The flow coefficient (Cv in US units, Kv in metric) sums up the capacity of a valve: the water flow that passes at a unit pressure drop. This guide presents the formulas for liquids, the conversion between Cv and Kv, a numerical example, the selection margin, the limitations with gases and steam, and the phenomena of cavitation and flashing.
Why a valve is sized
A control valve must meet two opposite conditions: be large enough to pass the maximum flow and small enough to regulate the normal and minimum flow accurately. If it ends up too large, it works almost closed, any small movement produces an abrupt change in flow and the seat wears. If it ends up small, it does not reach the maximum flow and the loop saturates. When a single loop is not enough, cascade, ratio and feedforward control are explained in cascade, ratio and feedforward control.
The tool that allows a good choice is the flow coefficient, which measures how much fluid the fully open valve lets through.
What Cv and Kv are
- Cv (US units): the volume of water, in US gallons, at about 60 °F (16 °C), that passes through the valve per minute at a pressure drop of 1 psi.
- Kv (metric units): the water flow, in m³/h, that passes through the fully open valve at a pressure drop of 1 kgf/cm², approximately 1 bar, per the VDI/VDE 2173 definition, with water of density 1000 kg/m³.
Two catalogs may express the capacity of the same valve in either coefficient. The conversion is:
Cv = 1.156 × Kv and, conversely, Kv = Cv / 1.156.
Formulas for liquids
For liquids, with no vaporization or cavitation, the two expressions have the same form:
| Coefficient | Formula | Q | ΔP | Specific gravity |
|---|---|---|---|---|
| Cv | Cv = Q · √(SG / ΔP) | gpm (US) | psi | SG (water = 1) |
| Kv | Kv = Q · √(SG / ΔP) | m³/h | bar | SG (water = 1) |
Each term has a physical reading:
- A larger Q requires more capacity.
- A larger pressure drop allows a smaller valve, since the driving force is greater: flow grows with the square root of the pressure drop.
- A denser fluid needs more capacity for the same volumetric flow.
To solve for flow, the expression is Q = Cv · √(ΔP / SG), which is used to estimate how much passes through a known valve.
What the “valve” pressure drop is
The ΔP in the formula is the pressure drop across the valve, not the line pressure. It results from subtracting the losses of the rest of the circuit (pipes, fittings, equipment) from the available pressure. A usual design rule in process engineering is that the valve absorbs a significant fraction of the total circuit drop at normal operating conditions, because if it absorbs a very small fraction it loses authority to regulate. The exact value of that fraction varies with the type of loop and each project’s criterion.
Numerical example (illustrative)
The data are made up to show the calculation; they do not correspond to any installation.
Metric case. Water (SG = 1), maximum flow of 50 m³/h and available pressure drop across the valve of 0.5 bar.
- Kv = 50 × √(1 / 0.5) = 50 × 1.414 = 70.7.
- In US units: Cv = 1.156 × 70.7 ≈ 81.7.
US units case. A liquid with SG = 0.85, maximum flow of 220 gpm and a drop of 10 psi.
- Cv = 220 × √(0.85 / 10) = 220 × 0.2915 = 64.1.
- Kv = 64.1 / 1.156 ≈ 55.5.
Choosing the valve. With a required Kv of 70.7 at maximum flow, a valve with a full-open Kv of 100 would work at 70.7 % of its capacity at maximum flow. That leaves margin upward and, if the normal flow is 60 % of the maximum, the valve will work with an opening in a reasonable range. A valve with a Kv of 400 would also pass the flow, but at normal flow it would be almost closed: the typical oversizing.
Important: the full-open coefficient of a specific model is given by the manufacturer’s catalogs. Also, the relationship between opening and capacity depends on the flow characteristic, covered in the guide on valve types and positioners.
Selection margin
The valve is not chosen with a Kv exactly equal to the calculated one. The following is recognized:
- A margin for uncertainty in the process data and for future growth. An excessive margin, however, leads to oversizing.
- That the maximum and minimum flow are met simultaneously: at maximum, with an opening that leaves control reserve; at minimum, with an opening above the zone where the valve loses resolution.
- That the calculation is done at several operating points: normal, maximum, minimum, start-up.
The acceptable opening ranges are set by the manufacturer according to the valve type and its characteristic; there is no universal number.
How to read the catalog
The manufacturer publishes the full-open coefficient and, for many models, a table of the coefficient at different percentages of travel. That table lets you check, for each flow in the calculation, at which point of travel the valve would sit. If the minimum flow falls in a stretch where the coefficient changes very little per percent of travel, or if the maximum demands almost the whole travel, consider another size or a different characteristic. Also check that the catalog coefficient corresponds to the exact size and trim type, because one body offers several trims with different capacities.
