ISO 5167-4:2022 classical Venturi tube sizing for liquid, gas and steam. Machined, rough cast and rough welded sheet-iron convergent inlet types. Fixed discharge coefficient per construction type. DP transmitter range recommendation.
A classical Venturi tube is a converging-diverging flow element inserted permanently into a pipeline. Fluid accelerates through the convergent inlet, reaching maximum velocity at the cylindrical throat where static pressure is lowest. The divergent outlet then decelerates the fluid, recovering most of the pressure. This differential pressure between the inlet and throat is proportional to the square of the flow rate.
The key advantage over orifice plates is pressure recovery: while an orifice plate permanently wastes 50–80% of the measured differential pressure to turbulence, a Venturi tube recovers 80–95% through its divergent cone, resulting in only 5–20% permanent pressure loss. This makes Venturi tubes the preferred choice for large-diameter pipes and high-flow applications where energy cost matters.
This calculator implements all three classical Venturi tube types per ISO 5167-4:2022: machined convergent inlet (Sec.6), rough cast convergent inlet (Sec.7), and rough welded sheet-iron inlet (Sec.8). The discharge coefficient is fixed per construction type — no iterative Cd calculation is required.
ISO 5167-4:2022 recognises three classical Venturi tube construction types, each with its own fixed discharge coefficient, dimensional ranges and manufacturing requirements.
| Cd | 0.9900 ± 0.0010 (±0.10%) |
| β range | 0.316 – 0.775 |
| D range | 50 – 500 mm |
| ReD | 2×10⁵ – 2×10⁶ |
| Convergent angle | 21° ± 1° |
| Throat length | 0.3d – 0.45d |
| Divergent angle | 7° – 15° |
| Uncertainty | Lowest of all three |
All internal surfaces machined and polished. The inlet cone, throat and divergent section are machined to tight dimensional tolerances giving the lowest Cd uncertainty (±0.10%). Best choice for custody transfer and high-accuracy applications. Suitable for pipes 50–500 mm.
| Cd | 0.9842 ± 0.0070 (±0.71%) |
| β range | 0.316 – 0.775 |
| D range | 100 – 800 mm |
| ReD | 2×10⁵ – 2×10⁶ |
| Convergent angle | 10.5° ± 1.5° (half-angle) |
| Throat length | ≥ 0.3d |
| Divergent angle | 5° – 15° (half-angle) |
| Uncertainty | Moderate — ±0.71% |
Cast iron or ductile iron body with a rougher as-cast surface finish. More economical than machined type and suitable for large diameters (100–800 mm). Higher Cd uncertainty (±0.71%) reflects the less controlled surface finish. Common in water treatment, HVAC and large-bore process applications.
| Cd | 0.9850 ± 0.0110 (±1.12%) |
| β range | 0.400 – 0.700 |
| D range | 200 – 1200 mm |
| ReD | 2×10⁵ – 2×10⁶ |
| Convergent angle | 21° ± 1° |
| Throat length | ≥ 0.3d |
| Divergent angle | 7° – 15° |
| Uncertainty | Highest — ±1.12% |
Fabricated by rolling and welding steel plate into a cone — the most economical construction for very large pipe diameters (200–1200 mm). The highest Cd uncertainty (±1.12%) reflects the as-welded surface condition. Where accuracy requirements are strict, confirm Cd with flow calibration. Widely used in large-bore water and wastewater applications.
Every input field explained — what it means, what value to enter, and how it affects the calculation.
Calculate Bore: Enter flow rates + max dP → sizes the throat diameter. Use for new designs.
Calculate Flow: Enter existing throat + max dP → calculates flow. Use to check existing meters.
Calculate dP: Enter existing throat + flow → calculates differential pressure. Use for transmitter verification.
Select the pipe size and wall schedule. The tool fills inside diameter D from ASME B36.10M data. For non-standard IDs (lined pipe, actual measured bore) select Custom and enter directly. Always use the actual measured bore ID — small errors in D cause errors in flow via the beta ratio (W ∝ D⁻²).
