Control valve sizing: calculating the Kv value

The Kv value states how many cubic metres of water per hour pass through a valve in a given position at a pressure drop of 1 bar. It therefore describes not the valve but the valve at a particular travel. The Kvs value is the rated value at full opening – the figure on the data sheet by which valves are graded.

In the English-speaking world the Cv value is used instead, based on US gallons per minute and 1 psi. The conversion is a fixed factor: Cv ≈ 1.156 · Kv. Both quantities are based on the IEC 60534 series; its sizing equations are in Part 2-1.

For a liquid in turbulent flow that does not vaporise in the valve:

Kv = Q · √(ρ / (1000 · Δp))

with the volume flow Q in m³/h, the density ρ in kg/m³ and the pressure drop Δp across the valve in bar. For water at 1000 kg/m³ this reduces to Kv = Q / √Δp: 30 m³/h at a pressure drop of 0.9 bar gives a Kv value of 31.6.

Density enters only under the square root, and so does pressure drop – but it is the quantity most often set wrongly. Doubling the assumed pressure drop reduces the calculated Kv value by almost 30 per cent.

The pressure drop across the valve is not an input. It is what remains when the losses in piping, equipment and fittings are subtracted from the available pressure – for instance the pump head. Those losses grow with the square of the flow, while the head of a centrifugal pump falls as flow increases.

It follows that the valve has the smallest pressure drop available at maximum flow and the largest at minimum flow. The required Kv range is therefore wider than the flow range. In the example in the table the flow changes by a factor of five, the Kv value by a factor of more than eight.

At least three points are therefore calculated – minimum, normal and maximum flow – each with the pressure drop the system actually provides in that condition.

Kvs values are graded; a value above the largest calculated Kv is selected. How far above only becomes clear from the travel. For an equal-percentage characteristic with rangeability R, Kv / Kvs = R^(h − 1), where h is the relative travel.

In the example the largest Kv value is 56.6. With Kvs 63 the valve would be about 97 per cent open at that point – with no margin at all. With Kvs 100 and a rangeability of 50:1 the three operating points lie at about 85, 71 and 31 per cent travel: normal operation sits in the upper middle, there is margin at the top, and at minimum flow the valve works far enough off the seat.

Rangeability is the ratio of Kvs to the smallest Kv value at which the characteristic is still maintained. For globe valves, values between 30:1 and 50:1 are often quoted; the data sheet governs. The smallest required Kv value must be safely above that limit.

Valve authority is the ratio of the pressure drop across the fully open valve at design flow to the pressure drop across the closed valve – that is, to the whole pressure available in the controlled section.

If it is small, the open valve takes only a small share of the pressure loss. The flow then changes sharply over the first few per cent of travel and hardly at all after that: control becomes jumpy at the bottom and ineffective at the top. The literature gives authorities from about 0.3 to 0.5 as a guide; below that, an equal-percentage characteristic is the minimum.

Authority is the reason a control valve is nearly always smaller than the line it sits in. A line-size valve almost never has enough pressure drop to control.

The equation assumes that flow grows with the square root of the pressure drop. That does not hold without limit. If the pressure at the narrowest cross-section falls to the vapour pressure, vapour bubbles form and the flow stops increasing even if the outlet pressure falls further. Under IEC 60534-2-1 the largest effective pressure drop is Δp = F_L² · (p1 − F_F · pv) – with the pressure recovery factor F_L of the valve, the inlet pressure p1, the vapour pressure pv and a factor F_F that depends on the fluid. Calculating with a larger pressure drop gives a Kv value that is too small.

An oversized control valve is rarely the result of a wrong equation. It results from margins that each party adds independently.