Find the flow rate through an orifice from the discharge coefficient, area, and pressure difference, solve for a missing variable, or back-calculate the discharge coefficient from a measured flow — Q = Cd·A·√(2ΔP/ρ).
Orifice & fluid properties
Sharp-edged orifice ≈ 0.60-0.65. Dimensionless.
Water ≈ 1,000 kg/m³ at room temperature.
Flow rate
—
Enter Cd, area, pressure difference, and density to compute.
Flow rate (L/min)—
FormulaCd·A·√(2ΔP/ρ)
Solve for a missing variable
Use scientific notation for very small flows, e.g. 6.2e-3.
Solved value
—
Choose a variable, set the target flow rate, and enter the other values.
Back-calculate Cd from a measured flow
Use this tab to calibrate an orifice meter: measure the actual flow rate through a known orifice at a known pressure difference, and back out its real-world Cd rather than assuming a textbook value.
Discharge coefficient
—
Enter the measured flow rate, area, pressure difference, and density.
Typical Cd by orifice geometry
Geometry
Typical Cd
Sharp-edged (thin-plate) orifice
0.60 – 0.65
Square-edged orifice, corner taps
0.60 – 0.80
Rounded / flow-nozzle
0.90 – 0.98
Venturi
0.95 – 0.98
Ideal (frictionless) orifice
1.00
Cd < 1 accounts for the vena contracta (the flow narrowing just past the orifice) and real-fluid friction losses that the ideal Bernoulli equation ignores.
4 min read3 steps7 terms3 examples6 FAQsQ = Cd · A · √(2ΔP / ρ)
📋
Walk-through
How to Use This Calculator
3 steps▸
1
Enter the orifice and fluid properties
On the Flow Rate tab, enter the discharge coefficient Cd (dimensionless, ~0.62 for a sharp-edged orifice), the orifice area A (m²), the pressure difference ΔP across the orifice (Pa), and the fluid density ρ (kg/m³). All four inputs must be greater than zero.
2
Read the flow rate
The result card shows the volumetric flow rate Q in both m³/s and L/min, plus an interpretation explaining how each input moves the result — flow scales linearly with area and Cd, but only with the square root of the pressure difference.
3
Solve for a missing value or check the discharge coefficient
On the Solve tab, pick area or pressure difference as the unknown, set a target flow rate, and fill in the rest — the calculator rearranges Q = Cd·A·√(2ΔP/ρ) to find it. On the Discharge Coefficient tab, enter a measured flow rate to back-calculate the real-world Cd of an orifice you've already installed, and see how it compares to typical geometries.
⚡
Reference
Formula & Methodology
3 formulas▸
Orifice-plate flow equation
Q = Cd · A · √(2ΔP / ρ)
Volumetric flow rate Q (m³/s) equals the discharge coefficient Cd (dimensionless) times the orifice's cross-sectional area A (m²), times the square root of 2 times the pressure difference ΔP (Pa) across the orifice, divided by the fluid density ρ (kg/m³).
Why Cd is less than 1
Cd = Q_actual / Q_ideal
The ideal (Cd = 1) form of the equation comes directly from Bernoulli's equation and assumes frictionless, uniform flow through the full orifice area. Real flow contracts just past the orifice (the vena contracta) and loses energy to friction, so the actual flow rate is always somewhat less than the ideal prediction — Cd is the ratio that corrects for this.
Validity condition
Steady, incompressible flow of a Newtonian fluid
The equation assumes the fluid is incompressible (a good approximation for liquids and for gases at low pressure ratios), the flow is steady, and the orifice geometry and Cd are known or calibrated. For compressible gas flow with a large pressure drop, an expansibility factor should be applied on top of Cd.
📖
Glossary
Key Terms Explained
7 terms▸
Orifice flow ↗The flow of a fluid through a restriction — a plate with a hole, a nozzle, or a similar constriction — driven by a pressure difference across it, following Q = Cd·A·√(2ΔP/ρ).
Discharge coefficient ↗A dimensionless correction factor Cd (typically 0.6-0.98) that scales the ideal Bernoulli flow-rate prediction down to match real measured flow, accounting for the vena contracta and friction losses. A sharp-edged orifice is typically Cd ≈ 0.60-0.65.
Orifice plate ↗A thin plate with a precisely sized hole, installed in a pipe or duct to create a measurable, repeatable pressure drop — one of the most common flow-measurement devices in industrial piping.
Pressure difference ↗The pressure drop ΔP (Pa) across the orifice — upstream pressure minus downstream pressure — that drives fluid through the restriction. Flow rate scales with the square root of this value, not linearly.
Flow measurement ↗The practice of inferring a fluid's flow rate from an indirect, calibrated signal — here, the pressure drop across a known orifice — rather than measuring volume or mass directly.
Vena contracta ↗The point just downstream of a sharp-edged orifice where the flow stream narrows to its smallest cross-section, smaller than the orifice itself. This narrowing is the main reason Cd is less than 1 for sharp-edged orifices.
Restrictor ↗Any deliberately sized flow restriction — an orifice, nozzle, or venturi — used either to measure flow rate (via the pressure drop it creates) or to limit flow rate to a target value.
👥
Scenarios
Real-World Examples
3 worked examples▸
🕳️
Standard orifice plate, water service
A sharp-edged orifice plate metering water flow in a pipeline
Discharge coefficient Cd 0.62Orifice area 0.001 m²Pressure difference 50,000 PaFluid density 1,000 kg/m³
Q = 0.62 × 0.001 × √(2 × 50,000 / 1,000) = 0.62 × 0.001 × 10 = 0.0062 m³/s, or 372 L/min — a typical result for a modest orifice under a substantial pressure drop, and a textbook sharp-edged Cd.
