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Flow over a Contracted Rectangular Weir

Mediumweirsopen channelflood control
A rectangular sharp-crested weir with a crest length of 1.0 m is installed in a channel that is wider than the weir, so the nappe contracts at both ends. The head over the crest is 0.6 m. Using (SI units), the discharge is most nearly:
  1. A0.58 m³/s
  2. B0.75 m³/s
  3. C0.86 m³/s
  4. D0.97 m³/s
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Answer: B. 0.75 m³/s

Because the weir is narrower than the channel, the end contractions shorten the effective crest, and the handbook's contracted form applies: Q = C(L − 0.2H)H^(3/2). The effective length is 1.0 − 0.2(0.6) = 0.88 m and H^(3/2) = 0.61.5 = 0.465, so Q = 1.84 × 0.88 × 0.465 = 0.75 m³/s. Using the suppressed formula Q = CLH^(3/2) with the full 1.0 m gives 0.86 m³/s and overstates the flow by about 14%. Raising H to the first power instead of 3/2 gives 0.97 m³/s, and squaring it gives 0.58 m³/s.
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