Final answer:
The power in the flow through the Hoover Dam, with a height of 150 m and a flow rate of 650 m³/s, is approximately 0.98 GW, making the answer (C) 0.98 GW. The ratio of this power to the Hoover Dam's average output of 680 MW is about 1.41.
Step-by-step explanation:
The question is asking to calculate the theoretical power output from the water flowing through the Hoover Dam. The given height from which water is taken is 150 m, and the flow rate is 650 cubic meters per second (m³/s). To calculate the power (P) in the flow, we can use the formula for hydraulic power: P = ρghQ, where ρ is the density of water (1000 kg/m³), g is the acceleration due to gravity (9.81 m/s²), h is the height, and Q is the flow rate.
By plugging in the values, we get P = 1000 kg/m³ * 9.81 m/s² * 150 m * 650 m³/s, which equals 955,650,000 W or 0.956 GW. Since this number is closest to option C, the power in the flow is approximately 0.98 GW.
For part (b), the ratio of this power to the facility's average can be determined by dividing the power in the flow by the average power of the facility: 0.956 GW / 0.680 GW, which gives a ratio of about 1.41.