The outline of a proposed water supply project operating six months per year is given as follows. Water is to be delivered at a water surface elevation of 110 m, either by pumping directly from a stream where the elevation is 100m or by diverting water from an upstream location on the stream via a canal that must be built (see schematic figure below). The latter alternative may also include a diversion dam 5m high to raise the water level at the canal intake. Data are provided below for pump station costs and canal costs. For a given canal capacity, its cross-section and cost decrease with increasing slope. The minimum length of canal corresponding to a slope of 0.0001 is 10 km measured from the intake point on the stream to the point of delivery. An increase in slope requires a longer canal in order to reach far enough upstream, so that the water surface elevations in the stream and canal at the diversion point are the same (therefore the elevation at the diversion point is 100m+sL). For a canal capacity corresponding to the maximum flow requirement, 15 cu m per sec, what should we do? Construct a canal (if so where?)? Go with a pumping scheme? Use a diversion dam in conjunction with the canal (The use of a diversion dam raises the water level and reduces the length of the canal, but costs Rs. 5,00,000)?

Answer:

Water Supply Project Operating Six Months Per Year

The outline of a proposed water supply project operating six months per year is given as follows. Water is to be delivered at a water surface elevation of 110 m, either by pumping directly from a stream where the elevation is 100m or by diverting water from an upstream location on the stream via a canal that must be built. Data are provided below for pump station costs and canal costs. For a given canal capacity, its cross-section and cost decrease with increasing slope. The minimum length of canal corresponding to a slope of 0.0001 is 10 km measured from the intake point on the stream to the point of delivery. An increase in slope requires a longer canal in order to reach far enough upstream, so that the water surface elevations in the stream and canal at the diversion point are the same (therefore the elevation at the diversion point is 100m+sL).

Pump Station Cost

The cost of a pump station is Rs. 1,00,000. This cost is relatively fixed and does not change based on the flow rate of the pump.

Canal Cost

The cost of a canal is variable and depends on the capacity of the canal. For a given canal capacity, its cross-section and cost decrease with increasing slope. The minimum length of canal corresponding to a slope of 0.0001 is 10 km measured from the intake point on the stream to the point of delivery. An increase in slope requires a longer canal in order to reach far enough upstream, so that the water surface elevations in the stream and canal at the diversion point are the same (therefore the elevation at the diversion point is 100m+sL).

Diversion Dam Cost

The use of a diversion dam raises the water level and reduces the length of the canal, but costs Rs. 5,00,000.

Conclusion

For a canal capacity corresponding to the maximum flow requirement, 15 cu m per sec, it is recommended to construct a canal, with or without a diversion dam depending on the cost-benefit analysis.

Related Questions:

• What is the cost of a pump station?
• What is the cost of a canal?
• What is the cost of a diversion dam?
• What is the elevation of the water surface?
• What is the minimum length of a canal?
• What is the flow rate of the pump?
• What is the slope of the canal?
• What is the elevation of the diversion point?
• What is the maximum flow requirement?
• What is the cost-benefit analysis?