Chapter 9, Problem 79RPP

Tidal energy Tides are now used so gene-ate electric power in two ways. In the first, huge dams can be built. across the mouth of a river where it exits to the ocean. As the ocean tide moves in and out of this tidal bas in or estuary, the water flows through tunnels in the dam (see Figure 9.19). This flowing water turns turbines in the tunnels that run electric generators. Unfortunately, this technique works best with large increases in tides—a 5-m difference between high and low tide Such differences are found at only a small number of places Currently, France is the only country that successfully uses this power source A tidal basin plant in France, the Rance. Tidal Power Station. makes 240 megawatts of power—enough energy to power 240,000 homes. Damming tidal basins can have negative environmental effects because of reduced tidal flow and silt buildup. Another disadvantage is that they can only generate electricity when the tide is flowing in or out, for about 10 hours each day.

A second method for collecting energy from the tidal flow (as well as all water flow) is to place turbines directly in the water—like windmills in moving water instead of in moving air. These water turbines have the advantages that they are much cheaper to build, they do not have the environmental problems of a tidal basin, and there are many more suitable sites for such water flow energy farms. Also the energy density of flowing water is about 800 times the energy density of dry air flow. Verdant Power is developing turbine prototypes in the East River near New York City and in the Saint Lawrence Seaway in Canada, and they are looking at other sites in the Puget Sound and all over the world. The worldwide potential tor hydroelectric power is about $25\text{ terawatts }=25\times {10}^{12}\text{ J/s}$—enough to supply the world's energy needs.

Suppose a tidal basin is 5m above the ocean a: low tide and that the area o' the basin is $4\times {10}^7{\text{ m}}^2$(about 4 miles by 4 miles). Which answer below is closest to the gravitational potential energy change if the water’s released from the tidal basin to the low- the ocean level? The density of water is ${\text{1000 kg/m}}^{\text{3}}$. (Hint: the level does no, change by 5 m for all of the water.)

$\begin{array}{l}\text{a}\text{. 5 }\times {\text{ 10}}^{\text{8}}\text{J}\hfill \\ \text{b}\text{. 5 }\times {\text{ 10}}^{\text{11}}\text{J}\hfill \\ \text{c}\text{. 1 }\times {\text{ 10}}^{\text{12}}\text{J}\hfill \\ \text{d}\text{. 5 }\times {\text{ 10}}^{\text{12}}\text{J}\hfill \\ \text{e}\text{. 1 }\times {\text{ 10}}^{\text{13}}\text{J}\hfill \end{array}$