What compressibility changes
A liquid arrives at the valve outlet with the same density it had at the inlet. A gas does not — it expands as pressure falls, so the volumetric flow at the outlet exceeds that at the inlet and the simple square-root relationship breaks down. IEC 60534 handles this with two additions to the liquid form:
Y falls from 1.0 (negligible drop, behaving almost like a liquid) to exactly 0.667 at full choking. That floor is not a coincidence — it is what the equation gives when x is clipped at its terminal value.
The choked flow rule
When x reaches Fγ·xT, velocity at the vena contracta goes sonic. Lowering downstream pressure further buys no extra flow at all. The sizing consequence is specific: you must substitute the choked value of x into the equation, not the actual larger one. Use the real x and the maths quietly returns a Cv that is too small — the valve will be undersized in service, and the error is invisible unless you check for choking explicitly. This calculator clips x automatically and tells you when it has.
Worked example
500 Nm³/h of air, P₁ = 6 bar abs, ΔP = 2 bar, 40 °C, globe valve (xT = 0.72), γ = 1.4:
- x = 2 ÷ 6 = 0.333; Fγ = 1.0, so xchoked = 0.72 → not choked
- Y = 1 − 0.333 ÷ (3 × 0.72) = 0.846
- Kv = 500 ÷ (4.17 × 6 × 0.846 × √(0.333 ÷ 313.15)) ≈ 723
- Cv = 1.156 × 723 ≈ 836 — and with margin, select a valve rated near 1,100
Raise ΔP to 5 bar and x becomes 0.833, above the 0.72 limit: the flow chokes, Y sits at 0.667, and the extra 3 bar of drop delivers nothing but noise and erosion.
Field notes
- Choked gas valves are loud. Sonic velocity at the trim generates aerodynamic noise that routinely exceeds 85 dBA — noise-attenuating trim or downstream diffusers are a design consequence, not an afterthought.
- xT is a valve property, so it changes the answer a lot. A butterfly valve chokes at x ≈ 0.25 where a globe valve keeps going to 0.72; rotary valves reach choking far earlier than people expect.
- Confirm the flow reference. Nm³/h at 0 °C and Sm³/h at 15 °C differ by over 5% before sizing even starts — see the actual ↔ standard converter.
- For steam, get the density right: take ρ₁ from the saturated steam table at the inlet pressure, and remember that a steam control valve is really controlling temperature through pressure.
- Liquid service uses a different equation — the liquid Cv calculator, with cavitation rather than choking as the failure mode. Sizing philosophy and travel targets are covered in our valve sizing guide.
Frequently asked questions
Why is gas valve sizing different from liquid?
Gas expands as it passes through the valve, so the density at the outlet differs from the inlet. The expansion factor Y accounts for that, and beyond a limiting pressure ratio the flow chokes — further pressure drop produces no additional flow, which cannot happen with an incompressible liquid.
What is choked flow in a control valve?
When the pressure drop ratio x = ΔP/P1 reaches the terminal value Fγ·xT, the velocity at the vena contracta reaches sonic and flow stops responding to further downstream pressure reduction. Sizing must use the choked value of x, not the actual one — otherwise the valve is undersized.
What is the xT factor?
The pressure drop ratio factor at choked flow, a property of the valve style: roughly 0.72 for a globe valve with parabolic plug, 0.75 for cage-guided, 0.25 for a butterfly valve and 0.15 for a full-bore ball. Vendor data should be used when available.
What is the expansion factor Y?
Y = 1 − x ÷ (3·Fγ·xT), ranging from 1.0 at negligible pressure drop down to 0.667 at fully choked flow. It corrects for the density change of the expanding gas across the valve.
Implements the IEC 60534 / ISA-75.01 compressible sizing relationships without piping geometry (Fp) or Reynolds corrections, for reference and education. Final selection must use vendor sizing software and the full standard. See our disclaimer.