Cv to GPM Conversion: Formula, Examples, and When It Applies

The Short Answer

The flow coefficient Cv and the flow rate in gallons per minute (GPM) are linked by the valve pressure drop and the fluid’s specific gravity. The conversion is Q (GPM) = Cv × √(ΔP / SG) for liquid service, where ΔP is in psi and SG is specific gravity relative to water. The same relationship rearranged gives Cv = Q × √(SG / ΔP). Both forms only apply while the liquid stays liquid across the valve — near flashing or choked conditions, the simple conversion breaks down.

What Cv Means in GPM Terms

Cv is defined so that a valve with Cv = 1 passes about 1 US gallon per minute of water at 60 °F with a 1 psi pressure drop. This definition makes the conversion between Cv and GPM direct for water-like liquids: at 1 psi, GPM equals Cv. At any other pressure drop or liquid density, the square-root relationship takes over. Because the flow through a valve grows with the square root of the pressure drop, doubling ΔP only increases the flow by about 41 percent, not by a factor of two — a point that surprises many first-time sizers.

The Conversion Formulas

Flow from Cv: Q = Cv × √(ΔP / SG)

Cv from flow: Cv = Q × √(SG / ΔP)

Where Q is in US gallons per minute, ΔP in psi, and SG is specific gravity relative to water. These two forms are the same equation seen from either side: if you know the valve, predict the flow; if you know the required flow, calculate the Cv to specify.

Worked Examples

Known	Given Values	Result
Cv to GPM	Cv = 40, ΔP = 4 psi, SG = 1.0 (water)	Q = 40 × √(4/1) = 80 GPM
Cv to GPM	Cv = 40, ΔP = 4 psi, SG = 0.8	Q = 40 × √(4/0.8) = 89.4 GPM
GPM to Cv	Need 100 GPM, ΔP = 2.25 psi, SG = 1.0	Cv = 100 × √(1/2.25) = 66.7

These are illustrative numbers to show the math; real sizing should use the exact fluid properties and the manufacturer’s data for the specific valve. The examples confirm the pattern: a lighter liquid (lower SG) passes more flow at the same Cv and ΔP.

When the Simple Conversion Does Not Apply

The square-root conversion assumes a liquid that does not change phase. Three situations break it:

• Flashing or cavitation. When the local pressure falls to vapor pressure, the liquid flashes and the flow no longer follows the liquid equation.
• Choked flow. Beyond the choke point, increasing ΔP does not increase flow, so the formula over-predicts.
• Gas or steam. Compressible flow requires expansion factors and pressure/temperature corrections; the liquid equation understates the pressure drop needed.

For gases and steam, conversion tools or the applicable sizing standard should be used instead of the liquid square-root form.

Common Unit Traps

The biggest practical error is mixing units. The formula expects US gallons per minute and psi. If the flow is given in liters per minute or the pressure in bar, convert first. Also check the specific gravity: SG is relative to water at the reference temperature, and using the wrong value shifts every result. Finally, remember that Cv is not a single number for a valve — it changes with opening — so the Cv used in a conversion should be the value at the operating position.

Where to Go Next

The meaning behind the coefficient is explained in the valve flow coefficient (Cv) guide, and a full worked example with sizing steps is available in the valve Cv calculation example.

This article provides general educational knowledge only and is not professional engineering advice.

Tags: Valve Calculations