Minimum Slope of a Half-Full Sewer
Mediumcollection systemsmanningsewer
A 400 mm diameter circular sanitary sewer with Manning roughness n = 0.013 flows half full. To maintain a self-cleansing velocity of 0.9 m/s, the minimum slope is most nearly:
- A0.0012
- B0.0030
- C0.0059
- D0.0118
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Answer: B. 0.0030
For a circular pipe flowing half full the hydraulic radius equals that of the full pipe: Rh = D/4 = 0.40/4 = 0.10 m. Rearranging Manning's equation V = (1/n)Rh^(2/3)S^(1/2) for slope gives S = (Vn/Rh^(2/3))² = (0.9×0.013/0.10^(2/3))² ≈ 0.0030, or about a 0.30 m drop per 100 m. Using Rh = D/2 instead of D/4 is the usual error and understates the required slope.
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