Flow Over a Rectangular Sharp Weir

Mediumweirdischarge
A rectangular sharp-crested weir has b = 1.2 m, H = 0.40 m and Cd = 0.62. Using Q = (2/3)·Cd·b·√(2g)·H^(3/2), Q is most nearly:
  1. A0.139 m³/s
  2. B0.556 m³/s
  3. C0.278 m³/s
  4. D1.11 m³/s
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Answer: B. 0.556 m³/s

Equation (given): Q = (2/3)·Cd·b·√(2g)·H^(3/2). Values: Cd = 0.62 is the discharge coefficient. b = 1.2 m is the crest length, the width of the notch in the front view. H = 0.40 m is the head, measured upstream from the crest level to the water surface, before the surface draws down. g = 9.81 m/s². Step 1: √(2g) = √19.62 = 4.43 m^½/s. Step 2: H^(3/2) = 0.401.5 = 0.40 × √0.40 = 0.253 m^(3/2). Step 3: Q = (2/3)(0.62)(1.2)(4.43)(0.253) = 0.556 m³/s. Measuring H at the weir plate, where the surface has dropped, underestimates the flow; using H instead of H^(3/2) gives 0.879 m³/s.
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