Orifice Meter Flow Calculator
Solve the ISO 5167 orifice-meter equation Q = Cd · A₀ · √(2·ΔP / (ρ·(1−β⁴))) for any of its four unknowns — volumetric flow rate, discharge coefficient, orifice diameter, or differential pressure — with step-by-step math, a live orifice-plate schematic with pressure taps, and companion Reynolds, velocity, mass-flow and permanent pressure-loss metrics.
The Bernoulli principle lies at the heart
The orifice meter is a direct application of Bernoulli's principle: as the fluid accelerates through the narrowing of the orifice, its velocity rises and its static pressure falls. The pressure difference between the upstream tap (where the fluid is still slow) and the downstream tap (where it is fast) is proportional to the square of the velocity, so the velocity is proportional to the square root of the differential pressure. Multiplying by the flow area gives the volumetric flow rate. This square-root relationship is what makes orifice meters so simple and so widely used, and it is also what limits their turndown: at one-third of full flow the differential is only one-ninth of full scale, which is often below the accuracy of the transmitter.
The (1−β⁴) term corrects for approach velocity
The simple Bernoulli equation Q = A₀·√(2ΔP/ρ) assumes that the fluid upstream of the orifice is stationary — but in a real pipe the fluid is already moving at the approach velocity, and this velocity depends on the flow rate and on the diameter ratio β. The factor 1/√(1−β⁴), called the velocity-of-approach factor E, corrects for this. When β is small (a small hole in a large pipe) the factor is close to 1; when β is large (a hole nearly as big as the pipe) the factor grows rapidly and the flow becomes much more sensitive to β itself. This is why ISO 5167 limits standard orifice plates to β ≤ 0.75, and why the orifice plate must be installed with a fully-developed velocity profile upstream.
Cd captures the real-fluid effects
The discharge coefficient Cd is the ratio of the actual flow to the ideal (frictionless, no-vena-contracta) flow. For a sharp-edged orifice plate, Cd is typically 0.60–0.63, and its value depends on the Reynolds number, the tap location (corner, flange, or vena contracta), the plate thickness, the edge sharpness, and the pipe roughness. The ISO 5167 standard provides a correlation (the Reader-Harris/Gallagher equation) that predicts Cd to within ±0.5 % for standard geometries over a wide range of Reynolds numbers. For non-standard geometries, Cd must be determined experimentally by calibration. The discharge coefficient is the single biggest source of uncertainty in an orifice-meter measurement.
Permanent pressure loss is the price of measurement
Not all of the differential pressure is recovered downstream of the orifice. As the fluid passes through the plate, it forms a vena contracta (the narrowest point, typically about half an orifice diameter downstream) where the velocity is highest and the pressure is lowest, and then it expands again and recovers most — but not all — of the pressure. The unrecovered portion is the permanent pressure loss, approximately ΔP·(1 − β²) for a sharp-edged orifice. At β = 0.5 this is about 75 % of the measured differential, which is why orifice meters have higher pumping costs than Venturi meters (which recover 80–90 % of the differential). The permanent loss is the design trade-off against the meter's sensitivity and cost.
How to Use This Calculator
The orifice meter equation links four quantities: Q, Cd, d and ΔP, with the pipe diameter D and the fluid density ρ as supporting inputs. Pick which one you want the tool to solve, then fill in the others.
1. Choose what to solve for
Pick Q, Cd, d or ΔP from the toggle. The calculator rearranges the equation for whichever variable you choose — for the orifice diameter the rearrangement is iterative because β depends on d, and the iteration is shown in the steps.
2. Select the fluid
Pick a fluid from the reference list in the advanced panel and click "Use this fluid" to set both ρ and μ, or enter the density directly. For gases, remember that the density must be evaluated at the actual upstream pressure and temperature, and that the expansion factor ε should be applied (this calculator assumes incompressible flow).
3. Enter the pipe diameter and orifice diameter
The pipe internal diameter D and the orifice diameter d define the ratio β = d/D, which is the most important geometric parameter of the meter. Standard ISO 5167 orifice plates have β between 0.2 and 0.75; values outside this range are either highly sensitive or inefficient.
4. Read the result and the verdict
The result card shows the answer plus the diameter ratio β, the Reynolds number, and a colour-coded verdict. The verdict checks whether β is in the ISO 5167 range and whether the Reynolds number is high enough for the assumed Cd to be valid.
5. Check the schematic and charts
The schematic shows the pipe, the orifice plate, the streamlines converging through the hole and recovering downstream, and the two pressure taps P₁ and P₂. The chart plots flow rate against differential pressure on log–log axes, which is a straight line of slope ½.
