Learn & Understand

The Flow Coefficient Cv, and the Point Where More Pressure Buys No More Flow

The companion calculator finds the supply pressure needed to push a target flow through a component, using its flow coefficient, Cv. That little number on a valve datasheet is a compact, standardized way to describe how freely a component passes fluid, and the square-root relationship behind it holds until a fascinating limit intervenes: at high pressure ratios, gas flow chokes, and no amount of extra pressure will push more through.

What Cv Actually Means

The flow coefficient is essentially a standardized measure of a component's flow capacity, how much fluid it passes for a given pressure drop. A higher Cv means a freer-flowing component; a lower Cv means a more restrictive one. Its value is defining components on a common footing: two valves of different design and size can be compared directly by their Cv, and the same number lets you predict the flow-versus-pressure behavior of any of them. The calculator uses it to work backward from a desired flow to the pressure required.

Why Flow Follows the Square Root of Pressure

The relationship is the mirror image of the pressure-drop square law: if pressure drop rises with the square of flow, then flow rises with the square root of pressure drop. Double the pressure across a fixed component and the flow does not double, it rises by roughly forty percent (the square root of two). This is why boosting supply pressure gives diminishing returns on flow, and why the calculator squares the flow-to-Cv ratio to find the pressure. Small flow increases near the top of the range demand disproportionately large pressure increases.

The Limit the Formula Ignores: Choked Flow

The square-root relationship assumes you can always get more flow by adding more pressure. For a gas, that assumption breaks down. As the pressure ratio across a restriction grows, the gas accelerates through the narrowest point, and at a critical ratio it reaches the local speed of sound there. Once the flow is sonic at the throat, it is choked: increasing the upstream pressure further (or lowering the downstream pressure) does not increase the mass flow at all. The restriction has hit its speed limit, and flow becomes fixed regardless of how much more pressure difference you apply.

Why Choked Flow Is Useful, Not Just a Curiosity

Choked flow is not merely a limitation, it is a tool. Because the flow through a choked orifice depends only on the upstream conditions and not on downstream pressure, choked orifices make excellent, stable flow-metering and flow-limiting devices, the downstream fluctuations simply do not reach them. Gas systems exploit this for predictable metering, and it is one reason gas pressure regulators and orifices behave the way they do. But it also means the simple square-root formula overstates the flow once a component is operating in the choked regime, a real consideration when supply pressure is high relative to the downstream side.

Where This Bites in Practice

For a burner fuel train running modest pressure ratios, the square-root Cv relationship the calculator uses is accurate and the pressure estimate is sound. But in high-pressure gas systems, or across a component with a large pressure ratio, choking can cap the flow below what the formula predicts, so a naive calculation would call for a pressure that cannot actually push the expected flow through. Recognizing when a component is likely choked keeps the estimate honest.

Using the Fuel-Pressure Figure Well

Take the calculator's required pressure as accurate for normal, sub-critical operation, where flow follows the square root of pressure through the component's Cv. Remember that flow gives diminishing returns on pressure, big flow gains near the top cost large pressure increases. And watch for choked flow at high pressure ratios, where the mass flow becomes fixed and extra pressure buys nothing, a limit the square-root formula does not show but real gas systems obey.