A trunk sewer for an urban centre.

Figure 1 shows the plan of a proposed trunk sewer for an urban centre. It is proposed that the 5 sewer lines
with the design flow rates given in Table 1 be used. Each node of the 5 sewer lines is located after a
reduction of 1 metre from the previous one as the contour lines on Figure 1 show.
Table 1 Sewer line design flow rates
Sewer line 1 - 2 2- 3 3 – 4 - 5 5 – 6 - 7 7 – 8 - 9
Design flow (m3
/s) 0.121 0.142 0.615 0.812 1.070
It is required that the sewer should be at least 1m below the ground surface and the excavation at any
location should not exceed 5m. Table 2 shows the available pipe sizes and Figure 2 is a hydraulic design
chart for obtaining the pipe diameter for a given flow rate and slope.
Determine the optimal design for the trunk sewer using dynamic programming.
Make the following assumptions:
A rate of R 20 per Kg of pipe material to determine the cost of the sewer line.
A rate of R 500 per metre run per metre depth of excavation for all the other costs.
Apply a reasonable discretization to solve the problem and make any reasonable assumptions that you
consider necessary. These assumptions should be clearly stated in your solution.
Submit the project on Wits-e by 11:59 pm on 14
th October 2020.
Only submissions in Ms Excel will be accepted.
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Figure 1 Trunk sewer location (From Peavy, Rowe and Tchobanoglous, Environmental Engineering)
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Table 2 Available pipe diameters (Nutec Pipes: www.everite.co.za)
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Figure 2 Hydraulic design chart (From Peavy, Rowe and Tchobanoglous, Environmental Engineering)