Control Valve Sizing: Kv, Cv, Flow Characteristic and Valve Authority

Kv is the flow of water in m³/h that passes through a fully open valve at a differential pressure of 1 bar, with water between 5 and 40 °C. Cv states the same idea in US units: flow in US gpm at 1 psi differential with 60 °F water. The two convert by a fixed ratio, Cv ≈ 1.156 × Kv and Kv ≈ 0.865 × Cv, so comparing catalogue figures without checking which letter is printed builds in a systematic error of about 16 percent.

For liquids the working equation is Kv = Q × √(SG / Δp), with Q in m³/h, Δp in bar and SG the specific gravity relative to water. Passing 40 m³/h of water across 0.8 bar therefore calls for a Kv of about 44.7 m³/h. That figure is the capacity the valve must reach wide open, not the valve you should order: a valve sitting at full travel has no control range left.

Manufacturers publish Kv against travel rather than as a single number, and the Kv100 value on a data sheet describes only the fully open condition. A sound control valve selection puts three Kv values, for minimum, normal and maximum flow, on the same travel curve. Where those three points land tells you almost everything about the quality of the selection.

Liquids are treated as incompressible, so flow rises with the square root of Δp. Gases and vapours expand inside the valve and lose density as they cross the restriction, which is why the liquid equation no longer holds. IEC 60534-2-1 handles the difference with an expansion factor Y and a pressure drop ratio x = Δp / P1 expressed in absolute pressures.

The defining event in compressible flow is choking: velocity at the narrowest section reaches sonic conditions and further Δp buys no extra flow. The threshold is not one universal ratio but a property of the valve, captured by its xT coefficient in the criterion x > Fγ × xT. On globe valves xT is typically 0.70 to 0.75; on butterfly and ball valves it is only 0.25 to 0.40, so a butterfly valve can choke at a Δp of roughly a quarter of the inlet pressure. Sizing past that point overstates the flow the valve will actually deliver.

Steam is sized on mass flow in kg/h together with inlet specific volume. Superheat lowers density, so the same kg/h needs a larger Kv than saturated steam at the same pressure. On saturated lines, quote inlet pressure and saturation temperature together; a line item reading only '8 bar steam' leaves the sizing to guesswork.

The flow characteristic describes how Kv changes with travel and is produced by the trim geometry. A linear trim gives Kv in direct proportion to travel, so 50 percent travel delivers roughly 50 percent of Kv100. An equal percentage trim produces an equal percentage change in Kv for every equal increment of travel, following Kv = Kv100 × R^(h−1), where inherent rangeability R is typically 30:1 to 50:1 on globe valves.

A quick opening trim delivers most of its capacity within the first 30 percent of travel. It is not a modulating characteristic and belongs on on/off, safety and rapid fill duties. A concentric butterfly disc behaves roughly like an equal percentage curve, while segmented V-port ball trims are shaped deliberately to approximate equal percentage.

The selection rule is short. If differential pressure across the valve falls noticeably as flow rises, choose equal percentage; if it stays nearly constant, choose linear. Most systems fed by a centrifugal pump have a falling head curve, which is why equal percentage is the default trim on process lines. Where valve authority is above 0.50 a linear trim also performs well, which is the usual case on constant-differential bypass legs and level control loops.

Valve authority is the pressure drop across the fully open valve divided by the total pressure drop of the circuit: N = Δp(valve, open) / Δp(total). It measures how much of its inherent characteristic the valve keeps once installed. As authority approaches 1 the installed curve resembles the inherent curve; as it falls the curve flattens, and an equal percentage valve starts behaving linearly while a linear valve behaves like quick opening.

The accepted floor is 0.25, and process control work usually targets 0.30 to 0.50. Drop to an authority of 0.10 and a linear trim already passes more than half its flow within the first 20 percent of travel, so the controller meets an extremely high process gain in that narrow band. The result is hunting around setpoint and an actuator that never stops moving.

Authority is bought with energy: every bar deliberately held across the valve shows up in pump shaft power. Authority targets and pump selection therefore have to be optimised together, and that trade-off sits at the centre of energy efficiency in process lines. Variable speed pumping reduces the throttling margin, but the control valve still should not be pushed below 0.25 authority.

