JRVAL
Aug 06 2025The flow coefficient is the single most important parameter for quantifying the performance of a control valve. It is a relative measure of a valve's efficiency at allowing fluid to pass through it. A higher flow coefficient indicates a greater flow capacity for a given pressure drop.
The Ultimate Guide to Valve Flow Characteristics & Sizing (Cv)
An archival-grade engineering reference for understanding, calculating, and applying flow coefficients (Cv/Kv) and valve characteristics for accurate system design and control.
Introduction to Flow Coefficients: Cv & Kv
Defining Cv (Imperial)
Definition of Cv
Cv is numerically defined as the volume of water at 60°F (in US Gallons per Minute) that will flow through a fully open valve with a pressure drop of 1 psi across the valve.
Cv is the standard measure in North America and regions that predominantly use Imperial units. It is a dimensionless number, although its definition is tied to specific units (GPM, psi, °F).
Defining Kv (Metric)
Definition of Kv
Kv is numerically defined as the volume of water at 20°C (in cubic meters per hour) that will flow through a fully open valve with a pressure drop of 1 bar across the valve.
Kv is the standard measure used in Europe and other regions following the International System of Units (SI). Its units are m³/h.
Conversion Formulas
It is often necessary to convert between Cv and Kv for international projects. The conversion factors are derived directly from the unit conversions of pressure and flow.
Cv = 1.156 × Kv | Kv = 0.865 × Cv
Inherent Flow Characteristics
The inherent flow characteristic describes the relationship between the valve's opening (travel) and the flow rate through it, assuming a **constant pressure drop** across the valve. This is a property of the valve's physical design (the geometry of the disc, ball, or plug). Understanding this is critical for selecting the right valve for a specific control application.
1. Quick Opening
A large increase in flow occurs with a small amount of initial valve travel. The curve flattens out as it approaches the fully open position. This characteristic is inherent to most gate valves and some simple butterfly valves.
- Best Use: On/off service, liquid dumping, or systems where immediate maximum flow is needed.
- Poor Use: Throttling or modulating control, as it provides very poor control precision.
2. Linear
The flow rate is directly proportional to the amount of valve travel. For example, at 50% open, the flow rate is 50% of the maximum flow. This is achieved by specially designed valve cages or plugs.
- Best Use: Liquid level control and applications where the pressure drop across the valve is expected to remain relatively constant.
- Common Valves: Globe valves with linear plugs, some v-notch ball valves.
3. Equal Percentage (or Logarithmic)
Each equal increment of valve travel produces an equal percentage change in the existing flow rate. For example, moving from 20% to 30% open might increase flow by 50%, and moving from 70% to 80% will also increase the *then-current* flow by 50%. This provides very fine control at low openings and coarse control at high openings.
- Best Use: The majority of modulating control applications, especially for pressure and temperature control where large variations in pressure drop are expected. It compensates for system dynamics.
- Common Valves: Most globe control valves, high-performance butterfly valves, segmented ball valves.
Inherent vs. Installed Characteristics
It is crucial to understand that these "inherent" characteristics are laboratory-defined under a constant ΔP. In a real piping system, as the valve opens, the system's pressure drop changes, which in turn alters the valve's performance. The resulting performance is called the **"installed flow characteristic,"** which is always a distortion of the inherent curve. An equal percentage valve is popular because its installed characteristic often becomes nearly linear, providing predictable control.
Core Sizing Formulas: Calculating Cv for Different Media
This section provides the fundamental engineering formulas (compliant with ISA/IEC standards) required to calculate the necessary flow coefficient (Cv or Kv) for a given application. Accurate calculation is the mandatory first step to correct valve selection.
Formulas for Liquids
Applicability Conditions
These formulas apply to Newtonian fluids in fully turbulent, non-choked flow. For highly viscous fluids, flashing, or cavitation conditions, advanced calculations including correction factors are required. These formulas provide the baseline requirement.
US Customary Units (Cv)
Cv = Q × √ ( Gf / ΔP )
- Cv = Required Flow Coefficient (Dimensionless)
- Q = Volumetric Flow Rate in US Gallons per Minute (GPM)
- Gf = Specific Gravity of the liquid (Water at 60°F = 1)
- ΔP = Pressure Drop across the valve in pounds per square inch (psi)
Metric Units (Kv)
Kv = Q × √ ( ρ / (1000 × ΔP) )
- Kv = Required Flow Coefficient (m³/h at 1 bar ΔP)
- Q = Volumetric Flow Rate in cubic meters per hour (m³/h)
- ρ = Density of the liquid in kilograms per cubic meter (kg/m³)
- ΔP = Pressure Drop across the valve in bar
Formulas for Gases & Vapors
Gas sizing is more complex due to its compressibility. Formulas are separated for sub-critical (non-choked) and critical (choked) flow conditions. **All pressures must be in absolute units.**
Non-Choked (Sub-Critical) Flow: ΔP < P₁/2 (General Rule)
This is the most common condition where flow rate increases as outlet pressure (P₂) decreases.
