Weir Flow Calculator

What is a Weir?

A weir is a notch or barrier in an open channel over which water flows. Weirs are used to measure flow in rivers, canals, and industrial channels. The flow rate depends on the head of water above the weir crest — this predictable relationship makes weirs reliable flow measurement devices.

Rectangular Weir (Francis Formula)

Q = 1.84 × L × H^(3/2) (in m³/s, SI units)

Where:

• L = weir length (m)
• H = head above weir crest (m)

With end contractions (2 contractions): Q = 1.84 × (L − 0.2H) × H^(3/2)

Triangular (V-notch) Weir

Q = (8/15) × Cd × √(2g) × tan(θ/2) × H^(5/2)

For a 90° V-notch: Q = 1.38 × H^(5/2) (simplified)

V-notch weirs are more accurate at low flows; rectangular weirs handle higher flows.

Practical Examples

Example 1 — Rectangular weir: L = 2m, H = 0.3m. Q = 1.84 × 2 × 0.3^1.5 = 1.84 × 2 × 0.1643 = 0.605 m³/s = 605 L/s.

Example 2 — 90° V-notch: H = 0.2m. Q = 1.38 × 0.2^2.5 = 1.38 × 0.01789 = 0.0247 m³/s = 24.7 L/s.

Applications

Weirs are used in: irrigation canal flow measurement, water treatment plant intake monitoring, river flow gauging stations, and effluent discharge monitoring.