The most common sizing error is specifying a control valve at line size. On most process lines the control valve is one or two nominal sizes smaller than the pipe, so a DN80 or DN65 valve with concentric reducers in a DN100 line is a normal answer. Doubling Kv in the name of safety margin simply pushes the operating point below 20 percent travel.

In a healthy selection, normal flow sits at 50 to 70 percent travel, minimum flow stays above 20 percent and maximum flow below 85 percent. Below 10 percent opening the local velocity between plug and seat multiplies, and erosion, noise and vibration accelerate with it. Shut-off performance in that region also becomes questionable, which is why a seat leakage class such as ANSI/FCI 70-2 Class IV or Class VI belongs in the specification.

Oversizing is measurable damage rather than a hypothetical risk. A valve chosen at twice the required capacity shows markedly shorter trim life and more frequent packing leaks. Going one size up typically adds something in the 20 to 40 percent band to the purchase price, and that gap is repaid several times over in lost control quality and early trim replacement.

Liquid accelerates through the narrowest section of the valve and its static pressure falls accordingly. If that pressure drops below the vapour pressure Pv of the fluid at operating temperature, bubbles form. If downstream pressure recovers above Pv the bubbles collapse violently, which is cavitation. If pressure stays below Pv the fluid continues as vapour, and the phenomenon is called flashing.

The boundary is quantified by the allowable pressure drop: Δp(allowable) = FL² × (P1 − FF × Pv). That figure marks choked flow, meaning fully developed cavitation; bubble formation and noise begin below it. FL is the liquid pressure recovery factor and FF the critical pressure ratio factor; FL is typically 0.85 to 0.95 on globe valves but only 0.50 to 0.70 on butterfly and ball valves. Low-FL, high-recovery designs cavitate far earlier at the same Δp, which is the numerical reason a butterfly valve is a poor choice for high differential throttling.

If the calculation exceeds that limit, the answer is not a bigger valve. Multi-stage trim, a drilled cage or two valves in series split the drop so each stage stays below the cavitation threshold. In flashing service there is no bubble collapse, so erosion moves downstream and calls for hardened trim and an expanded outlet. On a liquid line, valve noise above 85 dB(A) usually points to cavitation rather than to flow turbulence alone, and early diagnosis within a cavitation and preventive maintenance programme keeps trim costs down.

A valve with the right Kv, the right characteristic and adequate authority will still destabilise a loop if it moves slowly or imprecisely. The variable that decides this is deadband: the change in control signal needed before the valve starts to move after a reversal. Packing friction, actuator spring preload and linkage backlash all enlarge it.

Without a positioner, assembly deadband easily reaches 2 to 5 percent. A well-tuned positioner brings that below 1 percent and resolution below 0.5 percent, and field studies treat 1 percent deadband as the practical ceiling for a well-behaved loop. In a PID loop with integral action, deadband above 2 percent tends to drive a limit cycle around setpoint that never settles.

Positioner selection covers 4-20 mA input, HART or digital communication, air consumption and stroking speed together. On large double-acting assemblies a volume booster shortens stroke time, and pneumatic actuator sizing should run alongside the valve calculation rather than after it. During commissioning, record two-directional position error at 5, 25, 50, 75 and 95 percent of travel.

A good quotation needs good data. Sizing requires fluid type and temperature, minimum, normal and maximum flow, P1 and P2 at all three points, vapour and critical pressure, density or specific gravity, and line size and pressure class. Without those seven items the calculation is at best a selection padded with safety margin.

The specification should state the travel percentages at the three operating points rather than a bare Kv100, together with target valve authority, flow characteristic, expected FL or xT, seat leakage class and positioner type. On the actuator side, name the ISO 5211 mounting, air supply pressure and fail position, fail-open or fail-close.

Within valve and valve control systems, Vanera runs the Kv calculation from your process data, reports the characteristic and authority check and shows the cavitation margin numerically. Send us the line data and you get two alternative configurations compared at the travel percentages of all three operating points, with the matching actuator and positioner named in the same quotation.