Determines the fixed Cd and all dimensional limits. Machined: highest accuracy, Cd = 0.9900 ±0.10%, for pipes 50–500 mm. Cast: economical for medium-large pipes 100–800 mm, Cd = 0.9842 ±0.71%. Welded: large bore only 200–1200 mm, Cd = 0.9850 ±1.12%. For critical applications with cast or welded types, request a flow calibration from the manufacturer.
Used to compute the thermal expansion factor Fa per ISO 5167. At operating temperatures above or below 20°C, the throat and pipe ID change slightly. For most ambient-temperature service the correction is negligible. At high temperature (>200°C) or cryogenic service it matters — select the actual material of the Venturi body and the pipe separately.
The fitting immediately upstream. Venturi tubes require significantly less straight run than orifice plates — typically 0.5D to 7D upstream vs 6D to 44D for orifice plates at the same beta ratio. This is one of the main practical advantages of Venturi tubes in congested pipe runs. If multiple disturbances are present, use the most demanding one.
Upstream static pressure P₁ and fluid temperature. For gas: used to calculate density (ρ = P·MW/Z·R·T) and the expansion factor Y. For liquid: pressure used for cavitation check (dP/P₁ < 0.25). For steam: pressure automatically gives saturation temperature via IAPWS-IF97; superheated steam also needs temperature input.
SG = ρ_fluid / ρ_water at 15°C. Enter at actual operating conditions, not standard conditions. Viscosity in cP at operating temperature — affects Reynolds number but not Cd (Cd is fixed for Venturi tubes). Select from the fluid database for automatic temperature interpolation between two reference points.
MW: Molecular weight in g/mol. Errors in MW directly produce proportional errors in density and flow. Z: Real gas compressibility factor (Z=1 for ideal gas; use EOS for high-pressure gas). k (κ): Cp/Cv ratio — used only in gas expansion factor Y. Air = 1.40, natural gas ≈ 1.28–1.32, steam ≈ 1.135.
Saturated: Enter pressure only — saturation temperature, density, viscosity and κ are automatically calculated server-side via IAPWS-IF97. Superheated: Enter both pressure and temperature — properties again from IAPWS-IF97. The saturation temperature display confirms there is sufficient superheat margin.
Used for cavitation awareness. If the throat pressure drops below the fluid vapour pressure, cavitation occurs — bubbles form and collapse at the throat, causing erosion and measurement errors. The cavitation index can be checked with: P_throat ≈ P₁ − (1 + β⁴) × ΔP/2. The calculator warns when dP/P₁ exceeds 0.25 as an approximate indicator.
The highest flow the meter must measure. The throat is sized so that at this flow the differential pressure equals the max dP range you enter. Set to 110–125% of normal flow for margin. Typically set from the process data sheet or equipment design flow.
Normal flow determines the DP transmitter range recommendation — the tool targets normal dP at 40–65% of transmitter span. Minimum flow is shown in the dP table to verify the minimum differential is above the transmitter noise floor. Venturi tubes have the same 3:1 to 4:1 flow turndown limitation as orifice plates (square-root relationship).
The DP transmitter measurement span — not the pressure loss. The tool sizes the throat so maximum flow produces this differential. The tool then checks: (1) dP/P₁ < 0.25 for liquid cavitation risk, (2) dP/P₁ vs critical pressure ratio for choked gas flow, (3) selects the nearest standard transmitter range (25, 50, 100, 160, 250, 400 mbar...) targeting normal dP at 40–65% of span.
Cause: Calculated throat diameter is larger than pipe ID or near zero.
Fix: Increase the max dP range (gives a smaller throat / lower beta), or select a larger pipe size. Valid beta: machined/cast 0.316–0.775; welded 0.400–0.700.
Below minimum: Increase max dP range or select smaller pipe. Very small beta means very small throat — machining tolerances become significant, and the already-low Venturi pressure loss increases.
Above maximum: Reduce max dP range or select larger pipe. Very large beta gives a weak dP signal.
Cause: Flow is too low, pipe too small, or fluid too viscous for ISO 5167-4 Cd to be valid.
Fix: Select a larger pipe size, increase flow, or reduce viscosity (increase temperature). Unlike orifice plates, there is no alternative Venturi type for low Re — consider a different meter technology (magnetic, Coriolis) for low-Re service.
Cause: Very high velocity — common in large-bore water pipes or low-viscosity fluids at high flow.
