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Formulas

Density

r =

The density computation assumes perfect gas behavior which is fine for these purposes.

Velocity

V =

Critical Velocity (Sonic Velocity)

Vs = 68.1

Critical velocity is evaluated at the downstream end of each segment, where the pressure and density are lower resulting in the highest velocity within the segment.

Reynolds Number

NRE =

Friction factor

fD = 4 squared

where A = + ^0.9

Equivalent length

This is the concept of equating the friction loss in fittings to an equivalent length of straight pipe.

Definitive pipe sizing

G = 1335.6 d2

where K = fD[Leq/D]

This formula is applicable to isothermal flow conditions. Vapor flow in manifolds will more closely resemble adiabatic conditions. Solution of the adiabatic equation is complex due to the requirement for trial-and-error for both pressure and temperature. Mak showed that for pipelines of length fL/D>10 the isothermal solution for pressure drop is never more than 4% greater than the adiabatic solution (Ref 4). Thus, the use of isothermal methods is slightly conservative and well within the accuracy required for practical engineering calculations.

Gas mixture viscosity

mix = +

where f12 =

and f21 = f12

This is the Wilke estimation method (Ref 5) for the viscosity of gas mixtures. The molar average method used in this article may be 5 to 10% erroneous (resulting in a pressure drop calculation that is 1% off). The Wilke method predicts the mixture viscosity within about 1% of actual.

NOMENCLATURE

d = pipe internal diameter (in.)

D = pipe internal diameter (ft.)

f = Chen friction factor

fD = Darcy friction factor

G = mass flow rate (lb/h)

k = ratio of specific heat capacities (Cp/Cv)

K = resistance coefficient due to friction loss

LEQ = equivalent length of piping system (ft.)

Mw = molecular weight of fluid (lb/lb-mol)

NRe = Reynolds Number

P1 = upstream pressure (psia)

P2 = downstream pressure (psia)

t = fluid temperature (F)

V = fluid velocity (ft/s)

Vs = fluid sonic or critical velocity (ft/s)

yi = mole fraction of component i

r = fluid density (lb/ft3)

= fluid viscosity (cP)

e = absolute pipe roughness (ft)

 

 

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