6. Switch to Advanced for depth
Advanced mode adds a flow-rate-versus-orifice-diameter chart, a sensitivity check on a +1 % input change, and companion metrics including the orifice area, the pipe and orifice velocities, the mass flow rate, the permanent pressure loss, and the fluid property reference panel.
What This Tool Offers
Built around the ISO 5167 orifice-meter equation Q = Cd·A₀·√(2ΔP/(ρ(1−β⁴))), the workhorse of industrial flow measurement.
Four-way solving
Solve for flow rate, discharge coefficient, orifice diameter, or differential pressure. The orifice-diameter solve is iterative, reflecting the fact that β depends on d, and the iteration is shown step by step.
Live orifice-plate schematic
The pipe cross-section with the sharp-edged orifice plate, converging and recovering streamlines, the vena contracta, and the two pressure taps P₁ and P₂ dimensioned with D and d — all updating in real time.
ISO 5167 validity verdict
The verdict checks whether β is in the standard range (0.2–0.75), whether the Reynolds number is high enough for the turbulent Cd assumption, and whether the differential pressure is within practical transmitter range.
Companion flow metrics
Beyond the volumetric flow rate: orifice area, pipe area, orifice and pipe velocities, mass flow rate, Reynolds number, permanent pressure loss, and pumping-power penalty.
Dual comparison charts
Flow rate versus differential pressure on log–log axes (slope ½) for three orifice sizes, plus a flow-rate-versus-orifice-diameter chart for three differential pressures.
Reference tables
A unit converter for flow and pressure, a flow-rate lookup grid across orifice diameters and differential pressures, a table of typical discharge coefficients for different meter types, and a fluid property reference.
Reference Tables & Conversions
A flow unit converter, a pressure unit converter, and reference tables of discharge coefficients and fluid properties.
Volumetric flow unit converter
Orifice Flow Lookup at β = 0.53, Cd = 0.61, water
Computed from the ISO 5167 equation with Cd = 0.61, ρ = 1,000 kg/m³, D = 150 mm, d = 80 mm (β = 0.533). Values in m³/h. Red cells exceed 1,000 m³/h (typical domestic transmission); amber cells are 100–1,000; teal cells are below 100.
| ΔP (kPa) \ d | 25 mm | 40 mm | 60 mm | 80 mm | 100 mm | 125 mm |
|---|
Typical Discharge Coefficients by Meter Type
Representative values for different flow-measurement devices. All are for turbulent flow (Re > 10⁴); at lower Reynolds numbers the Cd for orifice plates falls significantly and the ISO 5167 correlations should be used instead of a constant.
| Meter type | Cd range | Typical β range | Permanent loss | Notes |
|---|---|---|---|---|
| Sharp-edged orifice (corner taps) | 0.595–0.620 | 0.20–0.75 | ~ 1 − β² | Most common; ISO 5167 standard |
| Sharp-edged orifice (flange taps) | 0.600–0.620 | 0.20–0.75 | ~ 1 − β² | Slightly higher Cd than corner |
| Sharp-edged orifice (D–D/2 taps) | 0.610–0.625 | 0.20–0.75 | ~ 1 − β² | Higher Cd, more sensitive to tap position |
| Quadrant-edged orifice | 0.700–0.850 | 0.30–0.75 | ~ 0.6 (1 − β²) | Used for viscous flows |
| Conical entrance orifice | 0.720–0.850 | 0.30–0.75 | Lower | Low Reynolds numbers |
| ISA 1932 flow nozzle | 0.950–0.985 | 0.30–0.80 | ~ 0.4 (1 − β²) | Lower loss than orifice |
| Long-radius nozzle | 0.970–0.990 | 0.20–0.80 | ~ 0.4 (1 − β²) | Standard for steam and gas |
| Venturi tube | 0.965–0.985 | 0.30–0.75 | ~ 0.1 (1 − β²) | Very low loss; expensive |
| Venturi nozzle | 0.970–0.990 | 0.30–0.75 | ~ 0.15 (1 − β²) | Combined nozzle + Venturi |
Fluid Property Reference (Density and Viscosity)
Representative values at 20 °C and 1 atm unless noted. For gases, density varies strongly with pressure and temperature — use the actual operating conditions in the calculator.
