When selecting components for use in a gas system, certain factors must be considered which arise only because of the compressibility of the gaseous medium. The nature of gas compressibility is defined by the following two rules.

Boyle's Law – | The pressure and specific volume of a gas are inversely proportional to each other under conditions of constant temperature. |

Charles' Law – | The pressure and temperature of a gas are directly proportional to each other when the volume is held constant, and the volume and temperature are directly proportional when the pressure is held constant. |

Thus, a gas will expand to fill any container, and pressure and temperature will adjust to values consistent with the above rules. Gas flowing through valves and restrictors will be subject to an increasing specific volume as pressure drops take place, and temperatures will change as determined by the Joule-Thompson effect.

The combination of the above rules forms the basis for the “Equation of State" for perfect gases. This allows either pressure, temperature, or volume to be calculated for a known quantity of gas when the other two variables are known.

i.e. | p V = m R T | (click here for values of the Gas Constant, R) |

In general, the following comments apply to gas flow.

- Gas flow at high pressure ratios (P
_{1}/P_{2}> 1.9) is directly proportional to the upstream absolute pressure (click here). - Gas flow at moderate pressure ratios (P
_{1}/P_{2}< 1.9) is proportional to the down- stream absolute pressure, and to the pressure differential (click here). - Gas flow at low pressure ratios (P
_{1}/P_{2}< 1.1) is proportional to the pressure differential, similar to hydraulic flow. - When restrictions appear in series, the most downstream restrictor dominates in the determination of flow rate.
- When the absolute pressure ratio across a restrictor is above 1.9, the gas velocity will reach the speed of sound (sonic flow) in the restrictor throat. When restrictors appear in series the overall pressure ratio must be higher to achieve sonic flow.
- When equal restrictors appear in series, sonic flow can only occur in the most down- stream restrictor.
- Velocity of the gas stream cannot exceed the speed of sound in either a constant area duct, or a converging section.

The Rule of Forbidden Signals:*

“The effect of pressure changes produced by a body moving at a speed faster than the speed of sound cannot reach points ahead of the body."

This rule can be applied to pneumatic flow restrictors where the body is not moving, but the flow velocity relative to the body can reach, or exceed, the speed of sound. Whenever the downstream pressure is low enough to produce Mach 1 at the restrictor throat, any effect of changes in the downstream pressure cannot reach points upstream of the throat. Thus, **flow rate will be independent of downstream pressure**. This situation applies to a single orifice restrictor flowing air when the overall pressure ratio exceeds 1.89/1.

*von Kármán, Jour. Aero. Sci., Vol. 14, No. 7 (1947)

When selecting components for use in a gas system, certain factors must be considered which arise only because of the compressibility of the gaseous medium. The nature of gas compressibility is defined by the following two rules.

Boyle's Law – | The pressure and specific volume of a gas are inversely proportional to each other under conditions of constant temperature. |

Charles' Law – | The pressure and temperature of a gas are directly proportional to each other when the volume is held constant, and the volume and temperature are directly proportional when the pressure is held constant. |

Thus, a gas will expand to fill any container, and pressure and temperature will adjust to values consistent with the above rules. Gas flowing through valves and restrictors will be subject to an increasing specific volume as pressure drops take place, and temperatures will change as determined by the Joule-Thompson effect.

The combination of the above rules forms the basis for the “Equation of State" for perfect gases. This allows either pressure, temperature, or volume to be calculated for a known quantity of gas when the other two variables are known.

i.e. | p V = m R T | (click here for values of the Gas Constant, R) |

In general, the following comments apply to gas flow.

- Gas flow at high pressure ratios (P
_{1}/P_{2}> 1.9) is directly proportional to the upstream absolute pressure (click here). - Gas flow at moderate pressure ratios (P
_{1}/P_{2}< 1.9) is proportional to the down- stream absolute pressure, and to the pressure differential (click here). - Gas flow at low pressure ratios (P
_{1}/P_{2}< 1.1) is proportional to the pressure differential, similar to hydraulic flow. - When restrictions appear in series, the most downstream restrictor dominates in the determination of flow rate.
- When the absolute pressure ratio across a restrictor is above 1.9, the gas velocity will reach the speed of sound (sonic flow) in the restrictor throat. When restrictors appear in series the overall pressure ratio must be higher to achieve sonic flow.
- When equal restrictors appear in series, sonic flow can only occur in the most down- stream restrictor.
- Velocity of the gas stream cannot exceed the speed of sound in either a constant area duct, or a converging section.

The Rule of Forbidden Signals:*

“The effect of pressure changes produced by a body moving at a speed faster than the speed of sound cannot reach points ahead of the body."

This rule can be applied to pneumatic flow restrictors where the body is not moving, but the flow velocity relative to the body can reach, or exceed, the speed of sound. Whenever the downstream pressure is low enough to produce Mach 1 at the restrictor throat, any effect of changes in the downstream pressure cannot reach points upstream of the throat. Thus, **flow rate will be independent of downstream pressure**. This situation applies to a single orifice restrictor flowing air when the overall pressure ratio exceeds 1.89/1.

*von Kármán, Jour. Aero. Sci., Vol. 14, No. 7 (1947)