Control valve sizing
Sizing a valve is one question asked two ways: for a liquid, how much drop can the trim take before the fluid vaporises; for a gas, how much before the flow chokes. This computes the required Cv and Kv, flags the regime, and checks that the valve has enough authority to actually control the loop.
| Quantity | Value | Note |
|---|---|---|
| Flow | 12.0 m³/h | Liquid, at flowing temperature |
| Specific gravity | 1.00 | Relative to water at 15 °C |
| Upstream pressure | 5.00 bar a | Absolute |
| Downstream pressure | 3.20 bar a | Absolute |
| Pressure drop | 1.80 bar | P₁ − P₂ |
| Vapour pressure | 0.020 bar a | At the flowing temperature |
| Critical pressure | 220.6 bar a | Thermodynamic, from a property table |
| Critical pressure ratio Ff | 0.957 | 0.96 − 0.28 √(Pv/Pc) |
| Recovery factor FL | 0.90 | From the valve data sheet |
| Choked drop | 4.03 bar | FL² (P₁ − Ff Pv) |
| Cavitation index σ | 2.77 | (P₁ − Pv)/(P₁ − P₂) |
| Regime | normal | Single phase through the trim |
| Required Cv | 10.34 | Select the next size up |
| Required Kv | 8.95 | Cv / 1.156 |
Size the valve at 60–80% of its rated travel at design flow. A valve selected at 100% has no room for the extra flow a real plant always asks for, and one selected at 20% will hunt.
Cv = Q √(Gf / ΔP) · Q in US gpm, ΔP in psi.
ΔP_ch = FL² (P₁ − Ff Pv) · Ff = 0.96 − 0.28 √(Pv/Pc).
Q = 1360 Cv P₁ Y √(x / (Gg T Z)) · ISA-75.01, Q in scfh, P₁ in psia, T in °R.
Y = 1 − x / (3 Fk xT) · Floored at 0.667; Fk = k/1.4.
A clear path from inputs to results.
Sizing a control valve is one question asked two ways. For a liquid, how much pressure drop can the trim take before the fluid vaporises at the vena contracta. For a gas, how much before the flow chokes at sonic velocity. Either way the answer is a valve coefficient — and a valve sized past either limit will not pass the flow its data sheet promises.
How to use
- Choose liquid or gas service.
- Enter the design flow and the specific gravity.
- Enter upstream and downstream pressures in bar absolute — not gauge.
- For a liquid, add the vapour and critical pressures; for a gas, the terminal ratio and specific-heat ratio.
- Read the required Cv and Kv, the regime, and whether the flow is choked.
The formula
Reference: IEC 60534-2-1 and ISA-75.01.01; recovery factor and terminal ratio from the valve manufacturer's data sheet.
Worked example
12 m³/h of water dropping 5.0 to 3.2 bar
- Liquid flow 12 m³/h, specific gravity 1.0.
- Upstream 5.0 bar a, downstream 3.2 bar a.
- Vapour pressure 0.02 bar a, critical pressure 220.64 bar a.
- Recovery factor FL 0.9.
- 1
The working drop is 1.8 bar, which is 26.1 psi.
- 2
12 m³/h is 52.8 US gpm.
- 3
Cv = 52.8 × √(1.0 / 26.1) = 10.34, and Kv = 10.34 / 1.156 = 8.95.
- 4
Ff = 0.96 − 0.28 √(0.02/220.64) = 0.957.
- 5
The choked drop is 0.9² × (5.0 − 0.957 × 0.02) = 4.03 bar, well above the working 1.8 bar.
- 6
So the valve is not choked, and the cavitation index (5.0 − 0.02)/1.8 = 2.77 is comfortable.
Cv 10.34 · Kv 8.95 · not choked · σ 2.77.
Interpreting the result
The two numbers that matter are the coefficient and the regime. A valve selected at Cv 10.3 should be the next standard size above — a Cv 11 or 12 body — because a valve that runs at 100% of rated travel has no headroom for the extra flow a real plant always asks for. The regime tells you whether more pressure will buy more flow: past the choked drop, it will not.
Assumptions & limitations
- Pressures are absolute. A gauge reading will size the valve about 1 bar wrong, which is significant at these drops.
- The liquid is Newtonian and single-phase upstream; flashing downstream is flagged but not modelled as two-phase flow.
- The recovery factor FL and terminal ratio xT come from the valve data sheet, not from a generic default.
- Cv is in US customary units (gpm at 1 psi) and Kv in metric (m³/h at 1 bar); they differ by exactly 1.156.
- The gas equation uses the ISA constant of 1360 with flow in scfh, pressure in psia and temperature in °R, converted internally.
- Noise, cavitation damage and trim erosion are not modelled.
Frequently asked questions
What is the difference between Cv and Kv?
They measure the same thing in different units: Cv is US gallons per minute of water at a 1 psi drop, Kv is cubic metres per hour at a 1 bar drop. Kv = Cv / 1.156. Mixing them is a silent 16% sizing error that usually surfaces at commissioning.
What is cavitation and how is it different from flashing?
Both start with the liquid vaporising at the vena contracta. In cavitation the pressure recovers downstream and the bubbles collapse, damaging the trim. In flashing the downstream pressure stays below the vapour pressure, so the valve passes a two-phase mixture and never recovers.
Where should the valve sit in its travel at design flow?
Between 60% and 80%. Selecting at 100% leaves no room for the extra flow the plant will eventually ask for; selecting at 20% means the valve hunts and wears out. Size for the design flow, then check the minimum controllable flow against the rangeability.
What does choked flow mean?
For a gas, the velocity in the trim reaches sonic and no further pressure drop increases the flow. For a liquid, the pressure at the vena contracta falls below the vapour pressure and the flow stops responding to downstream pressure. Past that point the valve is a fixed restriction.
What is valve authority?
The valve's share of the circuit's total pressure drop at full flow. Below about 0.3 the valve cannot control the low end of the range, because most of the drop is elsewhere in the circuit. Above 0.5 the installed characteristic matches the data sheet.
Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.