US Customary Units (Cv)
Cv = Q / ( 1360 × √ ( (ΔP × P₂) / (Gg × T) ) )
- Q
= Gas Flow Rate in Standard Cubic Feet per Hour (SCFH) - P₁ = Inlet Pressure in pounds per square inch absolute (psia)
- P₂ = Outlet Pressure in pounds per square inch absolute (psia)
- ΔP = P₁ - P₂ (psi)
- Gg = Specific Gravity of the gas relative to air (Air = 1)
- T = Absolute temperature at the inlet in degrees Rankine (°R = °F + 460)
Metric Units (Kv)
Kv = Q / ( 514 × √ ( (ΔP × P₂) / (d × T) ) )
- Q
= Gas Flow Rate in Normal cubic meters per hour (Nm³/h) - P₁ = Inlet Pressure in bar absolute (bara)
- P₂ = Outlet Pressure in bar absolute (bara)
- ΔP = P₁ - P₂ (bar)
- d = Relative density of the gas (Air = 1)
- T = Absolute temperature at the inlet in Kelvin (K = °C + 273.15)
Choked (Critical) Flow: ΔP ≥ P₁/2 (General Rule)
At this point, the gas velocity reaches sonic speed at the vena contracta. Further decreasing P₂ will not increase the flow rate.
US Customary Units (Cv)
Cv = ( Q × √(Gg × T) ) / ( 680 × P₁ )
Metric Units (Kv)
Kv = ( Q × √(d × T) ) / ( 257 × P₁ )
(Variables are the same as in the non-choked flow formulas).
Formulas for Steam
Steam sizing also considers choked flow conditions. The choked flow threshold for steam is different from that of most gases.
Choked Flow Condition for Steam
For most applications involving saturated steam, choked flow occurs when the outlet pressure P₂ is less than or equal to approximately 58% of the absolute inlet pressure P₁. The condition is: P₂ ≤ 0.58 × P₁.
Saturated Steam (Non-Choked Flow)
US Customary Units (Cv)
Cv = W / ( 2.1 × √ (ΔP × P₂) )
- W = Steam Flow Rate in pounds per hour (lbs/hr)
- P₁, P₂, ΔP = Pressures in pounds per square inch absolute (psia)
Metric Units (Kv)
Kv = W / ( 6.17 × √ (ΔP × P₂) )
- W = Steam Flow Rate in kilograms per hour (kg/hr)
- P₁, P₂, ΔP = Pressures in bar absolute (bara)
Choked Flow Steam (Saturated or Superheated)
Use this simplified formula for any steam application where P₂ ≤ 0.58 × P₁.
US Customary Units (Cv)
Cv = W / ( 1.17 × P₁ )
Metric Units (Kv)
Kv = W / ( 3.44 × P₁ )
Superheated Steam (Non-Choked)
For superheated steam, a correction factor for the degree of superheat must be applied to the saturated steam formula.
US Customary Units (Cv)
Cv = ( W × (1 + 0.0007 × T) ) / ( 2.1 × √ (ΔP × P₂) )
- T
= Degrees of superheat in Fahrenheit (°F)
Metric Units (Kv)
Kv = ( W × (1 + 0.00126 × T) ) / ( 6.17 × √ (ΔP × P₂) )
- T
= Degrees of superheat in Celsius (°C)
Advanced Topic: Choked Flow & Pressure Recovery (FL)
While the basic formulas are sufficient for many applications, critical services require a deeper understanding of fluid dynamics inside the valve. Choked flow is a phenomenon that limits the maximum flow capacity of a valve, regardless of downstream pressure.
The Physics of Choked Flow
As fluid passes through the narrowest point of the valve (the vena contracta), its velocity increases and its pressure decreases, reaching a minimum at the vena contracta.
- For liquids: If the pressure at the vena contracta drops to the liquid's vapor pressure, the liquid begins to boil (a phenomenon called flashing). The vapor bubbles formed occupy a large volume, "choking" the passage and preventing any further increase in flow. If the pressure recovers downstream and the bubbles collapse, it is called cavitation, which is extremely destructive.
- For gases: If the velocity at the vena contracta reaches the speed of sound (Mach 1), the flow is choked. Information about a further pressure drop downstream cannot travel upstream past the sonic shockwave, so the flow rate becomes independent of the downstream pressure.
The Importance of the Pressure Recovery Factor (FL)
The Pressure Recovery Factor (FL) is a dimensionless number that indicates how much pressure "recovers" from the minimum at the vena contracta to the valve outlet. It is a property of the valve's internal geometry.
- A valve with a tortuous path (like a globe valve) has low pressure recovery. Its FL value is high (e.g., 0.9).
- A valve with a straight-through path (like a ball valve or butterfly valve) has high pressure recovery. Its FL value is low (e.g., 0.6-0.7).
A lower FL value means the valve is more susceptible to choking, flashing, and cavitation. This is a critical parameter provided by manufacturers for high-performance valves.
Calculating Maximum Allowable Pressure Drop (ΔPmax) for Liquids
The FL factor is used to calculate the actual pressure drop at which choking begins.
