Flow-cal

Flow Meter Calculator

Square-edge concentric orifice — ISO 5167-2 simplified form

β = —

Flow Meter Category

Only the selected category's calculation is shown on screen and included when you print — everything else stays out of the printout.

Meter Type

Thin plate with a sharp-edged bore d in a pipe of diameter D. ΔP is read across flange/corner taps straddling the plate. Input: D, d, ΔP, ρ, Cd — Output: Q / ṁ.

Smooth converging throat d, then a gradual diffuser recovers most of the pressure back toward D. P1 upstream, P2 at the throat. Input: D, d, ΔP, ρ, Cd — Output: Q / ṁ + low permanent loss.

Smooth elliptical/conical converging section to throat d, but no diffuser — flow re-expands abruptly downstream. Good at high velocity/temperature (e.g. steam). Input: D, d, ΔP, ρ, Cd — Output: Q / ṁ.

Calculation Mode

Fluid

Density at operating conditions

kg/m³ g/cm³

Dynamic viscosity, μ

cP (mPa·s) Pa·s

Isentropic exponent, κ (Cp/Cv)

Operating temperature

°C K

Geometry

Pipe internal diameter, D

mm inch

Orifice bore diameter, d

mm inch

Required flow rate

kg/hr m³/hr (actual) Sm³/hr

Convergent section type Machined As-cast Rough-welded sheet-metal

Nozzle type ISA 1932 nozzle Long radius nozzle

Discharge coefficient, Cd

Typical square-edge orifice (corner / D-D/2 taps): 0.60–0.62

Pressure

Differential pressure, ΔP

mmWC mbar kPa kg/cm² bar

Upstream line pressure, P1

kg/cm²(g) bar(g) kPa(g) kg/cm²(a) bar(a) kPa(a)

For gas service, P1 is used only for the expansibility factor (Y) and Sm³/hr normalization. Actual density above should already reflect P1/T1. Gauge values are converted to absolute using 1 atm = 1.01325 bar(a).

Results

Orifice Selection Guide

β = d/D	Guidance
< 0.20	Avoid if possible — high permanent pressure loss and high jet velocity through the bore for the pressure gained; only used when a very high ΔP is genuinely wanted (e.g. deliberate throttling).
0.20 – 0.65	Preferred working range. Best balance of measurement accuracy, permanent pressure loss, and manufacturing tolerance. Aim for β ≈ 0.4–0.6 at normal flow when there's no other constraint.
0.65 – 0.75	Usable, but Cd/expansibility uncertainty increases and bore machining tolerance becomes more critical. Prefer only when ΔP available is limited (e.g. low driving pressure).
> 0.75	Outside ISO 5167 validated range — do not use for fiscal/custody metering; re-check line size or ΔP instead.

Differential pressure (ΔP)
Pick the design ΔP to suit the DP transmitter span and desired turndown. Since flow ∝ √ΔP, a 4:1 flow turndown needs a 16:1 span turndown. Typical design ΔP: 2000–2500 mmWC (≈0.2–0.25 kg/cm²) for a 100% flow at ~80–90% of transmitter span, leaving headroom for surges.

Permanent pressure loss
Approx. PPL ≈ ΔP × (1 − β²). Lower β wastes more driving pressure — relevant where pumping/compression cost matters.

Reynolds number
Keep Re_D above ~5,000–10,000 at minimum flow so Cd stays stable per ISO 5167; below this the discharge coefficient correlation is no longer valid. Re_D and Re_d are now computed live below from your entered viscosity — check them at minimum flow, not just at the design point.

Straight-run requirements
Provide adequate straight, unobstructed pipe upstream (typically 10D–44D depending on upstream fitting type and β) and downstream (typically 4D–8D) of the orifice plate per ISO 5167 / plant P&ID standard.

Plate & edge
Square-edged plate, edge sharpness radius ≤ 0.0004d, plate thickness ≤ 0.05D (bevel the downstream face at 45° if thicker), bore measured and averaged at 4 diameters minimum.

Rangeability check
Verify the selected d also gives an acceptable ΔP (and Re) at minimum expected flow, not just at normal/design flow — a plate sized only for the high case can under-range at turndown.

Orifice vs Venturi vs Nozzle — Quick Comparison

Aspect	Orifice Plate	Venturi Tube	Flow Nozzle
Cd (typical)	0.60 – 0.62	0.995 machined / 0.984 as-cast / 0.985 rough-welded	0.98 ISA 1932 / 0.99 long radius
β range	0.20 – 0.75	≈0.30 – 0.75	≈0.20 – 0.80 (usable at higher β/velocity)
Permanent pressure loss	High: ≈(1−β²)×ΔP, often 40–90%	Low: ≈10–20% — diffuser recovers most	Similar order to orifice — no diffuser
Straight run needed	Longer: 10D–44D upstream	Shorter: 5D–20D upstream	Similar to orifice, slightly shorter
Best suited for	General clean-service, cost-sensitive metering	Where low permanent loss or erosive/dirty service matters	High-velocity / high-temperature service (steam), where cavitation risk rules out an orifice
Cost & footprint	Low cost, compact	Higher cost, longer laying length	Moderate cost, shorter than Venturi

Nozzle Cd is only weakly Reynolds-dependent at high Re (unlike orifice) — the values above are reasonable defaults for typical process Re, but ISO 5167-3 gives an exact Re-dependent correlation if higher accuracy is needed.

Mass Flow Meter (Coriolis / Thermal) — Sizing Check

Coriolis meters derive mass flow from a factory-calibrated flow calibration factor unique to each tube; thermal meters are calibrated to a specific gas's thermal properties. Neither has a generic first-principles equation like ISO 5167 — final model, bore, accuracy, turndown, and pressure drop must come from the vendor's own sizing software using your process data sheet. This section only gives a quick, vendor-independent velocity check to sanity-check a candidate bore before going to the vendor tool.

Tube(s) are vibrated at their natural frequency; mass flow twists/phase-shifts the tube ends. That twist is measured directly as mass flow — no ΔP or density term needed. Input: none beyond flow itself — Output: ṁ directly, from the factory-calibrated tube.

Mass flow rate

kg/hr

Fluid density

kg/m³

Candidate meter bore, D

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