Orifice & Valve Flow Rate Calculator

Liquid Flow Through an Orifice: Worked Example

Load the first preset — 10 mm orifice · water · 100 kPa — and the panel reproduces the classic hand calculation live. Step through it once and every number in the results row has a name:

1. Bore area. A = π·(10 mm)²/4 = 78.54 mm² — the opening itself, not the pipe cross-section.
2. Jet velocity. v = √(2·ΔP/ρ) = √(2 × 100,000 / 998) = 14.16 m/s — the speed the pressure drop can drive.
3. Real flow. Q = 0.62 × 78.54 mm² × 14.16 m/s = 6.89×10⁻⁴ m³/s — that is 41.4 L/min ≈ 10.9 GPM.
4. Mass flow. ṁ = ρ·Q = 998 × 6.89×10⁻⁴ = 2,477 kg/h (5,460 lb/h) — the number a process balance wants.
5. Permanent loss. At β = 0.5, ΔP_loss ≈ 100 × (1 − 0.5^1.9) ≈ 73.2 kPa — most of the drop is destroyed, not recovered.

The square-root law is visible right inside the example: raise the drop from 100 to 400 kPa and the flow only doubles, from 41.4 to 82.8 L/min. That diminishing return is the single most useful habit the equation teaches — and the reason “just add pressure” is an expensive way to buy flow.

Sizing in Reverse: From Target Flow to Cv or Orifice Diameter

Most sizing jobs start at the wrong end: you know the flow you need and the pressure you can afford to spend, and the question is what restriction delivers it. Flip the direction toggle in the liquid tab and the same engine solves backwards:

Two short runs show the shape of the answers. First, a valve: a branch needs 12 GPM of water and the control loop can spare 2 psi across the valve. Cv = 12/√2 = 8.49 — scan the catalogue table below and a 1″ globe (Cv 15–25) covers it with room to spare, while a 1/2″ ball at the low end of its 20–40 band would be marginal at best. Second, an orifice: 10 L/min at 50 kPa of water needs a bore of 5.85 mm — in practice you drill the nearest standard size, 6.0 mm, and the flow lands a few percent above target because flow grows with the square of the bore.

Notice the asymmetry the reverse equations expose. The valve coefficient you need grows linearly with the target flow — double the duty, double the Cv. But it grows only as the inverse square root of the pressure you are willing to spend: the same flow at a quarter of the ΔP needs double the Cv. Bore demand behaves the same way, which is why a tank drained through a 6 mm hole takes roughly twice as long as through a 9 mm one, not half as long — the areas differ by barely 2.25×.

📏Size up, then verify forward

Size up, then verify forwardPhoto: Unsplash

Cv, Kv, and Orifice Conversion Tables

The three numbers every orifice or valve calculation leans on — the discharge coefficient, the catalogue Cv, and the conversion between coefficient systems — with the data nature of each stated plainly, because a typical range quoted from a catalog and a value fixed by a standard deserve different levels of trust.

Typical discharge coefficients

Data nature: typical published ranges from the ISO 5167 device families and classic entrance-loss practice. The exact Cd of a given installation depends on tap layout, β, and Reynolds number — the calculator’s fixed defaults (0.62 / 0.97 / 0.975) sit at the practical midpoints.

Common valve Cv ranges

Typical catalogue ranges — always confirm with the manufacturer datasheet. Trim profile, seat design, and even the same model in a different size move Cv by double- digit percentages; this table is for narrowing the shortlist, not for signing a purchase order.

Mistakes That Skew Real-World Results

The equation is the easy half. What separates a planning estimate from a number that survives commissioning is knowing where the real device departs from the model — and by how much. Five departures cover most of the surprises.

1. The coefficient is a snapshot, not a constant

Because flow is directly proportional to Cd (Q ∝ Cd at fixed ΔP and bore), any drift in the coefficient passes straight into the flow at the same percentage. A sharp-edged plate wears in service: erosion rounds the inlet edge, the vena contracta forms less tightly, and the effective Cd rises by 1–5 % — so the same gauge reading now delivers 1–5 % more flow than the datasheet predicted. Upstream disturbances push the other way: an elbow too close to the tap leaves swirl in the approach flow, the jet attaches irregularly, and Cd drops 1–5 %, quietly shrinking delivered flow. Entrained gas is the third mechanism — bubbles displace liquid volume and lower the effective density, so the mass delivery falls while the volumetric figure barely moves. None of these announce themselves; they are the difference between “the line runs 41 L/min” on paper and 39 or 43 in the field. This is why the ISO 5167 straight-run requirements exist, and why a metering plate gets re-calibrated instead of trusted for a decade.