| Fluid | Density (kg/m³) | Dynamic viscosity (mPa·s) | Kinematic viscosity (cSt) | Notes |
|---|---|---|---|---|
| Air (20 °C, 1 atm) | 1.204 | 0.018 | 14.9 | Compressible; ε factor required |
| Natural gas (1 atm) | 0.75 | 0.011 | 14.7 | Composition-dependent |
| Water (4 °C) | 1,000 | 1.57 | 1.57 | Maximum density point |
| Water (20 °C) | 998 | 1.00 | 1.00 | Reference condition |
| Seawater (20 °C) | 1,025 | 1.08 | 1.05 | 3.5 % salinity |
| Ethanol (20 °C) | 789 | 1.20 | 1.52 | Pure, 100 % |
| Gasoline (20 °C) | 750 | 0.35 | 0.47 | Composition-dependent |
| Diesel (20 °C) | 850 | 2.50 | 2.94 | Grade-dependent |
| Light oil (20 °C) | 900 | 50 | 56 | ISO VG 46 |
| Mercury (20 °C) | 13,546 | 1.55 | 0.11 | Liquid metal |
| Steam (10 bar, sat.) | 5.15 | 0.015 | 2.91 | Compressible |
Variable Reference
| Symbol | Meaning | Typical range | Units |
|---|---|---|---|
| Q | Volumetric flow rate | 0.001 – 10⁶ | m³/h |
| Cd | Discharge coefficient | 0.60 – 0.99 | dimensionless |
| A₀ | Orifice area, π d²/4 | 10⁻⁶ – 1 | m² |
| d | Orifice diameter | 1 – 1,000 | mm |
| D | Pipe internal diameter | 10 – 2,000 | mm |
| β | Diameter ratio, d/D | 0.20 – 0.75 | dimensionless |
| ΔP | Differential pressure across the taps | 0.1 – 1,000 | kPa |
| ρ | Fluid density at operating conditions | 0.5 – 20,000 | kg/m³ |
| μ | Dynamic viscosity | 0.005 – 1,000 | mPa·s |
| Re | Reynolds number, ρ v D / μ | 10³ – 10⁸ | dimensionless |
| E | Velocity-of-approach factor, 1/√(1−β⁴) | 1.00 – 1.20 | dimensionless |
What Does the Orifice Meter Equation Measure?
The orifice meter equation gives the volumetric flow rate of a fluid through a pipe from the pressure difference measured across a sharp-edged orifice plate. It is the workhorse of industrial flow measurement, used in refineries, chemical plants, water utilities, power stations, and every branch of process engineering. The equation combines three classical results: the Bernoulli principle (which relates velocity to pressure), the continuity equation (which relates velocity to flow area), and an empirical discharge coefficient (which corrects the ideal theory for the real behaviour of viscous fluids). Together they give a formula that is simple, robust, and — with the appropriate corrections — accurate to within about 1 % of the true flow rate.
The Orifice Meter Formula
The defining relationship in SI units is:
where the orifice area and the diameter ratio are:
β = d / D
Rearranged to solve for the other three unknowns:
ΔP = ( Q / (Cd·A₀) )² · ρ · ( 1 − β⁴ ) / 2
d = iterative solution, because β depends on d
The velocity-of-approach factor E is defined as:
and the permanent pressure loss across the meter is approximately:
The upstream and downstream velocities are:
v = Q / Apipe = 4Q / (π D²) (pipe approach velocity)
The Reynolds number of the pipe flow, used to check the validity of the Cd assumption:
And the mass flow rate, useful for custody transfer and process control:
Orifice Meter Variables
| Symbol | Meaning | Notes |
|---|---|---|
| Q | Volumetric flow rate | The quantity the meter measures; m³/h or m³/s |
| Cd | Discharge coefficient | Ratio of actual to ideal flow; 0.60–0.63 for an orifice |
| A₀ | Orifice area | π d²/4; the geometric area of the hole |
| d | Orifice diameter | The diameter of the hole in the plate |
| D | Pipe diameter | The internal diameter of the pipe |
| β | Diameter ratio d/D | 0.20–0.75 for standard ISO 5167 plates |
| ΔP | Differential pressure | Measured between the two taps |
| ρ | Fluid density | At the actual operating conditions |
| E | Velocity-of-approach factor | 1/√(1−β⁴) |
| Re | Reynolds number | Determines whether Cd is constant |
How Each Variable Affects the Flow Rate
The flow rate is proportional to the discharge coefficient, proportional to the orifice area, and proportional to the square root of the differential pressure. Doubling Cd doubles the flow; doubling A₀ (which means multiplying d by √2) doubles the flow; quadrupling ΔP doubles the flow. This square-root relationship between flow and ΔP is the single most important characteristic of the orifice meter — it is what makes the meter simple and universal, and it is also what limits its accuracy at low flow.
