Gas-flow coefficient calculations depend on pressure ratio because a compressible gas can reach sonic velocity at a restriction. Swagelok’s simplified valve-sizing bulletin separates a low pressure-drop branch from a high pressure-drop branch and defines Cv, gas specific gravity, absolute pressures, upstream temperature and unit constants. These equations are useful for understanding the variables and checking an estimate; they are not a substitute for the applicable control-valve standard or a valve maker’s sizing software.

Gas valve flow coefficients and formulas

Conditions and units

Let p₁ be absolute upstream pressure, p₂ be absolute downstream pressure, and Δp = p₁−p₂. Gas specific gravity Gg is relative to air, with air equal to 1. T₁ is the absolute upstream temperature. The standard-flow basis must also match the unit constant N₂. For the U.S. row, the bulletin uses standard cubic feet per minute with pressure in psia and temperature in degrees Rankine; it lists N₂ as 22.67. Do not enter gauge pressure directly into the equations. Convert °F to °R or °C to K as shown.

The low pressure-drop relation applies when p₂ is greater than one-half of p₁. As p₂ falls toward half of p₁, the pressure ratio factor reduces the available flow. At p₂ below half of p₁, the simplified source uses the choked-flow branch, where further reduction of outlet pressure does not increase the predicted flow. The boundary belongs to this bulletin’s simplified model; control valves require their specific pressure-drop ratio and recovery data.

Worked example for a choked-flow estimate

Suppose an air system uses p₁ = 100 psia, T₁ = 520 °R, Gg = 1, and a valve with Cv = 1.0. At p₂ = 40 psia, the pressure ratio is below one-half, so use the high-pressure-drop equation. With N₂ = 22.67, q is approximately 0.471 × 22.67 × 100 × √(1/520), or about 46.8 standard ft³/min. If p₂ is reduced further, this simplified branch predicts the same flow because the gas is already choked. This is a worked check of the bulletin’s model, not a certified capacity for a specific installed valve.

To convert coefficient units, the Emerson Fisher handbook lists Kv = 0.865 × Cv. This is a unit conversion between customary and metric flow coefficients; it does not correct a valve for different trim, gas, piping geometry or installed conditions. A catalog Cv is measured for a particular valve and test setup.

Common mistakes

First, gauge pressure and absolute pressure are not interchangeable in a gas equation. Second, do not use a liquid square-root pressure-drop equation for a compressible gas. Third, do not assume air properties for a different gas: Gg, compressibility, molecular weight and temperature basis can change capacity. Fourth, do not use a simple half-pressure rule for final control-valve sizing when the valve’s recovery factor and choking ratio are available. The bulletin says its ideal-gas approach does not cover gases near liquefaction. For control valves, follow the current harmonized ISA/IEC sizing method and the exact manufacturer data.

Sources: Swagelok Valve Sizing Technical Bulletin and Emerson Fisher Control Valve Handbook.

The coefficient Cv is tied to a valve’s tested capacity and flow convention; it is not a property of the gas alone. In the equations, pressure and temperature must be absolute, while Δp is the difference between the two absolute pressures. Convert the upstream temperature before substitution and keep the standard flow reference consistent. A unit constant is valid only with the exact combination of flow, pressure and temperature units listed next to it. Mixing standard litres per minute with the U.S. constant changes the result substantially.

Swagelok’s bulletin describes these simplified air-like gas relationships and says the formulas do not apply near gas liquefaction. Control valves often need additional parameters, including pressure recovery, expansion factors, piping geometry and gas compressibility. For a design with safety or process consequences, use the current IEC 60534 / ANSI-ISA procedure and vendor sizing software with the actual valve trim and process data.