Fix: The Cd = constant assumption may not hold at very high Re. Request a flow calibration from the manufacturer, or select a larger pipe size to reduce velocity. ISO 5167-4 Cd values are validated only up to ReD = 2×10⁶.
Cause: Pipe ID is outside the ISO 5167-4 validated range for the selected construction type. Machined: 50–500 mm. Cast: 100–800 mm. Welded: 200–1200 mm.
Fix: Select a different construction type with a wider D range, or contact the manufacturer for a custom calibrated unit.
Cause: dP/P₁ ≥ critical pressure ratio (2/(κ+1))^(κ/(κ-1)). Gas velocity at the throat has reached the speed of sound — the Venturi equation is invalid.
Fix: Significantly reduce max dP, increase beta (larger throat), or raise operating pressure. For intentional choked flow measurement use a critical flow nozzle per ISO 9300.
Cause: dP/P₁ > 0.25. The throat pressure may drop below the fluid vapour pressure, causing flashing or cavitation — eroding the throat and producing inaccurate readings.
Fix: Reduce max dP range, increase operating pressure, or select a larger throat (higher beta). Note that the Venturi throat pressure is lower than for an orifice plate at the same beta and dP — cavitation risk is slightly higher.
Cause: Throat gas velocity exceeds 25% of sonic velocity. The gas expansion factor Y correction becomes important and the incompressible Bernoulli equation is no longer adequate.
Fix: Reduce max dP, increase beta (larger throat), or raise operating pressure. The Y factor calculated by the tool corrects for compressibility per ISO 5167-4 Sec.5.3 — verify Y < 0.98 and consider manufacturer consultation at Ma > 0.4.
The fixed Cd per ISO 5167-4 is valid down to ReD = 2×10⁵ but some manufacturers recommend conservatively using Cd values only above ReD = 5×10⁵ for high-accuracy applications. At borderline Re, request a flow calibration — or confirm the Cd with the manufacturer's test data.
Cast (±0.71%) and welded (±1.12%) Cd uncertainties are significantly higher than machined (±0.10%). For flow measurement where accuracy better than ±1% is required, either specify machined type or obtain a flow calibration certificate from the manufacturer — the calibrated Cd will reduce uncertainty substantially.
The beta ratio β = d/D (throat/pipe) governs the tradeoff between differential pressure signal strength, pressure loss and straight run requirements. The practical target range for most applications is 0.45 ≤ β ≤ 0.65.
Adjust beta by changing max dP range: increase dP range → smaller throat (lower beta), decrease dP range → larger throat (higher beta). Alternatively change pipe size.
For orifice plates, the discharge coefficient Cd depends on the Reynolds number, which depends on the flow, which depends on Cd — requiring iterative solution (typically 20–200 iterations). For Venturi tubes, Cd is a fixed constant per construction type with no Reynolds dependence within the valid range. The only iteration needed is for the gas expansion factor Y in compressible flow, which converges in 3–5 iterations. This makes Venturi sizing faster and more numerically robust.
This equation is identical to ISO 5167-2 (orifice plate) and is explicitly confirmed applicable to classical Venturi tubes in ISO 5167-4:2022 Sec.5.3. For liquids Y = 1.0. For gases at moderate differentials (ΔP/P₁ < 0.25) Y is typically 0.97–0.99. Valid for all three construction types within their respective validated ranges.
The most important practical advantage of Venturi tubes over orifice plates is dramatically lower permanent pressure loss. The divergent outlet cone decelerates the fluid and converts kinetic energy back to pressure — a process called pressure recovery.
For a pump system, permanent pressure loss translates directly to additional pump head and energy consumption. On a 12-inch water line flowing 1,000 m³/hr at 500 mbar differential: an orifice plate wastes ~350 mbar (70%) permanently — requiring the pump to overcome this every hour of operation. A Venturi tube in the same service wastes only ~60 mbar (12%). At $0.10/kWh and 8,760 hours/year, the Venturi tube can save tens of thousands of dollars annually in pumping energy. This payback typically justifies the higher initial cost of a Venturi tube for large-bore high-flow applications.
Minimum upstream straight pipe lengths (in pipe diameters D). Venturi tubes require far less straight run than orifice plates — typically 0.5D to 7D upstream vs 6D to 44D for orifice plates at the same beta ratio. The downstream requirement is a constant 4D for all beta ratios.