🧮
Sizing an orifice for a target flow
Solving for the required orifice area to hit a specific flow rate
Rearranging for area: A = Q / (Cd × √(2ΔP/ρ)) = 0.0062 / (0.62 × 10) = 0.001 m² — the same 0.001 m² orifice from the baseline example, confirming the Solve tab's algebra round-trips correctly.
📐
Calibrating a rounded nozzle
Back-calculating Cd from a measured flow through a rounded, low-loss restriction
Measured flow rate 0.0093 m³/sOrifice area 0.001 m²Pressure difference 50,000 PaFluid density 1,000 kg/m³
Cd = Q / (A × √(2ΔP/ρ)) = 0.0093 / (0.001 × 10) = 0.93 — well above the sharp-edged range and consistent with a rounded, flow-nozzle-style restriction, which loses far less energy to the vena contracta than a thin plate.
🔗
Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Orifice plates are one of the oldest and most widely used flow-measurement devices in industrial piping: install a plate with a precisely sized hole, measure the pressure drop across it, and the flow rate follows directly from Q = Cd·A·√(2ΔP/ρ). The formula looks like a straightforward rearrangement of Bernoulli's equation, and it is — the only wrinkle is the discharge coefficient Cd, which quietly does the work of correcting an idealized prediction for how real fluids actually behave.
How the Orifice Flow Calculator works
▸
The calculator applies Q = Cd·A·√(2ΔP/ρ) directly on the Flow Rate tab: the discharge coefficient Cd times the orifice area A, times the square root of 2 times the pressure difference ΔP divided by the fluid density ρ. The Solve tab rearranges the same equation to isolate the orifice area or the pressure difference given a target flow rate and the other three values. The Discharge Coefficient tab runs the equation in reverse — given a flow rate you've actually measured, it isolates Cd, letting you calibrate a real orifice rather than assume a textbook value.
Inputs and what they mean
▸
The discharge coefficient Cd is dimensionless and, for a standard sharp-edged (thin-plate) orifice, typically falls between 0.60 and 0.65 — round, well-machined nozzles and venturis can reach 0.95-0.98 because they avoid the sharp vena-contracta losses of a plain hole in a plate. Orifice area A (m²) is the cross-sectional area of the hole itself, not the pipe it sits in. Pressure difference ΔP (Pa) is the drop measured across the orifice, usually with taps just upstream and downstream. Fluid density ρ (kg/m³) is a property of the fluid — water is about 1,000 kg/m³, while gases vary enormously with pressure and temperature. Of these, ΔP has the gentlest effect on the result: because flow depends on its square root, doubling the pressure drop only increases flow by about 41%, not 100%.
Limits and edge cases
▸
This formula assumes steady, incompressible flow of a Newtonian fluid, and a discharge coefficient that's either known from a standard reference (ASME/ISO orifice-plate tables) or independently calibrated — the calculator does not derive Cd from geometry alone, since real Cd values depend on Reynolds number, tap location, and manufacturing tolerances in ways a single formula can't fully capture. For compressible gas flow across a large pressure ratio, an additional expansibility (Y) factor is normally applied on top of Cd, which this calculator does not include. Treat results here as a solid engineering estimate for liquid flow and low-pressure-ratio gas flow, and consult an ASME/ISO flow-measurement standard for precision metering applications.
❓
Questions
Frequently Asked Questions
6 questions▸
What is the formula for orifice flow?+
Q = Cd·A·√(2ΔP/ρ), where Q is the volumetric flow rate (m³/s), Cd is the dimensionless discharge coefficient, A is the orifice area (m²), ΔP is the pressure difference across the orifice (Pa), and ρ is the fluid density (kg/m³).
What discharge coefficient should I use?+
A sharp-edged (thin-plate) orifice typically has Cd ≈ 0.60-0.65. Square-edged orifices with corner taps run 0.60-0.80, and rounded flow nozzles or venturis can reach 0.90-0.98 because they avoid the sharp vena-contracta losses of a plain hole. If you have a measured flow rate for your specific installation, the Discharge Coefficient tab lets you back-calculate the actual Cd instead of guessing.
Is this calculator for flow measurement?+
Yes — the orifice-plate equation is the working principle behind one of the most common industrial flow meters. Given a known orifice size and discharge coefficient, measuring the pressure drop across the orifice tells you the flow rate without any moving parts.
What units does the calculator use?+
Area is in square meters (m²), pressure difference is in pascals (Pa), density is in kilograms per cubic meter (kg/m³), and the discharge coefficient is dimensionless. The resulting flow rate is shown in both cubic meters per second (m³/s) and liters per minute (L/min).
Can I solve for the orifice area instead of the flow rate?+
Yes — the Solve tab lets you pick orifice area or pressure difference as the unknown, enter a target flow rate and the discharge coefficient, area/pressure, and density as appropriate, and the calculator rearranges the equation to find the missing value.
What is the vena contracta and why does it matter?+
The vena contracta is the point just downstream of a sharp-edged orifice where the flow stream necks down to a cross-section smaller than the orifice hole itself, before expanding back out. This narrowing — plus friction losses — is the main reason the discharge coefficient is less than 1 for sharp-edged geometries, and why rounded or venturi-style restrictions (which avoid a sharp vena contracta) have a higher Cd.
📄
Save & share
Get a branded PDF of your results
Download a one-page PDF of your numbers instantly. Add your email to also get our occasional calculator tips — no spam, unsubscribe anytime. Privacy.