Orifice Plate Flow Rate Calculator

Measuring flow with an orifice plate

An orifice plate is a thin plate with a central hole clamped between flanges in a pipe. The flow speeds up through the hole and the pressure falls. The pressure difference between the upstream and downstream sides is measured and the flow rate follows from it: Q = Cd × A × √(2 × Δp / (ρ × (1 − β⁴))), where A is the bore area, β the ratio of bore to pipe inside diameter and Cd the discharge coefficient.

Why is the discharge coefficient around 0.61?

The flow separates at the sharp edge and the jet keeps contracting after the bore. The narrowest section is smaller than the hole and the eddies dissipate energy. Both effects are lumped into Cd. For a thin sharp edged plate at high Reynolds numbers the value lies between 0.60 and 0.62. The exact figure depends on diameter ratio, Reynolds number and where the pressure tappings sit.

Example

A plate with a 60 mm bore sits in a pipe of 100 mm inside diameter and the difference read for water is 30 kPa. Then β = 0.6 and 1 − β⁴ = 0.8704. √(60 000 / 870.4) = 8.30 m/s and the bore area is 0.002827 m². With Cd = 0.61 the flow rate is 0.61 × 0.002827 × 8.30 = 0.01432 m³/s, or 14.3 litres per second.

Limits

The calculation is for liquids in a full pipe. Gases and steam need an expansibility factor. The measured difference is not the permanent pressure loss, since part of the pressure recovers downstream. Custody transfer and plate design follow ISO 5167.