Valve Flow Coefficients: Understanding Cv, Kv, and Flow Calculations

The flow coefficient of a valve, designated Cv in the US customary system and Kv in the metric system, is the fundamental parameter used to size control valves and evaluate the pressure drop through fully open isolation valves. The Cv value quantifies the valve's hydraulic capacity: how much flow it passes at a given pressure drop. Proper understanding of Cv and the equations that relate it to flow rate, pressure drop, and fluid properties is essential for engineers who size control valves, calculate system pressure drops, and evaluate whether existing valves have sufficient capacity for new or modified process conditions.

Definition and Measurement of Cv

The Cv of a valve is numerically defined as the flow rate of water in US gallons per minute that passes through the valve at a pressure drop of 1 PSI at 60 degrees Fahrenheit. This seemingly arbitrary definition has the advantage of making Cv a pure numeric constant for a given valve opening position that captures all the geometric complexity of the valve flow passage in a single number. Cv values are measured experimentally by flowing water through the valve at multiple flow rates while measuring the upstream and downstream pressures, then calculating the Cv from the resulting data. Manufacturers publish Cv values at rated travel (full open) and at multiple intermediate positions to define the flow characteristic.

• Cv definition: GPM of water at 1 PSI drop and 60°F, dimensionless capacity index

• Kv conversion: Kv equals 0.865 times Cv (metric system, cubic meters per hour at 1 bar drop)

• Cv at full open: maximum capacity rating of the valve

• Cv vs. travel curve: defines the inherent flow characteristic of the control valve

• Valve sizing: required Cv calculated from design flow rate and available pressure drop

Cv Equations for Liquid Service

For incompressible liquid flow through a control valve, the ISA standard sizing equation relates Cv to flow rate and pressure drop. For non-flashing liquid service (pressure drop less than about half the difference between inlet pressure and fluid vapor pressure), the equation is Cv equals Q divided by N1 times Fp times the square root of the quantity (delta P divided by Gf), where Q is flow rate in GPM, N1 is a numerical constant (1.0 for US units), Fp is the piping geometry correction factor, delta P is the pressure drop across the valve in PSI, and Gf is the specific gravity of the liquid relative to water at 60 degrees Fahrenheit. When significant pressure drop causes the liquid to flash, a choked flow correction factor is applied.

Cv Equations for Gas and Steam

Compressible flow through control valves requires different sizing equations that account for the density changes as gas expands across the pressure drop. For gas service, the ISA equation includes factors for the gas expansion due to pressure drop, critical pressure ratio (choked flow conditions), and compressibility. The key concept is that gas flow becomes choked (independent of outlet pressure) when the pressure drop ratio exceeds a critical value that depends on the specific heat ratio of the gas and the valve's pressure recovery factor. For steam, equivalent sizing equations using steam specific volume or steam tables account for the steam state (superheated or saturated). Most valve manufacturers provide selection software that performs these calculations automatically when given the inlet pressure, outlet pressure, temperature, and fluid properties.