Zerdly

Orifice Flow Rate Calculator

Calculate the discharge through a sharp-edged orifice from its diameter, the driving head and a discharge coefficient. Returns the flow in both m³/s and L/s plus the orifice area.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the orifice diameter in millimetres.
  2. Enter the head of liquid above the orifice in metres.
  3. Leave Cd at 0.61 for a sharp-edged circular orifice, or change it for a rounded or metering orifice, then read the flow rate.

How it works

The flow is Q = Cd · A · √(2·g·h), where A = π/4 · (d/1000)² is the orifice area, √(2·g·h) is Torricelli's ideal jet velocity for head h, and Cd corrects for jet contraction (the vena contracta) and losses. A sharp-edged circular orifice has Cd ≈ 0.61.

Worked example

Worked example. A 50 mm sharp-edged orifice under a 2 m head has an area of π/4 × 0.05² = 0.0019635 m². The ideal jet velocity is √(2 × 9.81 × 2) = 6.264 m/s, so Q = 0.61 × 0.0019635 × 6.264 = 0.0075 m³/s, i.e. about 7.5 L/s.

Common mistakes

  • Entering the orifice diameter in metres instead of millimetres — the tool expects mm and converts internally.
  • Using the sharp-edged Cd of 0.61 for a rounded, re-entrant or metering orifice, which have different coefficients.
  • Measuring the head to the water surface rather than to the centre of the orifice, which changes h.

Frequently asked questions

What value of Cd should I use?

About 0.61–0.62 for a sharp-edged circular orifice, ~0.5 for a re-entrant (Borda) mouthpiece, and closer to 0.97–0.99 for a well-rounded bellmouth. Metering orifice plates use coefficients from standards such as ISO 5167.

Does this work for a submerged orifice?

Yes — for a fully submerged orifice use the difference in head across the orifice (upstream minus downstream level) as h. The same Q = Cd · A · √(2·g·h) applies with the appropriate coefficient.

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