The dependence on the diameter ratio β is more subtle. The flow appears to be proportional to A₀ = πd²/4, which grows with the square of d — but the (1−β⁴) term in the denominator also grows with d, so the net effect is that the flow increases slightly less than d². In practice, for β in the standard range of 0.2–0.75, the flow increases by roughly d² · (1 + β⁴/2) for small changes in d. This is why the sensitivity of the meter to the orifice diameter is very high: a 1 % error in d produces about a 2 % error in Q, and this is one of the reasons that the orifice diameter must be measured with a micrometer to within ±0.05 % if high accuracy is required.
The dependence on the fluid density is inverse-square-root: halving the density (for example, switching from water to air) increases the volumetric flow by a factor of √2 ≈ 1.41 for the same ΔP and the same geometry, because a lighter fluid accelerates more easily through the same pressure drop. This is why the same orifice meter calibrated for water cannot be used directly for air, and why the fluid density must be known accurately (to within 0.1 % for custody-transfer applications). For gases, the density varies with pressure and temperature, and the ISO 5167 standard requires an additional expansion factor ε to account for compressibility; the simple formula used here is only strictly valid for incompressible flow.
Finally, the accuracy of the meter depends critically on the accuracy of the differential-pressure measurement and the discharge coefficient. Modern differential-pressure transmitters achieve 0.05–0.1 % of span, which translates directly into 0.025–0.05 % of flow. But the discharge coefficient for a real-world installation is typically only known to ±0.5 % (or ±2–3 % for a non-standard installation without calibration), and this dominates the overall uncertainty. For critical applications, the orifice meter is calibrated in situ against a reference flow meter (a prover, a weighing system, or a laser-Doppler anemometer), and the calibration certificate becomes part of the meter's documentation.
Orifice Meter Calculation Examples
A₀ = π × 0.080² / 4 = 5.027 × 10⁻³ m²
β = 80/150 = 0.5333, β⁴ = 0.0809
1 − β⁴ = 0.9191
√(2 × 25,000 / (1,000 × 0.9191)) = √54.40 = 7.376 m/s
Q = 0.61 × 5.027×10⁻³ × 7.376 = 0.02262 m³/s = 81.4 m³/h
Q = 0.06944 m³/s, A₀ = 5.027 × 10⁻³ m²
√(2ΔP/(ρ(1−β⁴))) = 7.376 m/s
Cd = 0.06944 / (5.027×10⁻³ × 7.376) = 1.873 — this is not physical for an orifice. The given flow rate is too high for this combination of d and ΔP.
Iteration: start with d = 40 mm (β = 0.267, β⁴ = 0.005)
A₀ = 0.02262 / (0.61 × √(2×25,000/(1,000×0.995))) = 0.02262 / (0.61 × 7.090) = 5.23 × 10⁻³ m²
d_new = √(4×5.23×10⁻³/π) = 81.6 mm
Iterate again: β = 0.544, 1−β⁴ = 0.912, √(2×25,000/(1,000×0.912)) = 7.404
A₀ = 0.02262 / (0.61 × 7.404) = 5.01 × 10⁻³, d_new = 79.9 mm
Converged: d ≈ 80.0 mm
ΔP = (Q/(Cd·A₀))² × ρ(1−β⁴)/2
= (0.02262/(0.61×5.027×10⁻³))² × 1,000 × 0.9191/2
= (7.376)² × 459.6 = 25,000 Pa = 25.0 kPa ✓
Q = 0.61 × 5.027×10⁻³ × √(2×25,000/(1.204×0.9191))
= 3.066×10⁻³ × √(45,190) = 3.066×10⁻³ × 212.6 = 0.652 m³/s = 2,347 m³/h
That is 28.8× the water flow for the same ΔP — the density ratio in the square root.
