A pressure gauge reads a few kPa across a plate in your pipe — and from that single number you can know exactly how much fluid is flowing. That's the elegant principle behind orifice plates and venturi meters, the two most common differential-pressure flow meters in industry. Squeeze the flow through a constriction, measure the pressure drop, and Bernoulli's principle gives you the flow rate. This free Orifice & Venturi Flow Meter Calculator applies the ISO 5167 equations to turn your differential-pressure reading into volumetric and mass flow — or reverse-solve the bore size you need — for both liquids and gases.
Table of Contents
The Flow Meter Calculator
Choose orifice or venturi, then solve for flow rate from your differential pressure, or reverse-solve the bore diameter for a target flow. The tool returns volumetric flow, mass flow, velocity, beta ratio and the velocity-of-approach factor. Consistent SI units.
Orifice & Venturi Flow Meter Calculator
How Differential-Pressure Flow Meters Work
Orifice plates and venturi meters share one principle. When fluid is forced through a constriction, it speeds up — and by conservation of energy (Bernoulli), its pressure drops. The faster the flow, the bigger the pressure drop. So by measuring the differential pressure ΔP = P1 − P2 across the constriction, we can back-calculate the flow rate.
The ISO 5167 Flow Equation
The international standard ISO 5167 governs these meters. Its volumetric flow equation is:
where C is the discharge coefficient, E the velocity-of-approach factor, ε the expansibility factor (1 for liquids), d the bore/throat diameter, ΔP the differential pressure, and ρ the density. Mass flow follows immediately:
The square-root dependence on ΔP and the density term connect directly to the physics in our pressure drop & head loss calculator — the same Bernoulli energy balance underlies both.
Beta Ratio & Velocity of Approach
The beta ratio is the heart of the geometry:
Because the upstream pipe area is finite, the incoming fluid already has some velocity — corrected by the velocity-of-approach factor:
| Beta β | E factor | Behaviour |
|---|---|---|
| 0.2 | 1.001 | Large ΔP signal, high permanent loss |
| 0.5 | 1.033 | Balanced — common choice |
| 0.7 | 1.147 | Low loss, weaker signal |
| 0.75 | 1.210 | ISO 5167 upper limit |
The Discharge Coefficient
Real flow isn't ideal — the stream contracts (the vena contracta), and friction bites. The discharge coefficient C corrects for all of this:
| Device | Discharge coefficient C |
|---|---|
| Orifice plate (sharp-edged) | ~0.60 – 0.61 |
| Venturi, cast convergent | 0.984 |
| Venturi, machined convergent | 0.995 |
| Flow nozzle | ~0.95 – 0.99 |
For orifices, C varies slightly with beta and Reynolds number via the precise Reader-Harris/Gallagher equation, but ~0.61 is an excellent working value. The venturi's high, stable C is its big advantage. The flow regime (via the Reynolds number) determines whether your C is in its valid range.
Orifice vs Venturi: Which to Use?
| Feature | Orifice Plate | Venturi Tube |
|---|---|---|
| Cost | Low — cheap plate | High — precision casting |
| Permanent pressure loss | High (~50–75% of ΔP) | Low (~10–20%) |
| Discharge coefficient | ~0.61 (lower) | ~0.98–0.99 (higher, stable) |
| Size / space | Compact (thin plate) | Large & long |
| Installation / service | Easy to inspect & replace | Permanent, bulky |
| Best for | General, dirty fluids, tight budgets | Large pipes, energy-sensitive, clean fluids |
Liquids vs Gases: The Expansibility Factor
For liquids (incompressible), density is constant and the expansibility factor is exactly ε = 1 — the basic equation applies directly.
For gases, the pressure drop makes the gas expand and its density fall across the constriction. The expansibility factor ε < 1 corrects for this. For a venturi (ISO 5167-4):
where κ is the isentropic exponent (1.40 for air) and P1 the absolute upstream pressure. In practice ε is usually 0.98–1.00.
Worked Example
Water through an orifice plate: pipe D = 100 mm, bore d = 50 mm, ΔP = 20 kPa, ρ = 1000 kg/m³, C = 0.61:
- β = 50/100 = 0.5
- E = 1/√(1 − 0.5⁴) = 1/√0.9375 = 1.0328
- Bore area = (π/4)(0.05)² = 0.001963 m²
- Q = 0.61 × 1.0328 × 1 × 0.001963 × √(2×20000/1000)
- Q = 0.61 × 1.0328 × 0.001963 × 6.325 ≈ 0.0078 m³/s = 28.2 m³/hr
- Mass flow = 0.0078 × 1000 ≈ 7.8 kg/s
Swap to a machined venturi (C = 0.995) and the same ΔP yields ~46 m³/hr — the venturi's efficiency in action.
Common Mistakes
- Standard-condition gas density. Always use density at operating P and T — the biggest gas error.
- Forgetting the velocity-of-approach factor E. At high β it's a significant correction, not optional.
- Wrong discharge coefficient. ~0.61 for orifice, ~0.98–0.99 for venturi — don't mix them up.
- Beta ratio out of range. Keep 0.2 ≤ β ≤ 0.75 for a valid ISO 5167 measurement.
- Skipping expansibility for gases. Liquids ε = 1, but gases need ε < 1.
- Ignoring installation requirements. You need 10–40 pipe diameters of straight run upstream for a good profile.
- Confusing ΔP with permanent loss. The measured ΔP is not the permanent pressure loss — some recovers downstream.
Frequently Asked Questions
How do you calculate flow rate from differential pressure?
Use Q = C·E·ε·(π/4)d²·√(2ΔP/ρ), where E = 1/√(1−β⁴) and β = d/D. Multiply by density for mass flow. Liquids use ε = 1.
What is the difference between an orifice and a venturi meter?
Both use a constriction and DP, but an orifice is a cheap thin plate with high permanent loss and C ≈ 0.61, while a venturi is a smooth, costlier tube with low permanent loss and C ≈ 0.98–0.99.
What is the beta ratio?
β = d/D, the bore-to-pipe diameter ratio. ISO 5167 requires 0.2–0.75. Lower β gives a stronger signal but more pressure loss.
What is the discharge coefficient?
C corrects ideal flow for contraction and friction. Orifice ~0.60–0.61 (Reader-Harris/Gallagher); venturi ~0.984 (cast) to 0.995 (machined).
Does the calculator work for gases?
Yes — set the expansibility ε < 1, use operating-condition density, and keep ΔP/P₁ ≤ 0.25. Liquids use ε = 1.
Why is a venturi better than an orifice plate?
Its gradual diverging section recovers most of the pressure, so permanent loss is far lower — more energy-efficient, though costlier and bulkier than an orifice.
Conclusion
Orifice and venturi meters turn a simple pressure reading into a precise flow measurement using one elegant equation: Q = C·E·ε·(π/4)d²·√(2ΔP/ρ). Get the beta ratio, discharge coefficient and (for gases) expansibility right, keep β in the ISO 5167 range, and use density at operating conditions — and you can measure flow reliably with nothing more than a differential-pressure gauge.
Use the calculator above to convert your ΔP reading to flow rate, or to size the bore for a target flow, in either device — backed by the same ISO 5167 method used across industry.
For more fluid mechanics, pipe-flow and CFD tutorials plus free engineering calculators, explore Free CFD Tutorial. If this tool helped you, please share it with your fellow engineers and students.