The Three Gorges Dam in China is the largest hydroelectric power plant in the world. The dam is of the concrete gravity type, of length 2,309 m and height 185 m above sea level. When filled to the normal water level height of 175 m above sea level, the total reservoir storage capacity is 39.3 km³ or 39.3 billion m³. (a) (b) (c) (d) (f) The potential energy would have gone to waste if the dam was not built. However, it took several years to store the water to that height. To maintain the water level height of 175 m, the flow rate Q that can be discharged to generate hydroelectricity must be equal to the rain fall collected by the reservoir. It is estimated that the sustainable Q is 20,000 m³/s. If the downstream river surface is at 65 m above sea level, what is the potential yearly revenue of electricity that it can generate assuming 100% efficiency and 1 KW-Hr of electricity can be sold at $0.10? What is the total horizontal force and turning moment exerted by the reservoir water on the dam, assuming the upstream river bed is 60 m above sea level? If the dam is sitting on frictionless floor, and all the 6.4 billion people on earth were to push horizontally against the dam, can they generate sufficient force to hold it in place? Support your answer with appropriate calculations and assumptions. The Hoover dam in USA is higher at 221 m but shorter at 379 m length. It is a concrete arch-gravity dam with the convex side pointing upstream to reduce the stresses within the dam. If the Three Gorges Dam also adopts the arch shape instead of a straight dam, will the horizontal force calculated be larger because of the larger surface area? Explain. The Three Gorges Dam has 23 surface sluice gates. If the discharged water level of the sluice gate is the same as the downstream river surface, what is the discharge water velocity if all loses are neglected? When a dam is built, the potential energy is converted to electricity. If the dam is not built, what happen to the energy? Explain clearly in term of the law of conservation of energy.