The rectangular diversion channel is originally designed to have a width, B, of 12 m and depth, Y, of 2 m which is lined with concrete that has a roughness of 0.021. The distance from the city to the bay is around 8 km with a difference in elevation of 20 m. However, due to limited budget, it is proposed that the original design of the diversion channel be modified into most efficient rectangular hydraulic section. Knowing that the most efficient rectangular section is the one with a depth equal to half of its width or Y= 0.5B, determine the (a) new dimensions, Y and B of the modified rectangular channel
The rectangular diversion channel is originally designed to have a width, B, of 12 m and depth, Y, of 2 m which is lined with concrete that has a roughness of 0.021. The distance from the city to the bay is around 8 km with a difference in elevation of 20 m. However, due to limited budget, it is proposed that the original design of the diversion channel be modified into most efficient rectangular hydraulic section. Knowing that the most efficient rectangular section is the one with a depth equal to half of its width or Y= 0.5B, determine the (a) new dimensions, Y and B of the modified rectangular channel and compute the total savings in (b) excavation cost, (c) land acquisition cost, and (d) concreting cost if the modified design is to be implemented but adhering to same discharge capacity. The unit cost of excavation is 400 per cubic meter, cost of the land is 1,500 per square meter, and concreting cost is 300 per square meter of lining.
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