Inputs

For incompressible, non-flashing liquid service using the basic liquid Cv relation. For viscous, flashing, cavitating, two-phase, gas, or steam service, use a full valve-sizing method and manufacturer data.

Solve for

Liquid specific gravity

For water density at temperature, see the water properties reference. Use the reference-water density specified by your Cv data to calculate SG.

Flow rate

Flow unit

Pressure drop

Pressure unit

Results

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Flow rate

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Pressure drop

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Equation

Q(gpm) = Cv √(ΔP(psi) / SG)

The US Cv definition uses US gallons per minute and psi. Kv is also reported using the conversion Cv = 1.156099 Kv. This simple equation does not include corrections for high viscosity, choked liquid flow, flashing, cavitation, piping geometry factors, or valve-specific recovery behavior.

Worked examples: Cv, flow rate, and pressure drop

Use US gpm and psi in these equations. All three examples assume a single-phase liquid with specific gravity SG = 1, negligible viscosity corrections, and no flashing or choked flow.

1. Calculate the required valve Cv

Select Cv under Solve for. Enter SG = 1, flow = 100 gpm, and pressure drop = 10 psi.

Cv = Q × √(SG / ΔP) = 100 × √(1 / 10) = 31.6228

The required Cv is approximately 31.6. Check the manufacturer's Cv at the intended valve opening before selecting a valve.

2. Calculate flow rate from Cv

Select Flow rate. Enter SG = 1, Cv = 30, and pressure drop = 10 psi.

Q = Cv × √(ΔP / SG) = 30 × √(10 / 1) = 94.8683 gpm

This is approximately 21.5469 m³/h. Cv alone does not determine flow; pressure drop and liquid specific gravity are also needed.

3. Calculate pressure drop across a valve

Select Pressure drop. Enter SG = 1, flow = 100 gpm, and Cv = 30.

ΔP = SG × (Q / Cv)² = 1 × (100 / 30)² = 11.1111 psi

This is approximately 76.6084 kPa. It is the valve pressure drop only; add pipe and fitting losses separately.

What Cv means

Cv is a valve flow-capacity coefficient. In the traditional U.S. liquid definition, Cv is related to water-like liquid flow in gpm, pressure drop in psi, and liquid specific gravity. A larger Cv means more flow capacity at the same pressure drop. Cv is a property of a particular valve size, trim, and opening position, not simply the nominal pipe size.

This calculator uses the basic incompressible liquid relation Q = Cv√(ΔP/SG). It is appropriate for quick calculations when the liquid is not flashing or choked and viscosity effects are small. Full control-valve sizing can require additional factors for valve geometry, attached reducers, liquid pressure recovery, viscosity, cavitation, and choked flow.

When to use it

Estimating required Cv for a non-flashing liquid service.
Estimating flow through a valve when Cv and available pressure drop are known.
Estimating valve pressure drop at a known flow and Cv.
Comparing candidate valve capacities at a preliminary design stage.

Assumptions and limits

Single-phase, incompressible liquid service.
The basic turbulent-flow Cv relation is adequate for the service.
The entered Cv corresponds to the actual valve opening, size, and trim.
Specific gravity is referenced to water using the vendor sizing convention.
No correction is made here for attached reducers, high viscosity, flashing, cavitation, or liquid choking.

Common mistakes

Choosing a valve from line size alone. Valve size and required Cv are related but not interchangeable.
Using the wide-open Cv for a throttled operating point. Control valves have a Cv-versus-travel characteristic supplied by the manufacturer.
Ignoring choking or flashing. Once local pressure falls sufficiently, increasing downstream pressure drop may not produce the flow increase predicted by the simple equation.
Ignoring viscosity corrections. Very viscous liquids or low-Reynolds-number valve flow can require a corrected sizing method.
Using gas or steam in the liquid equation. Compressible sizing requires different equations and additional thermodynamic inputs. See the gas control valve sizing calculator for its supported gas-service model and limits.

Design note

The calculated Cv is a capacity requirement, not a final valve selection. Final sizing should check the manufacturer's published Cv data, travel, rangeability, noise, cavitation or flashing risk, allowable pressure drop, materials, actuator requirements, and the applicable control-valve sizing standard.

For line losses outside the valve, use the Pipe Friction Loss Calculator. For pump duty created by the required flow and pressure, use the Pump Power Calculator.

Reference background: Emerson's Control Valve Handbook covers liquid Cv sizing, viscosity corrections, pressure recovery, cavitation, and choked flow. Control Valve Handbook.

K-factor reference

K-Factor Guide ↗ · Look up typical fitting losses and check velocity bases, fT correlations, equivalent length, and valve data.

Equation values and input guide

Choose Cv, flow or valve pressure drop as the unknown. Enter liquid specific gravity at operating conditions. Compare required Cv with the manufacturer’s Cv-versus-travel curve, not just its fully open Cv.

Q: Liquid volume flow in US gpm in the displayed equation; other selected input units are converted.
Cv: US valve flow coefficient: numerically the water flow in US gpm producing a 1 psi valve pressure drop under its rating conditions. It is not pipe diameter or valve size.
ΔP: Pressure drop across the valve in psi in this equation. Do not substitute total system pressure loss unless it all occurs at this valve.
SG: Liquid specific gravity relative to water, dimensionless. Use the actual liquid at its operating condition. This simple equation does not apply to choked, flashing or gas flow.

Use the unit selectors beside the inputs. Units shown in the equations must be consistent when checking the math by hand.