Q = 0.1389 m³/s
Iterate: d ≈ 42 mm gives β = 0.42, β⁴ = 0.031, √(1−β⁴) = 0.984
√(2×30,000/(0.75×0.984)) = √81,300 = 285.2 m/s
A₀ = 0.1389/(0.61×285.2) = 7.99 × 10⁻⁴ m², d = 31.9 mm
Iterate: d = 32 mm gives β = 0.32, β⁴ = 0.0105, √(1−β⁴) = 0.995
A₀ = 0.1389/(0.61×286.3) = 7.96 × 10⁻⁴, d = 31.8 mm
Converged: d ≈ 32 mm, β ≈ 0.32
Frequently Asked Questions
An orifice meter is a flow-measurement device consisting of a thin, sharp-edged plate with a central hole, clamped between two flanges in a pipe. The plate constricts the flow, causing the fluid to accelerate and the static pressure to fall; the pressure difference between the upstream and downstream taps is measured and converted into a flow rate using the ISO 5167 equation. Orifice meters are used because they are cheap, simple, have no moving parts, work over a wide range of temperatures and pressures, and can be manufactured in almost any size. Their disadvantages are a relatively high permanent pressure loss, a limited turndown ratio (typically 3:1 to 5:1), and a discharge coefficient that must be calibrated for non-standard geometries. Despite these drawbacks they remain by far the most common flow meter in process industry, largely because they are so well understood and so thoroughly standardised.
Because it is a direct consequence of Bernoulli's principle. When a fluid accelerates from the approach velocity to the orifice velocity, its kinetic energy increases by ½ρ(v₀² − v²), and this energy comes from the static pressure, which falls by ΔP. Rearranging the energy balance gives v₀ = √(2ΔP/ρ) for the ideal case, and multiplying by the area gives Q ∝ √ΔP. The square-root relationship means that the differential pressure is very small at low flow — at one-tenth of full flow the differential is only 1 % of its full-scale value — which is why an orifice meter cannot measure low flows accurately and why the turndown ratio is limited. Conversely, the differential grows very quickly with flow, which makes the meter very sensitive at high flow but requires a transmitter with a wide dynamic range.
The discharge coefficient Cd is the ratio of the actual flow through the orifice to the ideal flow that would occur if the fluid were frictionless and if all the streamlines converged to exactly the geometric orifice area. It captures three real-fluid effects: viscous friction in the boundary layer, the vena contracta (which is smaller than the geometric hole), and the small pressure recovery at the taps. For a standard sharp-edged orifice plate under turbulent flow, Cd is typically 0.60–0.63, and the ISO 5167 standard provides a correlation (the Reader-Harris/Gallagher equation) that predicts its value to within ±0.5 % for standard geometries over a wide range of Reynolds numbers. For non-standard geometries (unusual tap locations, plate thicknesses outside the standard, or non-circular orifices) Cd must be determined experimentally by calibration. In practice, most industrial orifice meters are either built to ISO 5167 dimensions and use the standard correlation, or are calibrated in situ against a reference meter.
The vena contracta is the point downstream of the orifice where the flow stream is narrowest. Because the fluid has inertia, it continues to accelerate past the geometric edge of the hole and reaches its maximum velocity (and minimum pressure) at a point about half an orifice diameter downstream. The cross-sectional area at the vena contracta is smaller than the geometric orifice area, by a factor called the contraction coefficient Cc, which for a sharp-edged orifice is typically about 0.62. This is one of the reasons that the actual flow is less than the ideal flow, and it is why the downstream pressure tap should ideally be located at the vena contracta. In the ISO 5167 standard, the corner-tap and flange-tap geometries put the downstream tap at or near the vena contracta in a way that is reproducible and covered by the standard's Cd correlation.
The permanent pressure loss is the fraction of the measured differential pressure that is not recovered downstream of the meter. For a sharp-edged orifice, approximately ΔP·(1−β²) is lost to turbulence and is never recovered; at β = 0.5, that is about 75 % of the measured differential. This loss is a real cost, because it must be made up by additional pumping power. For a Venturi meter, which has a smooth contraction and expansion, the loss is only 10–15 % of the differential, but a Venturi is much more expensive to manufacture. The choice between an orifice and a Venturi therefore comes down to a trade-off between capital cost (orifice is cheaper) and operating cost (Venturi has lower pumping penalty). For high-flow or high-pressure applications the pumping cost dominates and a Venturi or a flow nozzle is preferred; for low-flow or low-pressure applications an orifice plate is usually sufficient.
The diameter ratio β = d/D is the ratio of the orifice diameter to the pipe internal diameter. It is the single most important geometric parameter of the meter, because it appears in the (1−β⁴) correction term and because it sets both the sensitivity of the meter and the permanent pressure loss. Standard ISO 5167 orifice plates are limited to β between 0.20 and 0.75, because outside this range the Cd correlation is not valid: at very small β the vena contracta behaviour becomes unpredictable and the discharge coefficient has a much higher uncertainty, and at very large β (close to 1) the orifice offers almost no restriction and the differential pressure for a given flow is very small, so the meter has almost no sensitivity. In practice, most orifice meters are designed with β between 0.4 and 0.7, which gives a good compromise between sensitivity and pressure loss.