Limitations of the simple formulas
Gases and steam
The formulas above are for liquids. For gases, Cv can be used, but it requires a more complex equation with absolute pressures and not just the difference. When the outlet pressure is less than about half the absolute inlet pressure, the air flow in a valve reaches sonic velocity internally and no longer depends on the downstream pressure. For steam, temperature and the superheat factor are added. For these services, the equations of the sizing standard (IEC 60534 and ISA 75 family) or the manufacturer’s software are used.
Cavitation and flashing
In liquids, the pressure inside the valve drops at the narrowest point. If it falls to the vapor pressure of the liquid, bubbles form:
- Flashing: the bubbles remain downstream because the pressure does not recover above the vapor pressure. It produces erosion and a lower flow than the formula predicts.
- Cavitation: the pressure recovers downstream and the bubbles collapse, with noise, vibration and damage to the trim.
In both cases the flow does not rise even if the pressure drop increases: the flow is choked. The simple formula stops being valid and the calculation requires pressure recovery factors from the standard or the manufacturer, plus anti-cavitation trim if the risk is high.
Viscosity and laminar flow
If the fluid is very viscous, the real flow is lower than that calculated with the water formula and a correction factor is applied.
Reducers and fittings
When the valve is smaller in diameter than the pipe and there are reducers, the effective capacity falls and must be corrected.
Data the calculation needs
| Data | What it is for |
|---|---|
| Fluid, state and composition | Density, viscosity, vapor pressure |
| Operating temperature | Fluid properties |
| Inlet and outlet pressure | Available pressure drop |
| Minimum, normal and maximum flow | Range it must cover |
| Line diameter and specification | Reducers and velocities |
| Desired flow characteristic | Trim selection |
| Maximum allowed noise level | Acoustic verification |
| Shutoff class | Seat selection |
Common mistakes
- Mixing units. Using bar with the Cv formula or psi with the Kv one gives a coefficient off by a factor close to 3.8 (√14.5).
- Using the line pressure instead of the drop across the valve.
- Calculating only at maximum flow. The valve must also cover the minimum.
- Applying the liquid formula to gases.
- Stacking successive margins. Each area adds its own margin and the result is an enormous valve.
- Choosing by line diameter.
- Not checking cavitation and noise when the pressure drop is high.
- Not keeping the calculation data. When the process changes, there is no basis for reviewing the valve.
Checklist
- Process data for at least three operating points.
- Units consistent with the formula applied.
- Pressure drop across the valve calculated from the circuit balance.
- Required coefficient at maximum, normal and minimum.
- Coefficient of the chosen valve with its opening at each point.
- Check for cavitation, flashing and noise.
- Correction for viscosity and reducers where they apply.
- Flow characteristic consistent with the circuit.
- Datasheet with the calculation record filed.
Engineering support
Calculating the coefficient is only one step: the result depends on process data, the hydraulic circuit and the project’s criteria. To prepare the calculation record, the datasheet and the instrument specification, see our engineering design and studies service, delivered remotely and worldwide. To verify the stroke, the response and the behavior of each valve at handover, see testing and commissioning, in Colombia or elsewhere on request. Write to us through contact.
Related guides
- Motor control center (MCC)
- ABB ACS880 drive
- WEG CFW500, CFW11 and MVW3000 drives
- Large motor starting and voltage drop
- Control valves: types and positioners
- Differential pressure flow measurement
- Industrial pneumatics basics: components and control
References
- Wikipedia, Flow coefficient (definitions and formulas for Cv and Kv, conversion, gases).
- IEC 60534 and ISA 75 family, control valve sizing (general reference, its content and figures are not reproduced).
- Kuphaldt, T. R., Lessons in Industrial Instrumentation, chapter on control valves (CC BY 4.0).
Frequently asked questions
What is the relationship between Cv and Kv?
Cv is approximately 1.156 times Kv. Cv is defined with US gallons per minute and pounds per square inch, and Kv with cubic meters per hour and bar. When comparing catalogs, check which units each coefficient uses.
Can I use the same formula for gas and for steam?
No. The simple Cv and Kv formulas are for liquids. For gases, equations with absolute pressures, temperature and the effect of compressibility are required, and there is a maximum flow limit when the flow becomes choked.
Why is it not enough to pick the valve with the same diameter as the pipe?
Because diameter does not determine capacity. A valve of the same diameter as the line is usually oversized and will work almost closed, with little resolution. It is sized by the flow coefficient that results from the calculation.
How much spare capacity should a control valve have?
It must be able to pass the maximum flow at an opening that leaves room to regulate, and control the minimum flow without working almost closed. The useful opening range is recommended by the manufacturer and by the applicable reference standard for the valve type.