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K = dimensionless parameter with the value 0.4 to initiate motion and 0.8 for adequate cleansing |
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g = acceleration due to gravity, m/s2 |
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f = dimensionless friction factor |
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Sp = specific gravity of the material removed |
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Dg = particle diameter, |
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Based on this model, the committee concluded that the self-cleansing velocity is independent of the sewer diameter. As 0.6 m/s was commonly accepted as the necessary velocity which must be achieved to remove grit, the committee supported the practice that flow velocity would be an effective surrogate to the tractive force for calculating slopes of sewers. This approach has been so popular in its simplicity that practising engineers everywhere have used it for decades. |
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More recent studies by Yao (1974) have shown that there is a direct relationship between the self-cleansing velocity and the critical boundary shear stress or tractive tension: |
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where n = Manning's roughness coefficient |
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R = hydraulic radius, m |
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tc = critical shear stress, N/m2 |
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w = specific weight of water, N/m3 |
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This model indicates that as the diameter of the sewer increases for a given tractive tension, the necessary self-cleansing velocity must increase. Using tractive tensions of 12 N/m2, which appear to be adequate for sanitary sewers, Yao concluded that the practice of using a constant minimum velocity for all sewer sizes results in the underdesigning of larger sewers and the overdesigning smaller sewers. |
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Using the tractive tension method rather than the minimum velocity method has significant cost implications. For example, if a sewer were designed for initial and final flows of 4.2 1/s and 8.3 1/s respectively, the required slope for a 150 mm diameter sewer is 0.0028 using a tractive tension of 1 N/m2, as compared with 0.0050 using a minimum velocity of 0.6 m/s. For a trench width of 0.65 m over a length 1000 m, the savings in excavation through the use of the tractive tension would be 1040 m3. In addition, the downstream end of the trench would be 3.2 m |
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