Cv (valve flow coefficient) is the universal language of control valve sizing. It defines the flow capacity of a valve in a single number: the number of US gallons per minute of water at 60°F that will flow through the valve with a 1 PSI pressure drop across it. A valve with a Cv of 50 passes 50 GPM of water with 1 PSI drop. A Cv of 200 passes 200 GPM under the same conditions. Every control valve manufacturer publishes Cv values for their valves at various openings and sizes.
The sizing process works in reverse: you know the required flow rate, the available pressure drop, and the fluid properties. You calculate the required Cv, then select a valve whose rated Cv meets or slightly exceeds your requirement. Getting this right is critical — an undersized valve cannot pass enough flow to satisfy the process, and an oversized valve operates at very low openings where controllability is poor and wear is accelerated.
This guide covers Cv sizing for liquids, gases (both sub-critical and critical flow), explains how specific gravity and temperature affect the calculation, describes choked flow conditions, and walks through matching a calculated Cv to a physical valve size.
Liquid Cv: The Basic Formula
The liquid Cv formula is: Cv = Q × √(G / ΔP) where Q is flow rate in GPM, G is the specific gravity of the liquid relative to water (water = 1.0), and ΔP is the pressure drop across the valve in PSI.
Example: Size a valve for 150 GPM of water with 25 PSI available pressure drop. Cv = 150 × √(1.0 / 25) = 150 × 0.2 = 30. You need a valve with a rated Cv of at least 30.
Specific gravity changes the calculation for liquids other than water. Gasoline (G = 0.72) is lighter than water and flows more easily for a given pressure drop. The same valve passes more GPM of gasoline than water. A heavy brine (G = 1.2) flows less easily. For 150 GPM of brine at 25 PSI: Cv = 150 × √(1.2 / 25) = 150 × 0.219 = 32.9. The heavier fluid requires a slightly larger Cv.
The pressure drop ΔP is the actual drop across the valve, not the total system drop. In a system with a pump providing 100 PSI and a process vessel at 60 PSI, the total available drop is 40 PSI. But the piping, fittings, and other equipment consume some of that drop. If 15 PSI is lost to piping friction, only 25 PSI is available across the valve. Always calculate or measure the actual pressure drop at the valve location. Using the total system drop will undersize the valve.
Cv = Q × √(G / ΔP)Q = flow rate (GPM)
G = specific gravity (water = 1.0)
ΔP = pressure drop across valve (PSI)
Rearranged to solve for flow:
Q = Cv × √(ΔP / G) Control Valve Cv / Flow Estimator
Calculate required valve Cv for liquid, gas, and steam service. Detect choked flow conditions and estimate valve size from standard Cv tables.
Gas Cv: Sub-Critical and Critical Flow
Gas sizing is more complex than liquid sizing because gas is compressible. As the pressure drop across the valve increases, the gas expands and its velocity increases. Up to a certain pressure drop, flow increases with increasing ΔP. Beyond that point (critical flow), the gas reaches sonic velocity at the valve vena contracta and flow no longer increases regardless of downstream pressure. This is choked flow.
For sub-critical gas flow (when ΔP is less than about half of P1), the ISA gas Cv formula is: Cv = Q / (N × P1 × Y × √(x × M / (T × Z))) where Q is flow in SCFH, N is a numerical constant (1360 for SCFH and PSIA), P1 is upstream absolute pressure, Y is the expansion factor, x is the pressure drop ratio (ΔP/P1), M is molecular weight, T is absolute temperature (°R), and Z is the compressibility factor.
A simplified formula for air or natural gas in non-critical conditions: Cv = Q / (22.7 × √(ΔP × (P1 + P2) / (T × G_g))) where Q is SCFH, P1 and P2 are upstream and downstream absolute pressures (PSIA), T is absolute temperature (°R), and G_g is gas specific gravity (air = 1.0). This formula is adequate for preliminary sizing when the pressure drop ratio is below 0.5.
For critical flow (ΔP/P1 ≥ 0.5 for many valve styles), the flow is limited by sonic velocity and depends only on upstream conditions. The downstream pressure no longer matters. The critical flow Cv formula replaces the ΔP term with a fixed critical pressure drop ratio that depends on the valve recovery coefficient (F_L). High-recovery valves like ball and butterfly valves reach critical flow at lower pressure drops than low-recovery globe valves.
