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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