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How to Calculate Flow Resistance for Gases

The Lohm Laws extend the definition of Lohms for gas flow at any pressure and temperature, and with any gas. The formulas work well for all gases because they are corrected for the specific gas, and for the flow region and incompressibility of low pressure gases.

The Lohm Law for Gas Flow is: Nomenclature
K = Gas units constant (see tables below)
fT = Temperature correction factor (see graph below)
P1 = Upstream absolute pressure (psia)
P2 = Downstream absolute pressure (psia)
Q = Gas flow (std L/min.)
ΔP = P1 - P2 (psid)

All you have to do is:
Compute the P1/P2 pressure ratio.
Select the correct formula for the flow region.
Look up the value of "K" for the gas.
Look up the temperature correction factor, "fT".
Use the formula to solve for the unknown.

Temperature Correction Factor Lohm Laws - Gas Flow EXAMPLE: What restriction will permit a flow of 1.00 std L/min. of nitrogen at 90°F, with supply pressure at 5 psig, discharging to atmosphere?

K = 276 (see tables below)
T1 = 90 fT = 0.98
P1 = 5.0 + 14.7 = 19.7 psia, P2 = 14.7 psia
P1/P2 = 19.7/14.7 = 1.34 (subsonic)
ΔP = 5.0 psid
Q = 1.00 std L/min. Units Constant "K" for Gas Flow

To eliminate the need to convert pressure and flow parameters into specific units such as "psia" and "std L/min.", the tables below list values of the Units Constant "K", which is used in the Gas Flow Lohm Formulas:  (Sonic: P1/P2 ≥ 1.9) (Subsonic: P1/P2 < 1.9)

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Units Constant "K" for Volumetric Flow
Abs. Pres psia bar kPa mm/Hg
Flow SLPM SCFM in3/min SLPM SCFM SLPM mL/min
H2 1030 36.3 62,700 14,900 526 149 19,900
He 771 27.2 47,100 11,200 395 112 14,900
Neon 343 12.1 20,900 4980 176 49.8 6640
Nat. Gas 319 11.3 19,400 4620 163 46.2 6160
N2 276 9.73 16,800 4000 141 40.0 5330
CO 274 9.69 16,700 3980 141 39.8 5300
Air 271 9.56 16,500 3930 139 39.3 5230
Ethane 251 8.86 15,300 3640 129 36.4 4850
O2 257 9.08 15,700 3730 132 37.3 4970
Argon 245 8.65 14,900 3550 125 35.5 4730
CO2 213 7.52 13,000 3090 109 30.9 4110
N2O 214 7.56 13,100 3100 110 31.0 4140
SO2 176 6.21 10,700 2550 90.1 25.5 3400
Freon-12 123 4.34 7510 1780 63.0 17.8 2380

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Units Constant "K" for Gravimetric Flow
Abs. Pres psia bar kPa mm/Hg
Flow PPH lbm/s kg/min. PPH kg/min. kg/min. gm/min.
H2 11.6 0.00322 0.0876 168 1.27 0.0127 1.69
He 17.3 0.00479 0.131 250 1.89 0.0189 2.52
Neon 38.7 0.0108 0.293 561 4.25 0.0425 5.66
Nat. Gas 34.8 0.00966 0.263 505 3.82 0.0382 5.09
N2 43.2 0.0120 0.326 626 4.73 0.0473 6.31
CO 43.0 0.0119 0.325 623 4.71 0.0471 6.28
Air 43.8 0.0122 0.331 636 4.81 0.0481 6.41
Ethane 42.2 0.0117 0.319 611 4.62 0.0462 6.16
O2 46.0 0.0128 0.348 667 5.04 0.0504 6.72
Argon 54.6 0.0152 0.413 792 5.99 0.0599 7.99
CO2 52.4 0.0145 0.396 759 5.74 0.0574 7.65
N2O 52.7 0.0146 0.398 764 5.77 0.0577 7.70
SO2 63.0 0.0175 0.476 914 6.91 0.0691 9.21
Freon-12 83.2 0.0231 0.629 1210 9.12 0.0912 12.2

EXAMPLE: A restrictor must flow 8.20 std L/min. of helium at room temperature (70°F), with an inlet pressure of 1,500 kPa, discharging to atmosphere. What Lohm rate is required?

K = 112 (see tables above)
T1 = 70°F. , fT = 1.00 (see Temperature Correction Factor graph above)
P1 = 1,500 kPa, P2 = 101 kPa
P1/P2 = 14.9 (sonic) EXAMPLE: A restrictor must flow 0.0015 lbm / s of oxygen at room temperature (70°F), with an inlet pressure of 1,200 psia, discharging to 850 psia. What Lohm rate is required?

K = 0.0128 (see tables above)
T1 = 70°F , fT = 1.00
P1 = 1,200 psia. , P2 = 850 psia.
P1/P2 = 1.41 (subsonic)
ΔP = 350 psid.
w = 0.0015 lbm / s 