How to Calculate Valve Cv: Liquid, Gas & Steam Worked Examples
Quick answer
For a liquid, the required valve Cv isCv = Q·√(SG/ΔP) — flow in gpm, ΔP in psi. For agas, use the ISA-75.01 expansion-factor equationCv = Q/(N8·P1·Y)·√(G_g·T1·Z/x) with Y = 1 − x/(3·F_k·x_T). For steam, use the mass-flow form Cv = w/(N6·Y·√(ΔP·P1·ρ1)). If the pressure ratio x = ΔP/P1 exceeds F_k·x_T (gas) or ΔP ≥ F_L²·P1 (liquid), the flow is choked and more ΔP will not pass more fluid. Worked examples for all three below — or skip the math and use thevalve Cv calculator.
1. What Cv Actually Measures
Cv is the valve flow coefficient: the number of US gallons per minute of 60 °F water that passes through the fully open valve at a pressure drop of exactly 1 psi. It is the industry's single most-used number for comparing flow capacity, because it folds the valve's internal geometry — seat bore, plug shape, disc angle — into one experimentally measured figure.
Three practical consequences:
- →Cv scales with the square of size. A 4" full-port ball valve (Cv ≈ 1,900) carries about 4.5× the flow of a 2" valve (Cv ≈ 420), not 2×.
- →Cv is comparable across manufacturers only for the same valve style — a globe valve's Cv is inherently 4–5× below a ball valve of the same NPS.
- →Cv is not a rating. It says nothing about pressure class, shutoff class, or cavitation limits — those come from ASME B16.34 and the seat design.
| NPS | Full-port ball Cv | Full-port gate Cv | Globe Cv |
|---|---|---|---|
| 2" | ≈ 420 | ≈ 380 | ≈ 100 |
| 4" | ≈ 1,900 | ≈ 1,700 | ≈ 420 |
| 6" | ≈ 5,000 | ≈ 4,500 | ≈ 1,100 |
Typical published reference values; real catalog values vary ±25%.
2. Liquid Sizing, Step by Step
The turbulent, non-choked liquid equation is refreshingly short:
Worked example. A cooling-water branch must pass 150 gpm of treated water (SG = 1.0) across a control valve dropping from 85 psig to 70 psig.
- ΔP = 85 − 70 = 15 psi.
- Cv = 150 · √(1.0 / 15) = 150 · 0.258 = 38.7.
- Check choking: for a globe valve F_L ≈ 0.9, so F_L²·P1 = 0.81 × 99.7 psia ≈ 81 psi — our 15 psi ΔP is far below. Not choked. ✓
- Select one size up: a 2" globe valve (Cv ≈ 100) or a 1.5" ball valve (Cv ≈ 230) depending on whether throttling or isolation is the duty.
For anything but water, only the specific gravity changes: diesel (SG 0.85) at the same duty needs Cv = 150·√(0.85/15) = 35.7. Viscous fluids above ~40 cSt need a viscosity correction (the F_R factor in ISA-75.01), which the basic equation ignores.
Skip the Spreadsheet
The calculator runs all three fluid equations with choked-flow detection and reverse solve modes.
Open the Valve Cv Calculator →3. Gas Sizing with the Expansion Factor Y
Gases compress, so the liquid equation fails. The ISA-75.01 / Fisher handbook form adds the pressure ratio x = ΔP/P1 and the expansion factor Y, which models the density collapse at the vena contracta:
Cv = Q / (N8 · P1 · Y) · √(G_g · T1 · Z / x)
Y = 1 − x / (3 · F_k · x_T), F_k = k / 1.4, N8 = 19.3
Worked example. A nitrogen header at 100 psia, 80 °F must vent 20,000 scfh through a full-port ball valve (x_T ≈ 0.25) to a 75 psia flare.
- x = (100 − 75)/100 = 0.25.
- Nitrogen: k = 1.40 → F_k = 1.00; choking threshold F_k·x_T = 0.25 — we are exactly at the choking boundary (flag this).
- Y = 1 − 0.25/(3 × 0.25) = 0.667 (the floor value).
- T1 = 80 + 460 = 540 °R; G_g = 0.967; Z ≈ 1.
- Cv = 20,000 / (19.3 × 100 × 0.667) · √(0.967 × 540 / 0.25) ≈ 15.5 × 45.7 ≈ 709.
- A 3" full-port ball valve (Cv ≈ 1,100) covers it with margin; at the choking boundary, any increase in ΔP buys zero extra flow.
Notice how strongly Y penalizes high pressure ratios: at x = 0.25, Y = 0.667, meaning the valve passes only two-thirds of what the incompressible equation would predict. Ignoring Y under-sizes gas valves by 10–30% in typical process duty.
