อัปเดต 2026-09-07

Weir & Flume Flow Meter

ISO 1438:2017 / USBR Water Measurement Manual

Computes open-channel discharge Q from a measured upstream head H for thin-plate weirs (rectangular suppressed/contracted, V-notch, Cipolletti) and the Parshall flume (free-flow only).

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Each device's forward law Q(H) is a closed-form power law derived from the orifice equation v=√(2gh) integrated over the notch/crest opening. Every law is strictly monotone in H, so the inverse (head for a target Q) is solved by bracketed bisection with a doubling search for the upper bound; validity envelopes (H/P, β, Re-style ranges) are checked but never block the calculation, only flag it.

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Rectangular weir discharge (Kindsvater–Carter)

Q = \frac{2}{3} C_{d} 2 g b_{e} h_{e}^{3/2}, C_{d} = 0.602 + 0.0832 \frac{H}{P}

ISO 1438:2017 §5; h_e = H + k_h (k_h ≈ 0.001 m), b_e = b − 0.1·n·H for contracted weirs (Francis end-contraction rule).

V-notch weir discharge (Kindsvater–Shen)

Q = \frac{8}{15} C_{e} tan (\frac{θ}{2}) 2 g h_{e}^{5/2}

ISO 1438:2017 §7; C_e ≈ 0.578 for a fully-contracted 90° notch, h_e = H + k_h (k_h ≈ 0.00085 m).

Parshall flume free-flow discharge

Q = C H_{a}^{n}

USBR Water Measurement Manual, 3rd ed., Ch. 8; C and n tabulated by throat width W (free-flow only — no submerged-flow correction).

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