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242 CHAPTER 8 Conservation of Energy

PHYSICS IN PRACTICE HYDROELECTRIC PUMPED STORAGE

The demand for electric energy by industrial and itational potential energy of the water.This gravitational poten-
Concepts
in commercial users is high during working hours, tial energy can then be held in storage until needed.
Context
but low during nights and on weekends.For max- The chapter photo shows the reservoirs of a large hydro-
imum efficiency, electric power companies prefer electric pumped-storage plant on Brown Mountain in New
to run their large nuclear or coal-fired power plants at a steady, York State.The upper reservoir on top of the mountain is linked
full output for 24 hours a day, 7 days a week. Thus electric to the lower reservoir at the base by a vertical shaft of more
power companies often have a surplus of electric energy avail- than 320 m bored through the mountain. Each of the four
able at night and on weekends, and they often have a deficit reversible pump/turbines (see Fig.8.17) and motor/generators
of energy during peak-demand times, which requires them to in the powerhouse at the base (see Fig. 1) is capable of gener-
purchase energy from neighboring power companies. ating 260 MW of electric power. The upper reservoir holds
7
3
Hydroelectric pumped-storage plants help to deal with this 1.9 10 m of water, which is enough to run the generators
mismatch between a fluctuating demand and a steady supply. at full power for about half a day.
A hydroelectric pumped-storage plant is similar to an ordi-
nary hydroelectric power plant. It consists of an upper water
reservoir and a lower water reservoir,typically separated by a few
hundred meters in height.Large pipes (penstocks) connect the
upper reservoir to turbines placed at the level of the lower reser-
voir. The water spurting out of the pipes drives the turbines,
which drive electric generators. However, in contrast to an
ordinary hydroelectric plant, the pumped-storage plant can be
operated in reverse.The electric generators then act as electric
motors which drive the turbines in reverse, and thereby pump
water from the lower reservoir into the upper reservoir. At
peak-demand times the hydroelectric storage plant is used for
the generation of electric energy—it converts the gravitational
potential energy of the water into electric energy. At low-
demand times,the hydroelectric storage plant is used to absorb FIGURE 1 Powerhouse at the lower reservoir of the Brown
electric energy—it converts surplus electric energy into grav- Mountain hydroelectric pumped-storage plant.

At the Brown Mountain hydroelectric storage plant, water
Concepts EXAMPLE 3
in from the upper reservoir flows down a pipe in a long vertical
Context
shaft (Fig. 8.6). The pipe ends 330 m below the water level of the (full) upper
reservoir. Calculate the speed with which the water emerges from the bottom of
the pipe. Consider two cases: (a) the bottom of the pipe is wide open, so the pipe
does not impede the downward motion of the water; and (b) the bottom of the pipe
is closed except for a small hole through which water spurts out. Ignore frictional
losses in the motion of the water.
SOLUTION: (a) If the pipe is wide open at the bottom, any parcel of water simply
falls freely along the full length of the pipe.Thus, the pipe plays no role at all in the
motion of the water, and the speed attained by the water is the same as for a reser-
voir suspended in midair with water spilling out and falling freely through a height
h 330 m. For such free-fall motion, the final speed v can be obtained either from
the equations for uniformly accelerated motion [from Eq. (2.29)] or from energy
conservation [see Eq. (7.41)]. The result is