Only with care. The simple equation Q = Cd·A₀·√(2ΔP/(ρ(1−β⁴))) assumes incompressible flow, which is accurate for liquids and for gases at low Mach numbers (below about 0.3, i.e., velocities below about 100 m/s in air). At higher velocities, the gas expands as it accelerates through the orifice, and the density changes between the upstream and downstream taps. The ISO 5167 standard introduces an expansion factor ε to correct for this, which depends on β, the differential pressure, the upstream pressure, and the isentropic exponent of the gas. For critical gas-flow applications, the ε factor must be applied. This calculator does not include ε, so it is appropriate for liquid service and for low-Mach-number gas flow, but not for high-velocity gas measurements without a correction.
The turndown ratio is the ratio of the maximum flow to the minimum flow that the meter can measure within its stated accuracy. For an orifice meter, the turndown is limited by two factors: the square-root relationship between flow and differential pressure, which means that the differential is very small at low flow; and the practical range of the differential-pressure transmitter, which is typically 100:1 but with accuracy that degrades at the low end. In practice, orifice meters achieve a turndown of about 3:1 to 5:1 without changing the transmitter range, and up to about 10:1 with a smart transmitter that has an expanded range. By comparison, a Coriolis meter can achieve 100:1 turndown, a magnetic flow meter 20:1 to 50:1, and an ultrasonic meter 30:1 to 50:1. For applications with widely varying flow, a different meter type is usually preferable.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Q | Volumetric flow rate | m3/s |
| Cd | Discharge coefficient | |
| A0 | Orifice cross-sectional area | m2 |
| dP | Measured pressure drop | Pa |
| rho | Fluid density | kg/m3 |
| beta | Orifice-to-pipe diameter ratio |
What it means
The orifice meter is a widely used device for measuring flow rate in pipes, based on the pressure drop across a sharp‑edged orifice plate. The flow rate Q is given by Q = C_d A_0 √(2 ΔP / [ρ (1 − β⁴)]), where C_d is the discharge coefficient (typically 0.6‑0.65), A_0 is the orifice area, ΔP is the pressure differential, ρ is fluid density, and β is the diameter ratio (orifice diameter / pipe diameter). This equation is derived from Bernoulli’s equation with an empirical discharge coefficient to account for losses and contraction. The orifice meter is simple, inexpensive, and has no moving parts, making it popular in industrial applications. However, it causes a permanent pressure loss. The discharge coefficient is a function of Reynolds number and β, and is obtained from standard tables (ISO 5167). Accurate flow measurement is essential for process control, billing, and energy management. Understanding the orifice equation is fundamental for instrumentation and process engineers.
Worked example
Orifice Meter Flow – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Cd | 0.62 |
| A₀ | 0.001 m² |
| ΔP | 5000 Pa |
| ρ | 1000 kg/m³ |
| β | 0.5 |
| Parameter | Value |
|---|---|
| Cd | 0.61 |
| A₀ | 0.0008 |
| ΔP | 8000 |
| β | 0.4 |
Common mistakes
- Discharge coefficient C_d: Depends on the orifice geometry and Reynolds number – use a typical value (0.6‑0.65) or correlation.
- Orifice area A₀: The cross‑sectional area of the orifice opening.
- Differential pressure ΔP: Pressure drop across the orifice – in Pa.
- Beta ratio β: d/D (orifice diameter / pipe diameter) – dimensionless.
- Units: Ensure all units are consistent (SI) to get Q in m³/s.
Applications
The orifice meter flow rate equation, Q = C_d·A₀·√(2ΔP/(ρ(1−β⁴))), is used to measure flow rate from the pressure drop across an orifice plate. Orifice meters are widely used in industry due to their simplicity, low cost, and reliability. Engineers use this equation to size orifice plates, to interpret pressure differential readings, and to calibrate flow meters. The discharge coefficient C_d accounts for contraction and friction losses, and depends on β (orifice‑to‑pipe diameter ratio) and Reynolds number. By applying this formula, professionals can achieve accurate flow measurement for billing, process control, and mass balance calculations. It is a standard tool in chemical, oil, and gas industries.
- Design and sizing of orifice plates for flow measurement
- Interpretation of differential pressure readings in control systems
- Calibration and verification of flow meters
- Process monitoring and mass balance closure
- Energy and emissions accounting in industrial plants
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