Engineering task and calculation objective
The CAV module calculates control valves for liquids and gases. Its core task is determining the required flow coefficient Kv from flow rate, pressure differential, and the fluid properties of the medium – the basis for selecting a valve with a suitable Kvs value from a manufacturer's series. Anyone who wants to size a control valve or calculate the Kv value must correctly identify the actual flow condition: the module distinguishes subcritical and critical (choked) flow conditions, laminar flow, and liquid or gaseous inlet.
For liquids, the risk of cavitation and flashing is additionally assessed: if the static pressure in the vena contracta drops below the vapour pressure of the liquid, the manufacturer's critical flow factor limits the achievable flow – more pressure differential then yields no additional flow, only noise and wear. For gases, the critical pressure ratio limits the flow. Pipe reducers immediately upstream and downstream of the valve are also captured with correction factors.
Characteristic data for valves from various manufacturers can be integrated via files or addressed externally, so sizing and valve selection are done in a single pass. The systematics correspond to the established control valve sizing by the flow coefficient method (IEC 60534 family).
Calculation workflow
- Define the medium and operating cases: For liquid or gas, the flow rate, upstream and downstream pressure, and temperature are recorded for the governing operating cases (minimum, normal, maximum flow). For liquids, density, viscosity, and vapour pressure are added; for gases, density or molar mass, compressibility, and isentropic exponent.
- Check the flow condition: The module determines whether subcritical or critical flow conditions exist: for liquids, the applied pressure differential is compared with the cavitation-limited pressure differential derived from the critical flow factor, critical pressure, and vapour pressure; for gases, the pressure ratio is compared with the critical value. For viscous media or small flows, laminar flow is additionally detected and a viscosity correction applied.
- Calculate the Kv value: With the relationship valid for the identified condition, the required Kv value is calculated for each operating case. Reducers upstream and downstream of the valve diminish the effective flow capacity and are accounted for by geometry corrections.
- Select the valve: From the integrated manufacturer data, a valve is selected whose Kvs value lies above the largest required Kv and whose rangeability still covers the smallest operating case within the controllable travel range.
- Check the operating behaviour: Finally, it is verified that all operating cases lie in a favourable opening range of the characteristic and that cavitation, flashing, or critical expansion are avoided in continuous operation or handled by design (e.g. with multi-stage trims).
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Volume flow | V | m³/s |
| Density | ρ | kg/m³ |
| Pressure difference | ΔP | Pa |
| Critical volume flow (referred to producer) | Cf | - |
| Upstream pressure (abs.) | P1 | Pa |
| Critical pressure | Pc | Pa |
| Vapour pressure of the liquid | PS | Pa |
| Valve diameter | DV | m |
| Tube diameter | di | m |
| Dynamic viscosity | η | mPa·s |
| Standard volume flow | VN | Nm³/h |
| Standard density of the gas referred to the standard density of air | ρN/1.293 | - |
| Temperature | ϑ | °C |
| Mass flow | m | kg/s |
| Standard density of the gas | ρN | kg/m³ |
| Reducer | Reduzierung | - |
| Medium | Gas | - |
| Flow | Strömung | - |
| Downstream pressure (abs.) | P2 | Pa |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Flow coefficient | Cv | gpm |
| Crit. pressure difference (full cavitation) | ΔPK | Pa |
| Flow coefficient | Kv | m³/s |
| Friction factor of the valve | ζ | - |
| Flow coefficient (subcritical flow) | Strömung | gpm |
| Flow coefficient (critical flow) | Strömung | gpm |
| Diameter of the valve outlet when flow reaches speed of sound | Dv,a | m |
Worked example
For a cooling water line, the required Kv value of a control valve is to be determined and a Kvs value proposed – a worked example of control valve sizing. Cavitation is not expected at the low pressure differential and low water temperature (vapour pressure ≈ 0.023 bar at 20 °C).
Given values
| Flow rate Q (maximum case) | 25 m³/h |
| Medium | Water, 20 °C, ρ = 998 kg/m³ |
| Pressure differential across the valve Δp | 1.6 bar |
Solution
Required Kv value (liquid, subcritical, turbulent)
Kv = Q · √( (ρ/ρ0) / Δp ) with ρ0 = 1,000 kg/m³, Δp in bar
Kv = 25 m³/h · √( 0.998 / 1.6 ) = 25 · 0.7898 ≈ 19.7 m³/h
Select the Kvs value
With a sizing margin of about 30 % on the maximum case, the demand comes to roughly 25.7 m³/h. From the manufacturer's series, the nearest step is selected, e.g. Kvs = 25 (the valve then utilizes about 79 % of its capacity in the maximum case), or conservatively the next larger step.
It remains to be checked that the smallest operating case still lies within the controllable travel range of the characteristic.
Result
| Required Kv value | ≈ 19.7 m³/h |
| Proposed Kvs value | 25 (manufacturer's series, next larger step if in doubt) |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
What is the difference between Kv, Kvs, and Cv?
The Kv value is the flow in m³/h of water at 1 bar pressure loss across the valve at the travel considered; the Kvs value is the Kv value at rated travel (fully open) and thus the catalogue characteristic of the valve. Cv is the US counterpart in US gal/min at 1 psi; the relation is Cv ≈ 1.17 · Kv. Sizing is done so that the largest required Kv lies well below the Kvs – typically around 70–80 % opening in the maximum case.
When does cavitation limit the flow through a liquid valve?
In the narrowest cross-section (vena contracta), the static pressure drops well below the downstream pressure. If it falls below the vapour pressure of the liquid, vapour bubbles form and implode during pressure recovery – cavitation. Beyond a certain pressure differential, which the manufacturer specifies via the critical flow factor (FL or Cf), the flow no longer increases despite a larger pressure differential (choked flow). If the downstream pressure remains below the vapour pressure, the medium vaporizes permanently (flashing) – then only erosion-resistant trims help.
Why is an oversized control valve a problem?
A valve that is too large operates in the lower travel range, where the characteristic is steep and the relative positioning accuracy is poor: small travel changes cause large flow changes, the control loop tends to oscillate, and seat and plug wear from throttling near the closed position. That is why the Kv demand is calculated for all operating cases and the rangeability Kvs/Kv,min is compared with the manufacturer's specification.
How do reducers directly upstream and downstream of the valve act?
If a valve of smaller nominal size is installed in a larger pipeline, the transition pieces create additional pressure losses and change the pressure recovery behaviour. The effective flow capacity of the combination is smaller than the catalogue Kvs of the valve; the calculation captures this via a piping geometry factor. If this effect is ignored, the valve is undersized in the field.