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Question 4 (2+3) The Hoover dam is a huge hydroelectric power plant in the desert close to Las Vegas. It creates power by converting the potential energy of water at a height into electrical energy. The power available for generating electricity is given by: P = pQgh, with p = 997 kg/mthe density of water, Q the flow rate of the water (in m3/s), g the gravitational constant and h = 221 m the height of the dam. The dam is able to supply electricity to 1.3 million households. Each household uses P = 1.6 kW on average. a) What is the flow rate of the dam required to power all the households? Due to a draught, the plant is only able to supply P = 1900 MW. Since the dam is in a desert, solar panels are put in place to supply the deficit of power. The theoretical maximum power generated by the panels is P = 1A, with I = 1400 W/m2 the intensity of the sun, and A the area which is illuminated by the sun. The solar panels only have an efficiency of 50%. b) What is the area of the solar panels required to fill the deficit in energy? In case you did not do (a), use Pdam = 2000 MW for the power supplied by the dam before the drought. Figure 2: The Hoover dam.

Answer 1

Pagh or) a) ohes Power (P) = Pagher 16 x 10° x 1.3 x 10° 997 x Q x 9.8 x 221 q- 963.87 m/s hight c flow rate of the dam ser due to de drought 1-6x102 1-3.x106 21.3.x106. 1900X206 2.08 & 109 1.9x109 6) deficit deficit um pouco 2 W E 9 0:18 x 10 W 180 MW Power to be supplied by Solar panels 180 x 106 1498 x A x so A a 0.254 x 106 m? 180 A = 5 2.54 x 10 Area of solar panels. the defilcit of z required to fel MAR WT F S S M TWTF S S M T W