Engineering calculators · Flow measurement
Weir flow calculator: V-notch and rectangular weirs
Work out the flow over a sharp-crested weir from the head, or the head a flow will produce. It covers 90° V-notch, contracted rectangular and suppressed rectangular weirs, using the standard equations from the US Bureau of Reclamation Water Measurement Manual. For a clarifier or DAF launder with many V-notches, enter the number of notches and the weir length to get the head per notch and the weir loading rate.
Inputs
Head is measured upstream of the weir, at least four times the maximum head away, above the crest (or the bottom of the notch). Crest height and launder length are optional: crest height is used for the approach check, and launder length for the loading rate.
Results
How the calculation works
The equations below are in the units USBR publishes them in, with Q in ft³/s and h and L in ft. The calculator converts your metric inputs to feet and the flow back to SI, so the coefficients are used exactly as published.
- 90° V-notch, fully contracted: Q = 2.49 h2.48 (the Cone equation) [USBR 7.11]. The notch edges and point should be at least two heads from the approach channel's sides and floor. USBR gives a head range of 0.2 to 1.25 ft (61 to 381 mm) for fully contracted notches [USBR 7.7].
- Rectangular, fully contracted: Q = 3.33 h1.5(L − 0.2h) (Francis, 1883). The 0.2h allows for the two end contractions. It applies while h is no more than about one-third of L, with the crest at least 2hmax above the floor [USBR 7.9].
- Rectangular, suppressed: Q = 3.33 L h1.5. The crest spans the full channel width, so there are no end contractions. It needs a head between 0.2 ft and L/3, a crest height of at least 3hmax, and an aerated nappe [USBR 7.10].
- Head from flow inverts the same equation numerically.
- Weir loading rate = total flow ÷ launder weir length. It is a common design criterion for clarifier and DAF outlet weirs. The limit depends on the process and the design guide you work to, so the calculator reports the value without judging it.
What this cannot tell you. These equations assume a thin, sharp crest, a free-falling aerated nappe, and slow, even approach flow. A drowned (submerged) weir, a rounded or dirty crest, or a fast approach all change the flow. A launder with uneven notches, or one that is not level, will not share the flow equally. For flow measurement that must be accurate, have the installation checked against the full requirements of the manual or ISO 1438.
Sources
- USBR Water Measurement Manual, ch. 7 sec. 11: Fully contracted standard 90-degree V-notch weir (Cone equation)
- USBR Water Measurement Manual, ch. 7 sec. 7: V-notch weirs (head limits for fully contracted notches)
- USBR Water Measurement Manual, ch. 7 sec. 9: Standard contracted rectangular weirs (Francis equation)
- USBR Water Measurement Manual, ch. 7 sec. 10: Standard suppressed rectangular weirs