Valve Cv Calculator (Liquid · Gas · Steam)
Size shutoff and throttling valves with the ISA-75.01 / IEC 60534-2-1 equations (Emerson/Fisher handbook form). Liquid sizing with Cv = Q·√(SG/ΔP), gas sizing with the expansion factor Y, automatic choked-flow detection, and reverse solve modes for known-Cv valves.
ρ₁ = – lb/ft³ (from P₁)
Required Cv
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Comparison at Selected NPS
Typical published rated Cv of full-port valves (reference only — confirm with the manufacturer).
Equation in Use
Typical Rated Cv of Full-Port Valves by NPS
| NPS | Ball valve Cv | Gate valve Cv | Globe valve Cv | Ball ÷ Globe |
|---|
Typical published reference values for full-port valves (±25% between manufacturers). A globe valve's contoured plug sacrifices roughly 4–5× flow capacity versus a full-port ball valve of the same size.
Methodology (ISA-75.01 / Fisher handbook)
The three equations
Liquid: Cv = Q · √(SG/ΔP)
Gas: Cv = Q/(N8·P1·Y) · √(G_g·T1·Z/x)
Y = 1 − x/(3·F_k·x_T), F_k = k/1.4, x = ΔP/P1
Steam: Cv = w/(N6·Y·√(ΔP·P1·ρ1))
choked when x ≥ F_k·x_T (Y floors at 2/3)
The gas form is the expansion-factor formulation of ISA-75.01 / IEC 60534-2-1 as presented in the Emerson/Fisher Control Valve Handbook: the expansion factor Y models the density collapse at the vena contracta, and the choking parameter x_T marks where flow becomes sonic and stops responding to additional ΔP.
Reading the results
- Choked warning — for liquids when ΔP ≥ F_L²·P1; for gases when x ≥ F_k·x_T. Beyond choking, more ΔP buys no more flow — size up the valve instead.
- Reverse modes — ΔP-from-Cv solves Y·√(x) = constant by bisection; if the target exceeds the choking capacity, the calculator tells you the valve is undersized.
- Steam uses the mass-flow form with saturated-steam density interpolated from inlet pressure; superheat shifts density slightly and is approximated via T₁.
- F_L and x_T are per-style reference values — use the manufacturer's data for final sizing.
These equations size the orifice, not the valve body: for line-size valves (common for ball, gate, check) the body is chosen one or two sizes up from the calculated Cv.
Frequently Asked Questions
What is valve Cv?+
Cv is the valve flow coefficient: the number of US gallons per minute of water at 60 °F that flows through a fully open valve with a pressure drop of exactly 1 psi. A valve with Cv = 100 passes 100 gpm of water at 1 psi ΔP, or 50 gpm at 4 psi ΔP. Higher Cv means lower flow resistance.
How do you calculate Cv for a liquid?+
For turbulent, non-choked liquid flow: Cv = Q·√(SG/ΔP), where Q is flow in gpm, SG is specific gravity relative to water, and ΔP is the pressure drop in psi. Example: 150 gpm of diesel (SG 0.85) at 12 psi ΔP needs Cv = 150·√(0.85/12) ≈ 40.
How do you calculate Cv for a gas?+
Using the ISA-75.01 / Fisher expansion-factor form implemented here: Cv = Q / (N8·P1·Y) · √(G_g·T1·Z/x), with Q in scfh, P1 in psia, T1 in °R, x = ΔP/P1 and expansion factor Y = 1 − x/(3·F_k·x_T), F_k = k/1.4. Non-choked results apply for x < F_k·x_T.
What is choked flow and how is it detected?+
Choked flow occurs when increasing the pressure drop no longer increases flow. For gases, choking begins when x = ΔP/P1 reaches F_k·x_T (for a full-port ball valve x_T ≈ 0.25, so choking starts near x ≈ 0.25). For liquids, the simplified screen is ΔP ≥ F_L²·P1. The calculator flags choked results and reports the maximum flow at the choking pressure ratio.
What is the expansion factor Y?+
Y corrects for the gas density change between the valve inlet and the vena contracta as the gas expands. In the Fisher/ISA convention Y = 1 − x/(3·F_k·x_T): it equals 1 at very small ΔP and floors at 2/3 when the flow chokes. Ignoring Y overstates Cv by 10–30% at typical pressure ratios.
How is steam sized differently?+
Steam is handled with the mass-flow form of the equation: Cv = w / (N6·Y·√(ΔP·P1·ρ1)), where w is mass flow in lb/h and ρ1 is the inlet saturated-steam density in lb/ft³ (interpolated from a steam table by inlet pressure). Superheat is approximated by raising the inlet temperature input; for precise design use manufacturer sizing software.
What are typical Cv values by valve type and size?+
Full-port valves of the same NPS differ enormously: a 2" full-port ball valve has Cv ≈ 420, a 2" gate valve ≈ 380, while a 2" globe valve is only ≈ 100. At 6" the gap widens: ball ≈ 5,000, gate ≈ 4,500, globe ≈ 1,100. The comparison table on this page shows published typical values — always confirm against the manufacturer's published Cv.
Can I work backwards from a known Cv?+
Yes — use the reverse modes. "Max flow from known Cv" computes the flow at a given pressure drop (with choked-flow capping), and "Pressure drop from known Cv" solves the expansion-factor equation iteratively for ΔP, warning you if the valve is undersized even at choking conditions.
Related Engineering Tools
Disclaimer: Cv calculations follow the ISA-75.01 / IEC 60534-2-1 simplified equations for preliminary sizing only. F_L and x_T are reference values per valve style, not manufacturer data; two-phase flow, cavitation damage limits, noise, and flashing are not evaluated. For final valve selection — especially control valves, safety-related service or high-pressure-drop gas duty — use the manufacturer's sizing software and verify with the manufacturer's published coefficients.