V-Notch (Triangular) Weir Flow

Integrate the velocity of a free jet over the triangular opening of a V-notch and the five-halves power falls out of the geometry: the width available grows with head at the same time as the velocity does. With a 90° notch, $C_d$ = 0.58 and 0.25 m of head, the discharge is (8/15) × 0.58 × 4.429 × 1 × 0.03125 = 0.0428 m³/s, about 43 L/s. The 90° notch is so common that the whole expression is often collapsed to the shortcut $Q(\mathrm{cfs}) = 2.49\,H^{2.48}$ with H in feet.

The V-notch is the instrument of choice for small and highly variable flows precisely because of that steep power law: halve the flow through a rectangular weir and the head falls 37%, but through a V-notch it falls only 24%, so low flows stay readable. The flip side is that head errors amplify by two and a half, so a centimetre of silt built up in the approach channel, which raises the apparent zero, is a serious error, not a nuisance. Keep the plate sharp and bevelled on the downstream side, keep the approach channel at least four times the head deep and wide, aerate the nappe, and take the head reading well back from the drawdown. For heads below about 50 mm surface tension takes over, the nappe clings, and no weir equation is trustworthy.