🚰 Orifice Plate Flow Calculator
Calculate fluid flow rate through an orifice plate using Bernoulli principle and discharge coefficient.
Inputs
Typical value is ~0.61 for standard orifice plates.
Results
Orifice Flow Diagram
Calculator Description
The orifice-flow equation relates the flow rate through a thin plate with a hole (orifice plate) installed in a pipe to the pressure drop (ΔP) it creates. It is both the principle of an orifice flow meter and the basic relation for fluid discharge through a pipe restriction.
What this calculator finds
From the orifice diameter d, pipe diameter D, fluid density ρ and pressure drop ΔP, it computes the volumetric flow rate Q. The beta ratio β = d/D and the discharge coefficient C_d correct for real-flow losses.
Why it matters
- Understanding flow conversion in differential-pressure (orifice) meters
- Sizing flow and pressure drop across a restriction in a pipeline
- Estimating discharge through openings in tanks and vessels
Formula
Orifice Flow Equation
It converts the driving energy from the pressure drop (2ΔP/ρ) into velocity, then multiplies by the orifice area A_o and the discharge coefficient C_d. A velocity-correction term for the area ratio, (1−β⁴), appears in the denominator.
- Q — Volumetric flow rate [m³/s (ft³/s)]
- C_d — Discharge coefficient (actual/theoretical flow, typically ≈ 0.61)
- A_o — Orifice area (π·d²/4) [m² (ft²)]
- ΔP — Pressure drop [Pa (psi)]
- ρ — Fluid density [kg/m³ (lb/ft³)]
- β — Beta ratio (orifice diameter / pipe diameter)
How the formula works
- A larger pressure drop ΔP increases flow proportionally to √ΔP.
- A larger density ρ reduces the flow for the same drop (denominator).
- As the beta ratio β approaches 1 (orifice ≈ pipe), the correction (1−β⁴) shrinks and flow grows.
- The discharge coefficient C_d depends on β, Reynolds number and installation; for standard orifices it is ≈ 0.6–0.62.
Worked example
For a 50 mm orifice (β = 0.5) in a 100 mm pipe with water (ρ = 1000 kg/m³) at a 10 kPa drop: correction (1−0.5⁴) = 0.9375, A_o = π·0.05²/4 ≈ 0.001963 m². Q ≈ 0.61 × 0.001963 × √[ 2×10000 / (1000×0.9375) ] ≈ 0.61 × 0.001963 × 4.62 ≈ 0.0055 m³/s (about 5.5 L/s).
Useful Tips
Practical tips
- Keep straight pipe runs (≥10D upstream, ≥5D downstream) for a stable turbulent profile and accurate C_d.
- Design beta ratio in roughly 0.3–0.7; too large a β gives a small, error-prone pressure drop.
- For compressible gas, apply an expansion correction for density change.
Limitations & cautions
- C_d is empirical; fouling, wear and installation error degrade accuracy over time.
- At high viscosity or low Reynolds number, C_d changes sharply and needs separate correction.
- Orifices cause significant permanent pressure loss and may be unsuitable where energy efficiency matters.