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Weymouth, Panhandle A and Bequations for Compressible Gas

Flow

For high pressure gas.Compute Flow, Diameter, Length,

Pressures

To: Darcy-Weisbach incompressible flow calculator

Choked gas flow Gas flow conversions (mass, standard, actual)

LMNO Engineering home page Unit Conversions Trouble printing?

Register to enable "Calculate" button.

Units: acfd=actual cfd, acfh=actual cfh, acfm=actual cfm, cfd=cubic foot per day, cfh=cubic foot per hour,

cfm=cubic foot per minute, cfs=cubic foot per second, cm=centimeter, hr=hour, kg=kilogram, km=kilometer,

lb=pound, m=meter, mm=millimeter, Mcfh=thousand cfh, MMcfd=million cfd, N/m2=Newton per square meter

(same as Pascal), s=second, psi=pound per square inch, psia=psi (absolute), psig=psi (gage), scfd=std cfd,

scfh=std cfh, scfm=std cfm, std=standard conditions (60F, 14.7 psia).

Introduction

The Weymouth, Panhandle A, and Panhandle B equations were developed to simulate compressible gas flow in

long pipelines. The Weymouth is the oldest and most common of the three. It was developed in 1912. The

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Panhandle A was developed in the 1940s and Panhandle B in 1956 (GPSA, 1998). The equations were

developed from the fundamental energy equation for compressible flow, but each has a special representation of

the friction factor to allow the equations to be solved analytically. The Weymouth equation is the most common

of the three - probably because it has been around the longest. The equations were developed for turbulent flow

in long pipelines. For low flows, low pressures, or short pipes, they may not be applicable.

If the pressure drop in a pipeline is less than 40% of P1, then our Darcy-Weisbach incompressible flow

calculation may be more accurate than the Weymouth or Panhandles for a short pipe or low flow. The Darcy-

Weisbach incompressible method is valid for any flowrate, diameter, and pipe length, but does not account for

gas compressibility. Crane (1988) states that if the pressure drop is less than 10% of P1 and you use an

incompressible model, then the gas density should be based on either the upstream or the downstream

conditions. If the pressure drop is between 10% and 40%, then the density used in an incompressible flow

method should be based on the average of the upstream and downstream conditions. If the pressure drop

exceeds 40% of P1, then use a compressible model, like the Weymouth, Panhandle A, or Panhandle B. You can

always run all models and compare the results.

Equations

The equations are shown below. The Weymouth, Panhandle A, and Panhandle B equations (GPSA, 1998;

Crane, 1988) are the equation beginning with Qs=... with the constants c, n, u, x, and y defined below. All of

the equations shown below use the English units indicated in the Variables section. Of course, our calculationuses a variety of units with all of the unit conversions handled internally by the program.

Variables:The units refer to the units that must be used in the equations shown above. However, a variety of units may be

used in our calculation.A = Pipeline cross-sectional area.

c = Constant. Weymouth: c=18.0625, Panhandle A: c=18.16125, Panhandle B: c=30.7083D = Pipe inside diameter [inch].

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E = Efficiency factor. Typically 0.85 to 1.0. The lower the number, the rougher (or older) the pipe. Typical

value is 0.92.L = Pipeline length [mile].

n = Constant. Weymouth: n=2.6667, Panhandle A: n=2.6182, Panhandle B: n=2.53P = Absolute pressure in pipeline [psia, i.e. pounds per square inch absolute].

Q = Volumetric flowrate [cfh, i.e. cubic foot per hour]S = Specific gravity of gas in pipeline, relative to air. That is, the ratio of the gas's molecular weight to the

molecular weight of air [unit-less].

T = Absolute temperature [Rankine]. Note: oR=oF+459.67u = Constant. Weymouth: u=1.0, Panhandle A: u=1.0788, Panhandle B: u=1.02

V = Velocity of gas = Q/A.W = Mass flowrate [lb/hr, i.e. pounds per hour].

Z = Gas compressibility. Value typically 1.0 at standard conditions. Typically decreases as pressure increases.

Can be as low as 0.4 or so. Exact computation depends on make-up of the gas, gas critical pressure andtemperature, and actual temperature and pressure.

p = Greek letter rho. Density [lb/ft3, i.e. pounds per cubic foot]. Note that the equation for ps uses a value of

1.0 for the compressibility.

Subscripts:1 = Upstream conditions.

2 = Downstream conditions.atm = Atmospheric conditions (14.73 psia).

s = Standard conditions (520 R, 14.73 psia)

Error Messages given by calculation

"Need D>0", "Need L>0", "Need S>0", "Need Qs>0", "Need W>0", "Need E,Z > 0". These are initial

checks. Diameter, length, specific gravity, and flows must be positive numbers.

"Need T>0 K", "Need P1>0 absolute", "Need P2>0 absolute", "Need P1>P2". Temperature must be

greater than absolute zero. Pressures must be greater than 0 absolute. And, pressure difference must be positive.

Since you may have entered temperature in other units or pressure as gage, the calculation does some initialcomputations to determine the validity of the input.

"P1 too small". This message can appear if P2 is being computed. P2 must be computed as less than P1, or

flow will not occur from 1 to 2.

References

Crane Co. 1988. Flow of Fluids through Valves, Fittings, and Pipe. Technical Paper 40 (TP-40). http://www.craneco.com

GPSA (Gas Processors Suppliers Association). Engineering Data Book. 11ed. 1998. http://gpsa.gasprocessors.com

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