Calculate single phase gas pipeline pressure loss using the Darcy Weisbach equation.
`Po = √(P^2 - m^2(fd.L / D + K) ls (16mma.SG.ZRoT)/(pi^2D^4) ) / (es) `
`ss = (z2 - z2) SG.mma.g / (Ro T Z) `
`es = e^(ss) `
`ls = (es^2 - 1) / (ss) `
where :
Po = outlet pressure
P = inlet pressure
fd = Darcy friction factor
L = piping length
D = piping inside diameter
K = total friction loss factor for fittings
m = gas mole flowrategas
mma = air molar mass
SG = gas specific gravity
Z = gas compressibility factor
Ro = universal gas constant
T = gas temperature
g = gravity constant
zi = inlet elevation
zo = outlet elevation
ss = elevation exponent
es = elevation pressure factor
ls = elevation length factor
For low Reynolds numbers Re < 2000, the fluid flow is laminar and the Darcy friction factor should be calculated using the Hagen-Poiseuille laminar flow equation. For high Reynolds numbers Re > 4000, the fluid flow is turbulent and the Darcy friction factor should be calculated using one of the turbulent flow equations. In the transition region 2000 < Re < 4000, the flow is unstable and the friction loss cannot be reliably calculated. The minor loss K factor is used to account for pipeline fittings such as bends, tees, valves etc..
The calculators use the Darcy-Weisbach pressure loss equation with the Darcy friction factor. The Fanning transmission factor combined with the Fanning equation is commonly used for gas flow. The results for the Darcy and Fanning equations are identical provided that the correct friction factor is used.
The gas specific gravity is the ratio of gas density over the density of dry air at base temperature and pressure. The compressibility factor is assumed to equal 1 at the base conditions. The gas specific gravity is proportional to the gas molar mass.
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