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)

f_{T} = Temperature correction factor (see graph below)

P_{1} = Upstream absolute pressure (psia)

P_{2} = Downstream absolute pressure (psia)

Q = Gas flow (std L/min.)

ΔP = P_{1} - P_{2} (psid)

**All you have to do is:**

Compute the P_{1}/P_{2} 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, "f_{T}".

Use the formula to solve for the unknown.

**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)

T_{1} = 90 f_{T} = 0.98

P_{1} = 5.0 + 14.7 = 19.7 psia, P_{2} = 14.7 psia

P_{1}/P_{2} = 19.7/14.7 = 1.34 (subsonic)

ΔP = 5.0 psid

Q = 1.00 std L/min.

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: P_{1}/P_{2} ≥ 1.9) |
(Subsonic: P_{1}/P_{2} < 1.9) |

*Swipe to the right for more table information*

Units Constant "K" for Volumetric Flow | |||||||
---|---|---|---|---|---|---|---|

Abs. Pres | psia | bar | kPa | mm/Hg | |||

Flow | SLPM | SCFM | in^{3}/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 |

O_{2} |
257 | 9.08 | 15,700 | 3730 | 132 | 37.3 | 4970 |

Argon |
245 | 8.65 | 14,900 | 3550 | 125 | 35.5 | 4730 |

CO_{2} |
213 | 7.52 | 13,000 | 3090 | 109 | 30.9 | 4110 |

N_{2}O |
214 | 7.56 | 13,100 | 3100 | 110 | 31.0 | 4140 |

SO_{2} |
176 | 6.21 | 10,700 | 2550 | 90.1 | 25.5 | 3400 |

Freon-12 |
123 | 4.34 | 7510 | 1780 | 63.0 | 17.8 | 2380 |

*Swipe to the right for more table information*

Units Constant "K" for Gravimetric Flow |
|||||||
---|---|---|---|---|---|---|---|

Abs. Pres | psia | bar | kPa | mm/Hg | |||

Flow | PPH | lb_{m}/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 |

O_{2} |
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 |

CO_{2} |
52.4 | 0.0145 | 0.396 | 759 | 5.74 | 0.0574 | 7.65 |

N_{2}O |
52.7 | 0.0146 | 0.398 | 764 | 5.77 | 0.0577 | 7.70 |

SO_{2} |
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)

T_{1} = 70°F. , f_{T} = 1.00 (see Temperature Correction Factor graph above)

P_{1} = 1,500 kPa, P_{2} = 101 kPa

P_{1}/P_{2} = 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)

T_{1} = 70°F , f_{T} = 1.00

P_{1} = 1,200 psia. , P_{2} = 850 psia.

P_{1}/P_{2} = 1.41 (subsonic)

ΔP = 350 psid.

w = 0.0015 lb_{m} / s