4. Choked Flow: When More ΔP Stops Helping
Choked flow is the single most-misunderstood concept in valve sizing. Past the choking point, the velocity at the vena contracta reaches sonic; the valve passes its maximum flow, and any additional pressure drop simply dissipates downstream as noise and vibration.
| Fluid | Choking criterion | What to do when choked |
|---|---|---|
| Liquid | ΔP ≥ F_L²·(P1 − F_F·P_v); simplified screen ΔP ≥ F_L²·P1 | Cap ΔP at the choking value; select a larger valve or multi-stage trim; check for cavitation damage and noise |
| Gas / steam | x = ΔP/P1 ≥ F_k·x_T (Y floors at 2/3) | Flow is capped at the choking pressure ratio; increase Cv — more ΔP is wasted energy |
Valve style matters enormously: a globe valve (x_T ≈ 0.70) resists choking, while a full-port ball valve (x_T ≈ 0.25) chokes at a quarter of the inlet pressure. That is one reason ball valves make poor pressure-reducing devices despite their high Cv.
5. Steam Sizing
Steam is most conveniently sized by mass flow, since process steam is specified in kg/h or lb/h:
Worked example. A steam trap bypass must pass 4,000 lb/h of saturated steam at 150 psia through a globe valve into a 110 psia header. From the steam table, ρ1 at 150 psia ≈ 0.332 lb/ft³.
- x = (150 − 110)/150 = 0.267.
- Steam k ≈ 1.3 → F_k ≈ 0.93; choking threshold 0.93 × 0.70 ≈ 0.65. Not choked. ✓
- Y = 1 − 0.267/(3 × 0.65) = 0.863.
- Cv = 4,000 / (2.09 × 0.863 × √(40 × 150 × 0.332)) = 4,000 / (1.804 × 44.7) ≈ 49.6.
- A 2" globe valve (Cv ≈ 100) provides healthy margin; verify noise level if the ΔP were higher.
Superheat shifts ρ1 downward (hotter steam is less dense); sizing on saturated density at the same pressure is slightly conservative, which is acceptable for preliminary sizing.
6. Reverse Problems: Flow or ΔP from a Known Cv
Field engineers often face the inverse question: the valve is already installed, the tag says Cv = 300 — what will it pass, or what ΔP will it develop at the required flow?
- →Liquid flow: Q = Cv·√(ΔP/SG) — direct substitution. Cv 300 at 25 psi water: Q = 300 × 5 = 1,500 gpm.
- →Gas ΔP: solve Y(x)·√x = Q·√(G_g·T1·Z)/(Cv·N8·P1) by bisection on x ∈ (0, F_k·x_T). If the target exceeds the choking capacity Y·√x at x = F_k·x_T, no ΔP exists — the valve is undersized.
- →Gas flow: Q = Cv·N8·P1·Y·√(x/(G_g·T1·Z)), using the choked value Y = 2/3 when x ≥ F_k·x_T.
The valve Cv calculatorimplements both reverse modes with the bisection solver built in — including the "undersized even at choking" diagnostic that spreadsheets miss.
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Liquid, gas and steam modes · choked-flow warnings · reverse solving — free, in your browser.
Valve Cv Calculator →Frequently Asked Questions
What is the formula for valve Cv?
For liquids: Cv = Q·√(SG/ΔP), with Q in gpm and ΔP in psi. For gases, the ISA-75.01 expansion-factor form: Cv = Q/(N8·P1·Y)·√(G_g·T1·Z/x), where x = ΔP/P1 and Y = 1 − x/(3·F_k·x_T). For steam, use the mass-flow form Cv = w/(N6·Y·√(ΔP·P1·ρ1)).
What is choked flow in a valve?
Choked flow is the condition where increasing pressure drop no longer increases flow. For gases it begins when x = ΔP/P1 reaches F_k·x_T; for liquids the simplified screen is ΔP ≥ F_L²·P1. A valve operated choked is at its maximum capacity regardless of how much more ΔP is available.
What is a typical Cv for a 2 inch ball valve?
A full-port 2" ball valve typically has Cv ≈ 420 (published values range roughly 380–460). A 2" gate valve is similar at ≈ 380, while a 2" globe valve is only ≈ 100 — the contoured plug sacrifices 4–5× flow capacity.
What units does the Cv formula use?
US customary: flow in gpm (liquid) or scfh at 14.696 psia/60 °F (gas), pressures in psia, temperature in °Rankine for gas, mass flow in lb/h for steam. Constants: N8 = 19.3, N6 = 2.09.
Should I pick a valve exactly at the calculated Cv?
No. Control valves are typically selected so the operating opening sits around 60–80% of rated travel, with 10–20% headroom; shutoff valves (ball/gate/check) are usually line-size regardless of the calculated Cv, because their rated Cv far exceeds the duty.