For multiple upstream disturbances, use the disturbance requiring the longest straight run. All three construction types use the same Table 1 values.
| UPSTREAM DISTURBANCE | β≤0.35 | β≤0.40 | β≤0.45 | β≤0.50 | β≤0.55 | β≤0.60 | β≤0.65 | β≤0.70 | β≤0.775 |
|---|---|---|---|---|---|---|---|---|---|
| Single 90° bend | 0.5 | 0.5 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 |
| Two 90° bends — same plane | 0.5 | 0.5 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 |
| Two 90° bends — different planes | 1.5 | 1.5 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.5 | 5.5 |
| Reducer (2D→D) | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1.0 | 1.0 |
| Expander (0.5D→D) | 1.5 | 1.5 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.5 | 5.5 |
| Gate valve (fully open) | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 |
| Globe / angle valve (fully open) | 2.0 | 2.0 | 2.0 | 2.0 | 3.0 | 4.0 | 5.0 | 6.0 | 7.0 |
| Thermometer pocket / well | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
| Downstream (all disturbances) | 4D — constant for all β and disturbance types | ||||||||
All values in pipe diameters (D). Highlighted values indicate disturbances requiring more than 1.5D. Source: ISO 5167-4:2022 Table 1. Compare with orifice plate Table 1 which reaches 44D at high β — the Venturi advantage in congested pipe runs is significant.
The square-root relationship between flow and differential pressure is the same for Venturi tubes as for orifice plates. Selecting the correct transmitter span is as important as sizing the throat.
This tool recommends a transmitter range from the standard instrument series (25, 50, 100, 160, 250, 400, 630, 1000, 1600, 2500 mbar...) targeting normal flow differential at 40–65% of the span. This gives 3:1 to 4:1 flow turndown with adequate accuracy. The Venturi's lower permanent loss means you can choose a lower dP range (and therefore a smaller throat / lower beta) at the same operating cost as an orifice plate with a higher dP range.
Choose a Venturi tube when: (1) energy cost matters — large-diameter pipes at high flow where permanent pressure loss represents significant pumping cost, (2) congested pipe runs — minimal straight run requirement (0.5D–7D) vs orifice plate (6D–44D), (3) slurry or dirty service — the converging-diverging profile is inherently self-cleaning, (4) high-velocity service — the smooth profile avoids the cavitation-prone vena contracta of orifice plates. Choose orifice plates when cost is the primary factor, when the pipe is small (<50 mm), or when you need to change the meter range in the field (you can change the orifice plate; you cannot change the Venturi).
At turbulent flow conditions (ReD > 2×10⁵), the flow through a well-formed convergent-divergent passage approaches ideal (Cd → 1.0) and becomes nearly independent of Reynolds number. The Venturi's smooth gradual convergence produces a stable, well-defined streamline pattern with minimal separation — unlike the sharp-edge orifice plate where the vena contracta contracts and expands with Re. This Reynolds-independence is actually a major practical advantage: once a Venturi is manufactured and installed, no Re-based Cd correction is needed at any flow within the valid range.
This tool implements ISO 5167-4:2022 and is suitable for preliminary engineering and instrument specification. For legal custody transfer the final calculation must be performed using certified software, and the Venturi tube must be manufactured and flow-calibrated to ISO 5167-4 tolerances. For machined types the tabulated Cd = 0.9900 ±0.10% can be used without calibration if ISO geometric tolerances are met — making machined Venturi tubes one of the few meter types that can be used for custody transfer without individual calibration.
The divergent (outlet) cone angle determines the pressure recovery efficiency. A smaller angle (7°–8°) gives better pressure recovery but a longer body — ideal when energy cost is the priority. A larger angle (12°–15°) shortens the Venturi but increases the permanent loss slightly due to flow separation in the diffuser. ISO 5167-4 permits 7°–15° for machined and welded types. The tool does not require you to specify the exact angle — the Xi = 0.10 (machined) and Xi = 0.15 (cast/welded) loss coefficients are representative midrange values per Miller (1996).
