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Measuring flow over a weir, and knowing when the reading is wrong

Converting head over a crest to discharge for common weir shapes, and the conditions that invalidate the reading.

The engineering question

A weir is installed to measure flow. What does the head actually mean, and when will the calculation be wrong?

Worked example

The figures below were produced by running the Weir Flow Calculator with the same inputs — during the build, from its authoritative engine.

Results
Discharge 0.1147 m³/s
Discharge 114.731 L/s
Discharge per metre of crest 0.0765 m²/s
Weir type Rectangular suppressed
Assessment Rectangular suppressed: Q = 0.115 m³/s (114.7 L/s) at 0.12 m head. Apply on a sharp-crested, fully ventilated crest — otherwise multiply by a carry-over/velocity-approach correction.
  1. Discharge is the coefficient times crest length times head to the 1.5 power.
  2. Head is measured upstream of the nappe, not at the crest face.
  3. Submergence of the nappe reduces discharge and needs a correction.

Sanity check

Doubling the head increases discharge by about 2.8 times, not 2. That is the signature of a weir relationship.

Tools for this problem

These are the EngiMetric calculators that compute the numbers in this topic. Each one shows its formula, its units and its limits rather than returning a bare result.

References & standards

  • ISO 1438-1 — flow measurement through open channels
  • USBR Water Measurement Manual

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