ΔPmax = FL² × ( P₁ - ( FF × Pv ) )
- ΔPmax = Maximum allowable non-choked pressure drop (psi or bar)
- FL = Liquid Pressure Recovery Factor (from valve manufacturer)
- P₁ = Inlet pressure, absolute (psia or bara)
- FF = Liquid Critical Pressure Ratio Factor (approx. 0.96 for most water)
- Pv = Vapor pressure of the liquid at inlet temperature, absolute (psia or bara)
If the actual ΔP in your system exceeds this calculated ΔPmax, you must use ΔPmax in the liquid sizing formula, as the flow is choked.
Advanced Topic: Valve Noise Prediction
High-velocity fluid flow through a control valve is a significant source of industrial noise. Excessive noise (typically >85 dBA) is a safety hazard and can also indicate severe mechanical vibration that can damage the valve and adjacent piping. Predicting noise levels is a key part of the specification process for critical applications.
Valve noise prediction is governed by international standards, primarily IEC 60534-8-3 (for hydrodynamic noise from liquids) and IEC 60534-8-4 (for aerodynamic noise from gases).
Sources of Valve Noise
- Hydrodynamic Noise (Liquids): Primarily caused by cavitation. The violent collapse of vapor bubbles creates intense, high-frequency noise and vibration, often described as "gravel passing through the pipe." Flashing also creates noise but is typically less damaging.
- Aerodynamic Noise (Gases): Generated by the turbulent shearing of the fluid stream after the vena contracta. It is the dominant noise source in gas, steam, and vapor applications. The noise level is a strong function of the mass flow rate and the pressure ratio.
How Noise is Predicted
The actual calculations are extremely complex and are typically performed by proprietary software provided by valve manufacturers. The process generally involves:
- Calculating the mechanical stream power of the fluid.
- Determining the "acoustic efficiency" of the valve (how effectively it converts mechanical power into acoustic power). This is based on the valve type, pressure ratio, and flow regime.
- Calculating the internal sound pressure level (SPL).
- Calculating the transmission loss through the pipe wall (which depends on pipe size, schedule, and insulation) to determine the external SPL at 1 meter.
For a formal project, you must request a noise prediction calculation from your valve supplier based on your specific process data.
Common Noise Abatement Strategies
- Source Treatment: Selecting a low-noise valve trim design. This is the most effective method and often involves multi-stage trims that break the total pressure drop into smaller, non-choking, and less noisy stages.
- Path Treatment: Using thicker pipe (increasing transmission loss), acoustic insulation or blankets around the valve and downstream piping, or installing a downstream silencer.
- System-Level Changes: Where possible, reducing the pressure drop across a single valve by using multiple valves in series or optimizing the overall system design.
The Golden Rules of Valve Selection & Sizing
Calculating a Cv value is a scientific process. Selecting the final valve is an engineering art, guided by the following inviolable rules. Ignoring them is a common cause of system underperformance, control instability, and premature equipment failure.
Rule #1: Size for Capacity, Select for Control
The calculated Cv tells you the required flow capacity. This only narrows down the potential valve sizes. The final selection must be based on the required flow characteristic (Rule #2) and its operating range (Rule #3).
Action: Never choose a valve based solely on its maximum Cv matching your calculation.Rule #2: Respect the Turndown Ratio
Turndown (or rangeability) is the ratio of maximum to minimum controllable flow (Cv_max / Cv_min). If your system requires control over a wide range of flows, you need a valve with a high turndown ratio (e.g., an equal-percentage globe valve). A valve sized only for max flow may be uncontrollable at low flow rates.
Action: Always verify that the valve's minimum controllable Cv is below your system's minimum required flow rate.Rule #3: Operate in the "Sweet Spot"
A control valve should ideally operate between 50% and 80% open at the normal design flow rate. This provides sufficient capacity for unforeseen process upsets (opens to 100%) and adequate control authority for reducing flow (closes towards 0%). Operating too close to the seat (<10%) causes poor control and high wear.
Action: If your calculated Cv requires a valve to be 95% or 15% open at normal flow, reconsider the valve size.Rule #4: Check the Velocity
A correctly sized Cv does not protect against excessive fluid velocity, which causes noise, erosion, and vibration. Perform a velocity check as a mandatory secondary step. General limits are <6 m/s (20 ft/s) for clean liquids and < Mach 0.3 for gases to avoid significant noise.
Action: Always calculate exit velocity, especially in high pressure drop applications. If it's too high, a larger valve or special trim is needed.Rule #5: Identify Choking and Cavitation
Use the FL factor and pressure data to proactively check for the possibility of choked flow, flashing, or cavitation. These phenomena render sizing formulas invalid and guarantee control problems and equipment damage. If identified, the solution is not a larger valve, but a different type of valve (e.g., anti-cavitation trim).
Action: In any liquid application with a pressure drop > 50% of the inlet pressure, a cavitation analysis is mandatory.Rule #6: The Manufacturer is the Final Authority
This guide is a comprehensive reference. However, the certified technical data sheet and installation manual for the specific valve model you procure is the ultimate source of truth. FL, Fd, xT, and other factors can vary slightly between manufacturers for the same valve type.
Action: Always base final engineering decisions on the certified documentation from your chosen supplier.
