Cv is a valve's flow rating: the gallons per minute of 60°F water that pass through it with a 1 psi pressure drop. A higher Cv means less restriction. For water, flow equals Cv times the square root of the pressure drop, so Cv tells you how much pressure a valve will cost at your flow rate.
The formula and what it tells you
The basic water formula is short. Swagelok's valve sizing bulletin, whose graphs are based on formulas adapted from the ISA S75.01 flow equations for control valves, writes it as flow equals Cv times the square root of the pressure drop divided by the liquid's specific gravity:
q = Cv × √(Δp ÷ G)
Here q is flow in U.S. gallons per minute, Δp is the pressure drop across the valve in psi, and G is specific gravity, which is 1.0 for water. For water, that leaves q = Cv × √Δp. Cla-Val's valve data sheet prints the same relationship three ways:
- Cv = Q ÷ √ΔP
- Q = Cv × √ΔP
- ΔP = (Q ÷ Cv)²
That last one is the useful one for owners. It says pressure loss climbs with the square of the flow. Double the flow through a valve and you lose four times the pressure.
A couple of limits keep the math honest. Swagelok says valve makers find Cv by testing "with water at several flow rates," in straight pipe the same size as the valve, "so that the effects of fittings and piping size changes are not included." Its water formulas also don't apply to liquids that are boiling or flashing, slurries or very viscous liquids. And temperature "usually is ignored in liquid flow calculations because its effect is too small."
Cv vs Kv
Kv is the metric version. Spirax Sarco defines Kv as the "Flowrate in m³/h of water at a defined temperature, typically between 5 °C and 40 °C, that will create a pressure drop of one bar across a valve orifice." It's widely used in Europe.
To convert, Spirax Sarco gives Cv (US) = Kv × 1.156 099. Watch the gallons, though. Spirax also lists an Imperial Cv and warns that both a U.S. and an Imperial Cv exist, with slightly different values. A European data sheet in Kv and a U.S. sheet in Cv can describe the same valve with different numbers.
A worked example
Cla-Val's data sheet for its Model 100-01 Hytrol valve, which it calls the basic valve used in nearly all its automatic control valves, lists a Cv of 54 for the 2-inch globe pattern and 200 for the 4-inch. Run those through ΔP = (Q ÷ Cv)²:
| Valve | Flow | Arithmetic | Pressure drop |
|---|---|---|---|
| 2-inch, Cv 54 | 54 gpm | (54 ÷ 54)² | 1 psi |
| 2-inch, Cv 54 | 108 gpm | (108 ÷ 54)² | 4 psi |
| 4-inch, Cv 200 | 200 gpm | (200 ÷ 200)² | 1 psi |
| 4-inch, Cv 200 | 400 gpm | (400 ÷ 200)² | 4 psi |
Same valve, twice the flow, four times the loss. That's the whole lesson in one table. Cla-Val's sheet also turns each Cv into an equivalent length of pipe. Its 2-inch globe valve is listed as equal to about 51 feet of pipe, figured on Schedule 40 steel.
One catch: Emerson ties Cv to "a given travel," meaning how far the valve is open. Spirax Sarco calls the fully open figure Kvs. A regulating valve that's partly closed passes less than its wide-open rating, and that's the point of one.
Where it shows up in building plumbing
Pressure reducing valves and control valves. Some PRVs and automatic control valves publish a Cv by size, like the Cla-Val sheet above. Cla-Val's PRV data sheet adds that "Many factors should be considered in sizing pressure reducing valves including inlet pressure, outlet pressure and flow rates." Cv is how those factors connect. For when you need a PRV in the first place, see does my building need a pressure reducing valve.
Backflow preventers. Backflow makers usually publish a flow curve instead of a single Cv. Zurn Wilkins' sheet for its 975XL2 reduced pressure assembly has a "Flow Characteristics" chart that plots pressure loss in psi against flow in gpm for each size, with rated flow "established by approval agencies." Read your design flow off the curve and you have the pressure drop directly. A reduced pressure assembly and a PRV do different jobs, covered in PRV vs RPZ.
Line size isn't flow size. Swagelok puts it bluntly: "Valve size often is described by the nominal size of the end connections, but a more important measure is the flow that the valve can provide." Two 2-inch valves can have very different Cv ratings.
Losses stack up. Water reaching a top-floor fixture has paid for the meter, the backflow assembly, the PRV, the pipe and every fitting along the way. When several fixtures run at once, flow goes up and so do the losses. Our page on why pressure drops when multiple fixtures run walks through that diagnosis, and commercial building water pressure requirements covers boosters and PRVs.
What to do with a Cv number
- 1Get the real number. Ask for the maker's data sheet for the exact model and size, with its Cv or flow curve.
- 2Use your peak flow, not the pipe size. Plug it into ΔP = (Q ÷ Cv)².
- 3Add up the drops for every valve and assembly in series, then compare against the pressure you actually have.
- 4Check the units. U.S. Cv, Imperial Cv and Kv aren't the same number.
The glossary entry on valve flow coefficient has more on reading the spec. Sizing a replacement on a commercial service is a job for a licensed plumber or engineer. HQ's certified techs test, repair and replace domestic and irrigation backflow assemblies, and estimates are free.