Orifice, Venturi, and Nozzle Meters: From ΔP to Flow Rate
Differential-pressure meters infer Q from a constriction. β ratio, Cd, the 1/√(1−β⁴) factor, permanent pressure loss, and ISO 5167 caveats.
Key takeaways
- Q = Cd a / √(1−β⁴) × √(2 ΔP/ρ) for incompressible flow.
- Typical Cd: orifice ~0.61, nozzle ~0.96, Venturi ~0.98.
- Keep 0.2 < β < 0.75 for standard tappings.
- Orifices waste ΔP; Venturis recover most of it.
An orifice plate, flow nozzle, or Venturi tube converts a known geometry into a flow reading through a measured pressure drop. Bernoulli plus continuity at the throat, corrected by a discharge coefficient, is the whole theory.
The meter equation
| Meter | Typical Cd | Permanent loss | Notes |
|---|---|---|---|
| Thin orifice | 0.60–0.63 | High (most of ΔP) | Cheap, sharp edge required |
| ISA / long-radius nozzle | 0.95–0.99 | Medium | Erosion-tolerant |
| Venturi | 0.97–0.99 | Low (recovered) | Long, expensive, best ΔP recovery |
Example: D = 0.2 m, d = 0.1 m, β = 0.5, ΔP = 25 kPa, water, Cd = 0.61. Approach factor 1/√(1−0.0625) = 1.033. Throat area = 0.00785 m². Q ≈ 0.61 × 0.00785 × 1.033 × √(2×25000/998) ≈ 0.035 m³/s (35 L/s).
Link to valves and Bernoulli
A control valve is a variable orifice with a published Cv instead of Cd and β. The energy story is the same constriction. A Venturi is a careful nozzle plus a recovery cone — the opposite of a sudden expansion.
Open solver: Valve Cv (related constriction)Open solver: Bernoulli at the throatOpen solver: Why recovery cones matterFrequently asked questions
Yes for compressible flow. The liquid formula assumes constant density. ISO 5167 gives Y for orifices, nozzles, and Venturis on gas.