Temporary Flow Measurement with Weirs and Orifices

The Problem

During startup and testing you constantly need a flow number in a place with no meter: verifying a pump against its curve, splitting flow between basins, confirming a drawdown. A plate with a notch in it is the oldest flow meter there is, and it still works — a sharp-crested weir converts a head reading you can take with a ruler into a flow, as long as you use the right formula and respect its fine print.

The Approach

The tool carries the standard sharp-crested family (US units, Q in cfs, h and L in ft) [1]:

90° V-notch (USBR):        Q = 2.49 · h^2.48
V-notch, other angles:     Q = 2.5 · tan(θ/2) · h^2.5
Rectangular, contracted:   Q = 3.33 · (L − 0.2h) · h^1.5   (Francis)
Rectangular, suppressed:   Q = 3.33 · L · h^1.5
Cipolletti:                Q = 3.367 · L · h^1.5
Submerged orifice:         Q = C_d · A · √(2gΔh)

with output in cfs, GPM, and MGD. The Cipolletti's trapezoidal 1:4 side slopes exist specifically to compensate for end contractions, which is why its coefficient looks like the suppressed rectangular's — a nice piece of 19th-century empiricism that still earns its keep.

A V-notch weir plate in a channel with head being read against a staff gauge upstream
Figure 1: A 90° V-notch running free — the notch reads roughly 0.9 to 450 GPM over 1–12 inches of head.

Device selection is half the value: V-notch for low or variable flows (best sensitivity at low Q), rectangular or Cipolletti when a V-notch would need excessive head, and a submerged orifice where there isn't enough drop for any weir to run free.

The accuracy fine print the formulas assume
  • Head range: most sharp-crested formulas are rated for roughly 0.2–2.0 ft of head. Below ~0.2 ft, surface tension and nappe clinging dominate — the tool warns.
  • Free nappe: air must circulate under the falling sheet. A clinging nappe over-reads; suppressed rectangular weirs need vents.
  • Approach conditions: a proper weir pool (low approach velocity), no submergence from downstream, crest at least ~2× the head above the channel bottom.
  • Sharp crest means sharp: ¼-in. plate chamfered downstream, or angle iron. A 2× lumber crest is a broad-crested weir with a different, mushier coefficient.

And the honest limit: a temporary weir is a startup verification device. For anything that needs defensible accuracy over days — billing, permit reporting — rent a flume or a real meter [1][2]. Single file, vanilla JS, localStorage persistence.

The tool: Weir & Orifice Flow Calculator.

References

  1. [1] USBR, Water Measurement Manual — weir and orifice formulas, installation conditions. https://www.usbr.gov/tsc/techreferences/mands/wmm/
  2. [2] ISO 1438 — Hydrometry: thin-plate weirs.