2. The square-root law at scale

Doubling flow needs four times the pressure drop; ten times the flow needs one hundred times the ΔP. At household scale the law is gentle — 41.4 to 82.8 L/min for 100 to 400 kPa — but at process scale it becomes the dominant cost line: pushing a line from 10 to 100 m³/h through the same restriction means the restriction alone consumes a hundred-fold pressure multiple, and the pump pays it continuously. The flip side is the sizing asymmetry from the reverse section: the Cv you need scales linearly with flow but only as 1/√ΔP with the pressure you spend, which is why valve vendors can serve enormous flow ranges from a modest catalogue — capacity grows linearly while the pressure budget does the heavy lifting. Read any “just raise the setpoint” proposal against the square of what it implies.

3. Two hard limits the math cannot cross

The √ΔP law operates inside two boundaries, and both are safety lines rather than suggestions. For gases, the critical pressure ratio is the ceiling: once P2/P1 falls below ≈0.53 for air, the throat runs sonic, flow stops responding to downstream pressure, and every additional unit of ΔP is bought for nothing — the metering assumption behind the reading fails at exactly the moment the system is working hardest. For liquids, the cavitation threshold is the floor: when the static pressure at the vena contracta approaches the fluid’s vapour pressure, the liquid flashes to vapour, the flow reading goes unstable, and the collapsing bubbles pit and erode the plate or valve seat — metal removed by implosion, not corrosion. The calculator’s choked badge and cavitation flag mark these lines so you can design up to them, not through them.

4. What happens with impossible inputs

The calculator refuses to guess. Empty fields, zeros, and negative values — a bore of 0, a ΔP of −50, a density left blank — each raise a named error badge, and the results panel stays empty until the input is fixed; nothing is silently clamped to a default. Out-of-range values are rejected with the limit stated: bore above 1,000 mm, ΔP above 70 MPa (≈10,150 psi), density above 25,000 kg/m³, P2 ≥ P1 in gas mode, β outside 0–1, k outside 1.01–2. The reasoning is deliberate — a silently corrected number teaches the wrong lesson, while a named rejection tells you which physical impossibility you typed.

5. A cautionary chain: ignoring the CHOKED badge

Watch what happens when the boundary is ignored. A designer wants twice the mass flow from a gas relief orifice and, trusting √ΔP, plans four times the pressure drop. Below the critical ratio the plan is arithmetically correct and physically dead: the flow is already choked, so the actual mass flow stays flat no matter how hard the upstream pressure climbs — but the sizing spreadsheet, still scaling with √ΔP, reports the target met. The valve arrives undersized for the real duty, the upstream pressure accumulates instead of relieving, and the discrepancy surfaces during the one test you did not want it to. The red badge is the cheapest inspection this page performs: when it lights, stop scaling and start resizing the bore.

Each of these departures has a longer treatment in the guide library, which pairs every calculator on this site with the reading that explains its assumptions.

Data Sources & References

1. ISO 5167 — Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full (orifice plates, nozzles, venturi tubes; discharge-coefficient classes and straight-run requirements). International Organization for Standardization (iso.org).
2. IEC 60534 — Industrial-process control valves (flow-capacity sizing and valve-coefficient practice), together with ISA RP75-style Cv conventions. International Electrotechnical Commission (iec.ch) · International Society of Automation (isa.org).
3. NIST — metric unit conversions and exact definitions underlying the GPM, L/min, kg/h, and lb/h factors on this page. NIST Metric Conversions (nist.gov).
4. Crane Technical Paper No. 410 — Flow of Fluids through Valves, Fittings, and Pipe (K factors, entrance-loss values, and the √ΔP working charts generations of engineers carry). Crane Co. (craneco.com).

Published and maintained by the Flow Calculator team (Flow-Calculator.com). The fixed coefficients used by the tool (Cd 0.62 / 0.97 / 0.975, Kv = 0.865·Cv, β^1.9 loss approximation) are stated openly so any result can be traced back to its assumption — which is the entire point of this page.