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