Lohm Laws for Gas – How to Calculate Flow Resistance for Gases

Every engineer will be interested in our simple system of defining the fluid resistance of Lee components. Just as the OHM is used in the electrical industry, we find that we can use the Liquid OHM or "Lohm" to quantify the restriction of hydraulic or pneumatic components.

When using the Lohm system for pneumatics, the effect of flow in the subsonic region and the compressibility of gasses is corrected for in the Lohm calculations. The resistance to flow of any component can be expressed in Lohms.

The Lohm has been selected so that a 100 Lohm restriction will permit a flow of 250 standard liters per minute of nitrogen at a temperature of 50 deg. F, and an upstream pressure of 90 psia discharging to atmosphere.

Standard Conditions used by Lee

U.S. Standard Conditions at sea level are per ICAO STD ATMOSPHERE

Pressure .................................14.70 psia (29.92 in.Hg.)
Temperature .........................59 deg. F (518.7 deg. R)

Other References may use somewhat different conditions.

Gas vs. Liquid Calibration

Most EFS products are calibrated on gas for both gas and liquid service. Should it be necessary to use a gas calibrated component for liquid service, or a liquid calibrated component for gas service, the following factors should be considered:
  • Allowance should be made for variations in liquids/gas correlation of up to ±15%. This is caused by the response of different fluids to the orifice geometry within the product.
  • Single-orifice restrictors will correlate directly from gas to liquid service, subject to the ±15% normal variation.
  • Multi-orifice restrictors will correlate directly only when the pneumatic pressure ratio is very low. (P1/P2<1.2)
  • When Multi-orifice restrictors are used at higher pressure ratios, the gas flow will be up to 30% higher than expected from a liquid calibration. This is caused by gas compressibility which results in a non-uniform distribution of pressure drops through the restrictor.
Warning: Do not substitute hydraulic restrictors in gas applications, or vice versa, without first considering the application and correlation accuracy as discussed above.

Gas Flow

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 compressibility of low pressure gasses.

The Lohm Law for Gas Flow is:

Sonic Flow - P1/P2 > 1.9 Sub Sonic Flow - P1/P2 < 1.9

K = Gas units constant
fT = Temperature correction factor
P1 = Upstream absolute pressure (psia)
P2 = Downstream absolute pressure (psia)
Q = Gas flow (std L/min)
DeltaP = 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.

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