Flow coefficient (Cv and Kv) for a liquid-service control valve, with a choked-flow / cavitation check.
Kv = Q · √(SG / ΔP); Cv = 1.156 · Kv
How it works
The flow coefficient expresses how much flow a valve passes per unit pressure drop. The tool sizes for liquid turbulent flow and checks whether the differential exceeds the choked-flow limit, where cavitation or flashing begins.
Worked example
50 m³/h of water across a 600 → 400 kPa drop (ΔP = 200 kPa). Requires Cv ≈ 41 (Kv ≈ 35); size the valve so this is ~60–80% of its rated Cv.
Inputs
Flow rate (m³/h)
Inlet pressure (kPa)
Outlet pressure (kPa)
Specific gravity
Vapor pressure (optional) (kPa abs) — At flowing temp — enables the choked-flow check.
Pressure recovery factor FL — From the valve maker (globe ≈ 0.9, ball ≈ 0.6).
Liquid critical pressure ratio FF — ≈ 0.96 − 0.28·√(Pv/Pc); 0.9 is a common default.
Frequently asked questions
What's the difference between Cv and Kv?
They're the same idea in different units. Cv uses US gpm and psi; Kv uses m³/h and bar. They're related by Cv = 1.156 · Kv.
What is choked flow in a control valve?
When the pressure drop is large enough, the liquid flashes or cavitates at the vena contracta and extra ΔP no longer increases flow. Size on the choked ΔP limit, and expect noise, vibration, and damage if you operate there.
Does this work for gas or steam?
No — compressible service needs the gas sizing equation with the expansion factor Y and pressure-drop ratio xT. This tool is liquid-only.
Assumptions
Turbulent, fully developed liquid flow; no Reynolds-number (FR) correction.
Piping geometry factor Fp = 1 (line-size valve, no reducers).
Choked check uses ΔP_choked = FL²(P1 − FF·Pv); confirm FL and FF from the valve manufacturer.
Gas/vapor service is not covered — that needs the compressible-flow equation (Y, xT).
Size the valve so the rated Cv gives roughly 60–80% opening at normal flow.
References
ANSI/ISA-75.01.01 / IEC 60534-2-1 — control valve sizing equations.
Cv = 1.156·Kv; liquid turbulent form Kv = Q√(SG/ΔP).
Related Fluid Mechanics tools
Pipe Pressure Drop — Frictional ΔP and head loss for single-phase flow in a circular pipe (Darcy–Weisbach, Swamee–Jain friction factor).
Fittings Pressure Drop (K-factors) — Minor losses through elbows, tees, and valves by the ΣK excess-head method — the companion to straight-pipe friction.
Pipe Velocity & Reynolds — Line velocity, Reynolds number, and flow regime from flow rate and pipe inside diameter.
Friction Factor (Moody) — Darcy (and Fanning) friction factor from Reynolds number and relative roughness — Colebrook–White solved exactly, with the Swamee–Jain explicit fit for comparison.