1. Determine the power required for a 2000-kg car to
climb a 100-m-long uphill road with a slope of 30° (from
horizontal) in 10 s (a) at a constant velocity, (b) from rest to
a final velocity of 30 m/s, and (c) from 35 m/s to a final
velocity of 5 m/s. Disregard friction, air drag, and rolling
resistance. Answers: (a) 98.1 kW, (b) 188 kW, (c) -21.9 kW
2. Water is pumped from a lower reservoir to a higher
reservoir by a pump that provides 20 kW of shaft power. The
free surface of the upper reservoir is 45 m higher than that of
the lower reservoir. If the flow rate of water is measured to
be 0.03 m^3/s, determine mechanical power that is converted
to thermal energy during this process due to frictional effects
{Para estos dos pbs (arriba y abajo), abrir archivo Figs01.pdf
anexo al pie de página.}
3. The demand for electric power is usually much
higher during the day than it is at night, and utility companies
often sell power at night at much lower prices to encourage
consumers to use the available power generation capacity and
to avoid building new expensive power plants that will be
used only a short time during peak periods. Utilities are also
willing to purchase power produced during the day from private
parties at a high price.
Suppose a utility company is selling electric power for
$0.03/kWh at night and is willing to pay $0.08/kWh for
power produced during the day. To take advantage of this
opportunity, an entrepreneur is considering building a large
reservoir 40 m above the lake level, pumping water from the
lake to the reservoir at night using cheap power, and letting
the water flow from the reservoir back to the lake during the
day, producing power as the pump–motor operates as a turbine–
generator during reverse flow. Preliminary analysis
shows that a water flow rate of 2 m^3/s can be used in either
direction. The combined pump–motor and turbine–generator
efficiencies are expected to be 75 percent each. Disregarding
the frictional losses in piping and assuming the system operates
for 10 h each in the pump and turbine modes during a
typical day, determine the potential revenue this pump–turbine
system can generate per year.