The 2022 revision made several important changes: (1) Cd for machined type changed from 0.995 to 0.9900 — a 0.5% reduction, which is significant for custody transfer applications; (2) the uncertainty on the machined type Cd was tightened from ±0.5% to ±0.10%; (3) ReD upper limit confirmed at 2×10⁶ for all types; (4) the standard structure was reorganised with clearer separation between construction types. This tool uses the 2022 values throughout. Reference tools still using the 2003 Cd = 0.995 will give slightly different (less accurate) throat diameters.
Fa = 1 + 2α(Top − 20°C) corrects the throat diameter (and pipe ID) for thermal expansion at the operating temperature. Tref = 20°C per ISO 5167 Sec.7.3.1 — this is the standard reference temperature for bore measurement. For service near ambient temperature (0–60°C) the correction is typically <0.05% and negligible. At high temperature (200°C): SS316 Fa ≈ 1.0024 — a 0.24% throat expansion. At cryogenic temperature (−100°C): Fa < 1 — the bore is smaller than the room-temperature measurement. For custody transfer or high-accuracy applications at elevated temperatures, ensure materials are specified correctly so Fa is calculated correctly.
| PROPERTY | VENTURI TUBE | ORIFICE PLATE |
|---|---|---|
| Standard | ISO 5167-4:2022 | ISO 5167-2:2022 |
| Permanent pressure loss | 5–20% of ΔP | 50–80% of ΔP |
| Discharge coefficient Cd | Fixed (0.9842–0.9900) | Re-dependent (RHG) |
| Best Cd uncertainty | ±0.10% (machined) | ±0.50% (standard) |
| Upstream straight run | 0.5D – 7D | 6D – 44D |
| Downstream straight run | 4D (constant) | 4D–8D |
| Pipe diameter range | 50–1200 mm | 50 mm minimum |
| ReD minimum | 200,000 | 5,000 (standard plate) |
| Capital cost | Higher (5–10× orifice) | Lower |
| Rangeability (field) | Fixed — cannot change in field | Changeable — swap plate |
| Solids / slurry handling | Good — self-cleaning profile | Poor — accumulates at plate |
Measurement of fluid flow by pressure differential devices — Part 4: Venturi tubes. Covers all three classical construction types. Key 2022 changes: machined Cd revised from 0.995 to 0.9900; uncertainty on machined type tightened from ±0.5% to ±0.10%; restructured by construction type. This tool implements the 2022 edition throughout.
General principles and requirements — the common part of the ISO 5167 series. Defines the fundamental mass flow equation, gas expansion factor Y, thermal expansion factor Fa, pipe Reynolds number and general installation requirements applicable to all differential pressure meters including Venturi tubes.
Measurement of fluid flow — Procedures for the evaluation of uncertainties. Used for the flow uncertainty calculation: δW/W = √[(δCd)² + (2δd)² + (2δD)² + (δρ/2)² + (δΔP/2)²]. The dominant term for machined Venturi is δd (throat measurement), not δCd — unlike cast and welded types where δCd dominates.
Petroleum liquids and gases — Standard reference conditions. Base conditions for standard volume flow: Pbase = 101.325 kPaa, Tbase = 15°C. Used when expressing gas flow in standard cubic metres (Sm³/hr).
Welded and Seamless Wrought Steel Pipe. Inside diameter data for NPS ½ to NPS 24, all standard schedules. Source for the pipe schedule dropdown in this tool.
Flow Measurement Engineering Handbook, 3rd Edition, McGraw-Hill. Source for the Venturi tube head-loss coefficient Xi used in the permanent pressure loss calculation (Sec.9, Table 9.5). Xi = 0.10 (machined), 0.15 (cast/welded) — consistent with ISO 5167-4 Sec.5.4 stating 5–20% of ΔP.
International Association for the Properties of Water and Steam — Industrial Formulation 1997. Used server-side to calculate steam density, viscosity and isentropic exponent from pressure and temperature for saturated and superheated steam. Accuracy: Region 2 (superheated) <0.01%, saturation T <0.5°C.
A viscosity equation for gas mixtures. Journal of Chemical Physics, 18(4):517–519. Used for gas mixture viscosity calculation via the Gas Mixture Builder. Gives results within 2% for most non-polar gas mixtures — the same method used in HYSYS, PRO/II and AspenPlus.