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Engineering Mathematics 1

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An irrigation engineer is designing a profile for a channel to pass through a farm that is in a shape of a square of side length 25 KM as shown in Fig 1. The proposed profile follows the following equation: 𝑦𝑦=𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴(𝑥𝑥)+𝐵𝐵𝐵𝐵𝐵𝐵𝐵 (𝑥𝑥)+𝐶𝐶𝐶𝐶𝐶 (𝑥𝑥)+𝐷𝐷𝐷 +𝐸𝐸
1. By selecting ideal reference points from the graph determine the values of arbitrary constants A, B, C, D & E.
2. The turning points for the profile represents the locations where the pumps needs to be installed to distribute the water to the other parts of the farm. Determine the location of the pumping stations to the nearest 0.1 m.
3. Determine the length of the channel.
The channel has x-section in a form of a parabola. The maximum width of the channel at the existing ground level as shown in Figure 2 is 2 meters.
4. Determine the depth of the channel below the existing ground level if the minimum cross section area of the channel is 8 m2 and hence determine the channel profile equation.
5. The excavated earth is used for the embankments alongside the channel. The cross section of the embankments as shown in Figure 2 is in a form of a symmetrical trapezium. The sides of the trapezium is tangential to the excavated channel at the ground level. Determine the height of the trapezium.
6. The maximum safe flow capacity of the channel is when the channel is full up to 0.8 of the full height of the channel. Determine the maximum safe area for the safe flow.
7. To reduce the scouring of the channel and the water seepage, it is suggested to use a lining material to the full height of the channel. If the lining material costs around $50.00 per sq. meter, determine the cost of lining per meter length of the channel.
8. If the cost of excavation is $10 per cubic meter, the cost of constructing the embankment is $15.00 per cubic meter and the cost of lining is $50.00, suggest an alternative profile for the channel x-section with less cost. The only constrains are the overall width of the channel should not be more than 9 meters and the minimum cross section for the water flow is 8 SQM.

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