How this instrument works
Every control or throttling valve leaves the factory with a flow coefficient stamped on its data sheet — a single number, Cv, fixed by clamping the valve at one travel position on a calibrated test loop and recording how many US gallons per minute of 60°F water cross it for exactly one psi of pressure drop. That bench number stays fixed for a given valve and opening; what changes is the flow it predicts once real pressure drop and a real fluid replace the test conditions. This page runs the calculation in that direction — coefficient already known, actual operating flow the unknown — the question a technician standing in front of an installed valve usually needs answered, rather than which valve to specify in the first place.
Picture the valve as a calibrated leak: fluid speeds up through its narrowest passage much as water gains speed falling out of a hole cut low in a tank wall, and Torricelli's centuries-old result for that case — exit speed scaling with the square root of how far the fluid falls — is the same relationship sitting inside Q = Cv√(ΔP ⁄ SG). Push twice the pressure across the same opening and the fluid speeds up by only about 41%, not 100%, because kinetic energy grows with the square of velocity while the pressure term supplying that energy grows only in direct proportion. This page's own reference numbers show the effect plainly: at Cv = 10 and SG = 1.0, a 20 psi drop passes 44.72 gpm, but quadrupling that drop to 80 psi only doubles the flow, to 89.44 gpm.
Specific gravity sits inside that same root for a parallel reason — moving a given volume of a heavier fluid up to speed costs more pressure than moving the same volume of water, so at fixed ΔP a denser fluid simply cannot reach the velocity water would. Quadruple specific gravity from 1.0 to 4.0 at that same 20 psi drop through the same Cv = 10 valve, and flow falls to exactly half, 22.36 gpm. The relationship holds only while flow stays liquid and turbulent all the way through the body: let local pressure inside the valve drop beneath the fluid's own vapor pressure and cavitation takes over — bubbles form and collapse downstream, flow abandons the square root, and it ceils out at a fixed maximum no further reduction in downstream pressure can lift. Steam and compressed-gas service need a separate, density-corrected form of the sizing relation entirely.
- Enter the valve's bench-tested rating into Valve flow coefficient, Cv — taken from the manufacturer's Cv-versus-travel curve for the opening position you care about; Cv is not one fixed number across the stroke.
- Enter the measured or budgeted differential into Pressure drop across the valve, psi — upstream gauge reading minus downstream, the valve alone, not the whole pipe run.
- Enter Fluid specific gravity relative to 60°F water: leave it at 1.0 for plain water, drop below 1.0 for light hydrocarbons, raise it for brine or a heavy process fluid.
- Read Flow rate, gpm — what that valve, at that opening, actually passes under those exact conditions.
- Repeat for other travel positions if you need the flow across the valve's full stroke rather than a single operating point.
Worked example — reading actual flow off an installed Cv = 10 valve
A maintenance technician needs to know how much a globe valve, already installed and rated Cv = 10 at its current handwheel position, is passing right now. A gauge pair across the valve shows a 20 psi drop, and the line carries plain water, specific gravity 1.0. There is no sizing decision left to make — the valve is already bolted in — so the formula runs forward exactly as written: Q = 10 × √(20 ⁄ 1.0) = 10 × 4.47213595 = 44.72135955 gpm.
That reading settles a real question: if the downstream process calls for 50 gpm and the valve only delivers 44.72 gpm at this opening and this pressure drop, either the stem needs to travel further open, the pump needs to work harder to raise ΔP, or the valve was undersized when it was specified. Note how little extra flow more pressure buys — even quadrupling the drop to 80 psi only lifts delivery to 89.44 gpm — so chasing the missing 5 or 6 gpm by opening the valve further is almost always cheaper than chasing it by raising pump pressure.
Questions
Where does a valve's Cv rating actually come from?
From a factory flow bench, not a formula. A sample valve is set to a fixed travel position, water is pushed through it, and the technician records how many US gallons per minute cross the valve for exactly a 1 psi drop — that reading becomes Cv for that position. Manufacturers repeat the test across the stem's travel and publish the results as a Cv-versus-percent-open curve, since a valve cracked a quarter open rates far lower than the same body fully open.
Will this formula tell me the flow through a valve carrying steam?
No. It assumes the fluid stays liquid and essentially incompressible from inlet to outlet, which steam and compressed gas never do. A gas expands and loses density as it crosses the valve, so its sizing relation carries a built-in density-correction term and switches to a compressible form once the downstream-to-upstream pressure ratio drops far enough. Running steam numbers through this liquid equation overstates the true flow, sometimes badly.
What happens if I keep raising the pressure drop?
Flow keeps climbing, but ever more slowly, until it stops climbing altogether. Past some point local pressure at the valve's narrowest section dips beneath the fluid's own vapor pressure, cavitation sets in, and flow plateaus at a fixed maximum no matter how much further downstream pressure is dropped. The square-root relationship here describes only the region before that ceiling; choked flow needs a separate correction factor from full sizing standards.
How do I convert this Cv into the metric Kv rating instead?
Multiply Cv by roughly 0.865 to get Kv, which restates the identical rating in metric terms: cubic metres of water moved each hour under a 1 bar drop, instead of gallons per minute under a 1 psi drop. A valve rated Cv = 10 on a US datasheet sits close to Kv = 8.65 on a European one — worth checking whenever a spec sheet crosses between the two conventions, since neither figure converts by a round number of its own.
Why does a denser fluid pass less flow at the same pressure drop?
Because moving a given volume of a heavier fluid up to speed costs more pressure than moving the same volume of water. At Cv = 10 and a 20 psi drop, plain water, specific gravity 1.0, passes 44.72 gpm; a fluid four times as dense, specific gravity 4.0, passes only half that, 22.36 gpm, under the identical pressure drop and identical valve — the 1⁄√SG scaling built into the formula, made concrete.
Can this equation be rearranged to pick a valve size instead?
Yes: Cv = Q ⁄ √(ΔP ⁄ SG) recovers the required coefficient from a target flow rate and an allowed pressure drop. That is the sizing direction — deciding which valve to buy before it exists on the line — rather than the checking direction this page is built for, which starts from a Cv already stamped on a nameplate and asks what it is delivering right now.