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shallower which could provide further savings in rock excavation, dewatering costs or in the elimination of lift stations. |
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Although the use of the tractive tension method has been advocated for over 20 years, it was not routinely used until the São Paulo, Brazil, water company developed a simple tractive tension design procedure in 1980 (Machado Neto and Tsutiya, 1985; Bakalian et al., 1994). In this procedure, the design slope for a reach of sewer is determined on the basis of the expected initial flow, assuming a tractive tension of 1 N/m2 and a minimum flow depth of 0.2 relative to the pipe diameter: |
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where Imin = minimum sewer slope, m/m |
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Qi = initial wastewater flow, 1/s |
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Based on the minimum slope calculated, the diameter of the sewer is determined using the projected final flow and limiting the depth of flow to no more than 75 per cent of the sewer diameter. A hydraulic table (Table 11.1) simplfies this determination by relating the ratio of the depth of flow to the pipe diameter (d/D) to (Qf / 1000)/I0.5min and V/I0.5 (Machado Neto and Tsutiya, 1985; Bakalian et al., 1994). The value of (Qf /1000)I0.5min or one near this value, is located in this hydraulic design table where d/D does not exceed 0.75. The final velocity (Vf) is computed from the corresponding V/I0.5 value in the table. If Vf is greater than 5 m/s, a new diameter is selected in which the depth of flow is somewhat less than 75 per cent of the pipe diameter. Excessive velocities are avoided because of the concern for air entrapment and cavitation at the joints. Manning's equation is used for these computations with a value of n of 0.013. A derivation of this method is provided elsewhere (Bakalian et al., 1996). |
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To illustrate the differences in the resulting designs between the minimum velocity and tractive tension methods, the size and slope of a sewer are determined for an initial flow of 45 1/s and a final flow of 60 1/s assuming n = 0.013. Following the minimum velocity method, assuming 0.6 m/s, the selected pipe diameter to carry 60 1/s is 375 mm with a corresponding slope of 0.0016. From a hydraulic elements chart, d/D is 0.73 and the velocity is 0.58 m/s. Initially, the d/D is 0.6 and the corresponding velocity is |
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