LOGOS Learning · 19
Control valve sizing step by step: Cv formula, choked flow and travel
For a turbulent, non-choked liquid with a line-size valve, IEC 60534 reduces to Kv = Q * sqrt(G / dP), and Cv = 1.156 * Kv. In the worked example, 50 m3/h at 1.2 bar needs Kv 45.6 and 15 m3/h at 2.7 bar needs Kv 9.1; a Kv 100 equal-percentage valve runs between 38.8 % and 79.9 % travel.
A control valve on a pumped water line must pass 15 to 50 m³/h. With the pressures the process gives in each condition, we will find the required Kv, check for choked flow, pick the rated Kv and see at what travel the valve will run.
- Step 1 of 8
Process data
Always size for at least two conditions: maximum and minimum flow, each with the real upstream and downstream pressures. At minimum flow the pump climbs its curve and the valve holds more ΔP.
Qmax = 50 m³/h · P1 = 6.0 · P2 = 4.8 bar(g)
Qmin = 15 m³/h · P1 = 6.8 · P2 = 4.1 bar(g)
Formulas in plain text
- Required Kv (liquid, IEC 60534 simplified)
Kv = Q * sqrt(G / dP) ; Cv = 1.156 * Kv- Kv = flow coefficient (m3/h at 1 bar drop) · Cv = flow coefficient (US gpm at 1 psi drop) · Q = flow (m3/h) · G = relative density to water (-) · dP = P1 - P2 across the valve (bar)
- Choked-flow limit
dP_choked = FL^2 * (P1 - FF * Pv), FF = 0.96 - 0.28 * sqrt(Pv / Pc)- FL = liquid pressure recovery factor (-) · FF = liquid critical pressure ratio factor (-) · P1 = upstream absolute pressure (bar a) · Pv = vapor pressure (bar a) · Pc = critical pressure of the liquid (bar a) · if dP >= dP_choked, size with dP_choked
- Equal-percentage characteristic
Kv(x) = Kv100 * R^(x - 1)- x = valve travel (fraction 0 to 1) · Kv100 = rated Kv at full travel · R = rangeability (50 in the example)
- Travel at a required Kv
x = 1 + ln(Kv / Kv100) / ln(R)- target: about 20 % <= x <= 90 % at Qmin and Qmax
Frequently asked questions
How to convert Kv to Cv?
Cv = 1.156 * Kv, and Kv = 0.865 * Cv. Kv is the flow in m3/h of water with a 1 bar drop; Cv is the flow in US gallons per minute with a 1 psi drop.
What is choked flow in a control valve?
When the pressure at the vena contracta falls to the vapor pressure, the liquid flashes and the flow stops growing with dP. IEC 60534 sets the limit dP_choked = FL^2 * (P1 - FF * Pv); in the example dP stays well below it at both conditions.
What travel should a control valve run at?
A common rule is roughly 20 % to 90 % travel between minimum and maximum flow. Near closed the valve is unstable and erodes; near fully open it has no authority left to raise the flow.
Why size a control valve for two conditions?
The available dP changes with flow: at minimum flow the pump climbs its curve and the valve holds more pressure drop. Checking Qmax and Qmin with their real pressures ensures the chosen Kv controls at both ends.