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THE HISTORY OF MODERN PIPELINE EQUATION
GROUP 2
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VISCOSITY EFFECT
ROUGHNESS OF PIPE WALL
FRICTION LOSSES
FRICTION LOSSES
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WALL SHEAR STRESS
KINETIC ENERGY PER UNIT VOLUME
FRICTION FACTOR
FRICTION FACTOR
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Fanning eq. Darcy-Weisbach Moody
FANNING, DARCY-WEISBACH,MOODY
f = 4f’
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• Ratio of fluid momentum forces to viscous shear forceDEFINITION
• Distinguish laminar and turbulent flowPURPOSE
THE REYNOLDS NUMBER, NRE
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BASIC EQ AND NATURAL GAS FLOW
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absolute roughness/
internal diameter
e/D
RELATIVE ROUGHNESS
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Hagen
Poiseuille
Moody
f = f(NRE, e/D)
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f = 64/NRE
LAMINAR SINGLE PHASE FLOW
!
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Smooth Wall Pipe
Rough Wall Pipe
! TURBULENT
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Gas Flow Equation
Weymouth Equation
Clinedinst EquationOliphant Equation
Panhandle’s Equation
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Panhandle’s Equati
on Panhandle A
Panhandle B
Develop in 1940s
Develop in 1956
• The friction factor is a function of
Reynold’s number.• Design for large diameter and long
pipelines.
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EQUATION OF PANHANDLE A
f varies with NRE
Pipeline Flow equation
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EQUATION OF PANHANDLE B
f varies with NRE
Pipeline Flow equation
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OLIPHANT EQUATION
1) Designed for low pressure gathering system
2) Extensively use for vacuum and low pressure (25-35 psig)
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0.
5
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WEYMOUTH EQUATION
Calculate the flow rate and pressure losses in
horizontal pipeline
w/o modifications, its being used for pipelines
operating in 35-100 psig
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Modified eq.
f varies with diameter
Original eq.
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No mechanical work steady flow isothermal flow constant compressibility factor horizontal flow no kinetic energy changes.
ASSUMPTIONS
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When discussing this topic, we will only consider Weymouth equation:
SERIES VS PARALLEL
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Consider an L-mile long, DA-in. internal diameter operating with total pressure drop of p1-p2.
SERIES
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The pipeline is altered by replacing the first LB miles with a DB-in. internal diameter line) and value of pressure drop, p1-p2 is constant.
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Using Weymouth equation, and since p1-p2 is constant, the equation can be written as:
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where K is a constant. The equivalent length of a DA-in. line, L’A that would have the same pressure drop as LB miles of DB – in. line is:
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Therefore, the series line shown have a total equivalent length of:
Percent of change in flow rate :
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The equivalent lengths and diameters can be expressed as:
If Weymouth equation with friction factor f is used, the equation will become:
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If there are more than 2 pipes in series, the equation will become:
In term of friction factor, f :
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Consider L-mile, DA-in. internal diameter. Suppose the full length is paralleled with new DB-in. internal diameter.
PARALLEL
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Old flow rate using only DA-in. line = qA . New flow rate with both lines is qt = qA + qb. The length, L is constant. Using Weymouth equation:
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The ratio of new to old flow rates is:
Pressure increase in capacity is:
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If the length of the two parallel lines is not equal, this equation shall be used:
The ratio of the flow rates becomes:
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Those equations may be extended to more than 2 lines in parallel. It will become:
In terms of friction factor,f:
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