, etc. Relationships of pressure and flow
rate to viscosity are also discussed. Conversion tables are
included.
A general discussion of non-Newtonian waxy crude viscosity
includes basic equa-tions and analytical correlations. It covers
practical aspects, principles, and equa-tions related to the
measurement of viscosity as well as the design and use of
viscometers. Laboratory measurement of non-Newtonian flow
properties and gel strength is discussed. An overview of computer
program HOTOIL is included.
Contents Page
1010 Viscosity 1000-31011 Absolute Viscosity
1012 Kinematic Viscosity
1013 Temperature and Viscosity
1014 Viscosity Index
1015 Pressure and Viscosity1016 Flow Rate and Viscosity1017
Measurement of Viscosity
1018 Viscosity of Blends
1019 Viscosity of Brine-in-Oil Emulsions1020 Gravity 1000-321021
Example
1030 Non-Newtonian Fluids 1000-38Chevron Corporation 1000-1
March 1997
1031 Laboratory Measurement of Flow Properties
1032 Laboratory Measurement of Gel Strength
-
1000 Fluid Properties Fluid Flow Manual1033 Constitutive
Relationships
1034 Calculation of Flow Parameters
1035 Hydraulics Equations1036 Computer Program HOTOIL1037
Estimating Pipeline Restart Pressure Gradient
1038 Wax Deposition
1040 References 1000-541041 Viscosity Conversion
1042 Viscosity Data
1043 Brine-in-Oil EmulsionsMarch 1997 1000-2 Chevron
Corporation
-
Fluid Flow Manual 1000 Fluid Properties1010 ViscosityViscosity
is a measure of the internal friction or resistance of a fluid to
the relative motion of its parts. It may be regarded as the
relationship between the force applied to a fluid and the rate of
deformation produced in the fluid.
1011 Absolute ViscosityThe force F required to move a fluid
layer with surface area A located a distance D from a stationary
surface, at a velocity V, can be expressed by:
(Eq. 1000-1)The coefficient is defined as the absolute, or
dynamic, viscosity. Its metric system dimensions are as
follows:
(Eq. 1000-2)where:
F = shearing force, dynes (dyne = gram cm/sec2)V/D = velocity
gradient, sec-1
A = area of shear, cm2
Since the poise is a relatively large number, absolute viscosity
is normally expressed in centipoise (0.01 poise).The English system
expression for absolute viscosity is as follows:
(Eq. 1000-3)
or(Eq. 1000-4)
Conversion factors for absolute viscosities are included as
Figures 1000-1 through 1000-5. Chevron Corporation 1000-3 March
1997
-
1000 Fluid PropertiesFluid Flow
Manual
March 1997
1000-4Chevron Corporation
Fig. 1000-1Conversion Factors for Absolute Viscosity
-
Fluid Flow Manual 1000 Fluid PropertiesFig. 1000-2 Viscosity
ConversionFrom Various Terms to Saybolt Universal (1 of 2) Courtesy
of Hydraulic InstituteChevron Corporation 1000-5 March 1997
-
1000 Fluid Properties Fluid Flow ManualFig. 1000-2 Viscosity
ConversionFrom Various Terms to Saybolt Universal (2 of 2) Courtesy
of Hydraulic InstituteMarch 1997 1000-6 Chevron Corporation
-
Fluid Flow Manual 1000 Fluid PropertiesFig. 1000-3 Viscosity of
Common Liquids (1 of 4) Courtesy of Hydraulic InstituteChevron
Corporation 1000-7 March 1997
-
1000 Fluid Properties Fluid Flow ManualFig. 1000-3 Viscosity of
Common Liquids (2 of 4) Courtesy of Hydraulic InstituteMarch 1997
1000-8 Chevron Corporation
-
Fluid Flow Manual 1000 Fluid PropertiesFig. 1000-3 Viscosity of
Common Liquids (3 of 4) Courtesy of Hydraulic InstituteChevron
Corporation 1000-9 March 1997
-
1000 Fluid Properties Fluid Flow ManualFig. 1000-3 Viscosity of
Common Liquids (4 of 4) Courtesy of Hydraulic InstituteMarch 1997
1000-10 Chevron Corporation
-
Fluid Flow Manual 1000 Fluid Properties(1) Figure 1000-5 is
based on these equations and should provide equal accuracy.(2) The
following correction for Saybolt Universal seconds at other
temperatures, is small and usually
unnecessary:
Fig. 1000-4 Viscosity Conversion Equations
Equation for Converting Kinematic Viscosity to Flow Times(1)
where: T = flow time, seconds (or Engler degrees)V = kinematic
viscosity, centistokes (CS)D,E,F,G,H,I = constants given below
Unit D E F G H I Range (CS)
Saybolt Universal(2) seconds at 100 F
4.6324 0.03264 0.039302 0.02627 0.002397 0.00001646
>1.8
Saybolt Universal(2) seconds at 210 F
4.6635 0.00677 0.039911 0.000938 0.000280 0.00000274
>1.8
Saybolt Furol seconds at 122 F
0.47170 0.0 0.4895 -0.005213 0.0000718 0.0 >48
Saybolt Furol seconds at 210 F
0.47916 0.0 0.3797 0.0 0.0001783 0.0 >48
Redwood No. 1 seconds at 140 F
4.0984 0.0 0.038014 0.001919 0.0000278 0.00000521
>40
Redwood No. 2 seconds
0.40984 0.0 0.38014 0.01919 0.000278 0.000521 >73
Engler degrees 0.13158 0.0 1.1326 0.01040 0.00656 0.0
>1.0
Equation for Converting Flow Times to Kinematic Viscosity(1)
where: V = kinematic viscosity, centistokes (CS)T = flow time,
seconds (or Engler degrees)A,B,C = constants given below
Unit A B C Range
Saybolt Universal seconds at 100 F
0.21587 11,069 37,003 SUS >32
Saybolt Universal seconds at 210 F
0.21443 11,219 37,755 SUS >32
Saybolt Furol seconds at 122 F 2.120 8,920 27,100 SFS >25
Saybolt Furol seconds at 210 F 2.087 2,460 8,670 SFS >25
Redwood No. 1 seconds at 140 F 0.244 8,000 12,500 R1 >35
Redwood No. 2 seconds 2.44 3,410 9,550 R2 >31
Engler degrees 7.60 18.0 1.7273 E >1.000
T DV1 EV+
F GV HV2
IV3
+ + +----------------------------------------------+=
V ATBT
T3
C+---------------=
SUS CS 1 0.000061 t 100F( )+[ ]
SUS100FCS100F------------------------- =Chevron Corporation 1000-11
March 1997
-
1000 Fluid Properties Fluid Flow ManualFig. 1000-5 Viscosity
ConversionCentistokes to Saybolt Universal or Saybolt FurolMarch
1997 1000-12 Chev