Cv = Q / (22.7 × √(ΔP × (P1+P2) / (T × G_g)))Q = SCFH, P1/P2 = PSIA, T = °R (= °F + 460)
G_g = gas specific gravity (air = 1.0)
Valid when ΔP/P1 < 0.5
Choked Flow and Valve Recovery
Choked flow occurs when the fluid velocity at the vena contracta (the narrowest point inside the valve) reaches sonic velocity for gases, or when the local pressure drops to the vapor pressure for liquids (cavitation/flashing). Once choked, increasing the pressure drop does not increase flow. This is the maximum capacity of the valve at that upstream condition.
For gases, the critical pressure drop ratio x_T depends on the valve style. Globe valves have x_T values around 0.7-0.8, meaning they do not choke until ΔP exceeds 70-80% of P1. Ball and butterfly valves have x_T values of 0.3-0.5, reaching critical flow much sooner. This is why globe valves are preferred for high-pressure-drop gas applications — they allow more of the available ΔP to produce useful flow.
For liquids, choked flow occurs when the valve pressure recovery causes the downstream pressure to drop below the liquid's vapor pressure. The liquid partially vaporizes (flashes) and the two-phase mixture limits the flow. The valve recovery coefficient F_L characterizes this: a globe valve with F_L = 0.9 recovers less pressure and is less prone to cavitation than a butterfly valve with F_L = 0.55.
Sizing a valve that will operate at or near choked conditions requires careful attention to the ISA/IEC sizing equations with the F_L and x_T correction factors. Using the basic formulas without these corrections will overpredict the flow capacity and result in an undersized valve. Always check whether the operating ΔP exceeds the critical ΔP for the selected valve style.
Matching Calculated Cv to Valve Size
Once you have a calculated Cv, you select a valve from the manufacturer's Cv table. Each valve model has a range of Cv values depending on the body size. For example, a Fisher ED globe valve: 1-inch body Cv = 10, 1-1/2-inch Cv = 20, 2-inch Cv = 46, 3-inch Cv = 108, 4-inch Cv = 195, 6-inch Cv = 435. These are full-open Cv values for the specific trim sizes.
The sizing rule of thumb is to select a valve where the normal operating Cv falls between 50% and 80% of the rated Cv. If your calculated Cv is 30, you want a valve rated 37-60 Cv so you operate in the 50-80% open range. This provides good controllability (you are in the steepest part of the inherent characteristic curve) and leaves margin for upsets and capacity increases.
Operating below 20% open causes poor controllability, seat wear, and noise. The valve may oscillate because small position changes produce large flow changes in the steep part of the quick-open region. Operating above 90% open provides almost no additional flow capacity and no room for upset response. Both extremes indicate a mis-sized valve.
When the calculated Cv falls between two valve sizes, it is almost always better to select the smaller size and use a larger trim (if available) than to select the larger body with a reduced trim. A smaller body with full trim costs less, weighs less, and has better controllability than a larger body throttled down. However, consider the line size — if the process piping is 4-inch, installing a 2-inch valve requires reducers that add cost and pressure drop.
1. Normal operating Cv should be 50-80% of rated Cv
2. Never size below 20% or above 90% of rated Cv at normal flow
3. Check Cv at minimum, normal, AND maximum flow conditions
4. Valve body should not be more than two pipe sizes smaller than the line
5. For rangeability, verify that min and max Cv needs fall within a single valve's turndown ratio (typically 50:1 for globe valves)
Common Cv Sizing Mistakes
Using line-size pressure drop: The most common error is using the total system pressure drop instead of the actual drop available at the valve. Piping losses, equipment losses, and elevation changes must be subtracted from the total available differential to get the true valve ΔP. A pump delivering 100 PSI into a system with 30 PSI of pipe and equipment losses and 50 PSI process pressure has only 20 PSI available for the valve, not 50 PSI.
Ignoring viscosity: The standard Cv formulas assume turbulent flow with viscosity similar to water. High-viscosity fluids (heavy oils, slurries, polymers) require a viscosity correction factor that increases the required Cv. ISA/IEC standards include a Reynolds number correction procedure. At very low Reynolds numbers (below 10,000), the correction can increase the required Cv by 50% or more.
Forgetting to check minimum flow: Many sizing exercises focus on the normal or maximum flow case and forget to check the minimum. If the process turndown is 10:1 (max flow is 10 times min flow), the Cv range is also 10:1 at the same pressures. If the valve has a 50:1 rangeability, this works. But if the minimum Cv puts the valve below 5% open, controllability will be poor at low flows. This is where characterized trim (equal percentage) provides better control than linear trim.
Selecting oversized valves for "future capacity": Sizing a valve for 150% of current requirements to allow for future expansion puts the valve at 40-50% of its range under normal conditions. This wastes throttling range, reduces controllability, and increases noise. If future capacity is needed, install the correctly sized valve now and plan for a trim change or valve replacement when the capacity increase actually materializes.