Deck 11: Hydroelectric Energy

Question 1

A Kaplan turbine runner has a diameter of 5 m, and the turbine/generator

Answer 1

Question 2

If electricity produced by the Three Gorges hydroelectric station is sold at

Answer 2

The number of kWh for each month is found from the graph in Energy Extra 11.2
by multiplying the output in MW times 1000 times the number of hours in the month. This
is shown in the table below

Question 3

A home owner in an area with substantial elevation changes and a large
annual rainfall (1.54 m) plans to supplement electricity needs of 1.1 kW average over the
year with a hydroelectric installation. An open tank of 15 m in diameter collects
precipitation that falls on its surface. Periodically the tank is drained through a penstock to
a hydroelectric generator at an elevation of 100 m below the tank. Discuss the merits of
this approach.

Answer 3

Question 4

If a high head hydroelectric facility is considered to be carbon free, what is

Question 5

A public utility is planning to construct a high head hydroelectric facility.

Question 6

A rectangular reservoir is 2 km wide by 10 km long. It is 50 m deep and
drains through a 93% efficient hydroelectric facility with an average head of 100 m.
(a) Calculate the total electrical energy that would be produced by the water in the
reservoir.
(b) What is the value of the electricity that is generated at rate of $0.10 per kWh.
(c) If the electricity is used by a city with a population of 100,000 with a per-capita power
requirement of 1 kWhe, how long would the electricity last?

Question 7

One cubic meter of water at 20°C is dropped from a vertical height of 100
m. If the change in potential energy is converted into heat with an efficiency of 100% and
this thermal energy is used to heat the water, what is its final temperature?

Question 8

Water flows through a 2 m diameter penstock at a velocity of 2.5 m/s. It
passes through a 87% efficient turbine/generator. What is the power output?

Question 9

The total flow of the Niagara River is Niagara Falls as given in the text and the fact that a maximum of 75% of the flow can be
utilized for hydroelectric power outside tourist season, calculate the maximum available
electric power if the generators are 85% efficient.

Question 10

Hydroelectric power accounts for about 6% of the primary energy used for

Question 11

The Amazon River has a flow rate of 2.09×105 m3/s (the largest in the
world) at an average velocity of 0.7 m/s. If 10% of this power could be extracted with a
run-of-the-river hydroelectric facility, what would be the output in MWe?

Question 12

Water falls from a head of converted into electrical energy at an efficiency of 90%. How many typical single-family
homes can this provide with electricity?

Question 13

A 1.2 m diameter penstock carries water from a reservoir with a 150 m

Question 14

The Three Gorges Dam is rated at 22.5 GWe maximum output. If its
generating efficiency is 90% and its head is 81 m, what is the rate of flow (in kg/s) of
water through its turbines at maximum output?

Question 15

A swimming pool with dimensions 8 m wide by 14 m long with an average

Question 16

Consider the run-of-the-river system described in Example 11.3. What is the
most reasonable turbine runner design for such a system and why?

Question 17

Use the total annual U.S. hydroelectric production and the information in
Chapter 2 to confirm the percentage of U.S. electricity that comes from hydroelectric
facilities as shown in Table 11.2.

Question 18

The term micro hydro refers to very small-scale hydroelectric power and
includes installations that can supplement other sources of electricity for single-family
residences. Typical efficiencies are less than commercial hydroelectric installations and
may be in the range of 75%. A home owner plans to install a micro hydro generator on a
stream that has an average flow of 1200 L/min and a vertical drop of 5 m. What is the
average electric power that can be expected from this facility? Should this project be
seriously considered if the construction cost is $3000.

Question 19

The reservoir created by the Three Gorges Dam has an area of 1045 km2. It
is anticipated that, in the long term, the capacity factor of this generating facility would be
around 0.5. Consider an alternative situation where the land area utilized by the Three
Gorges reservoir was utilized instead for a photovoltaic array with an average efficiency of
20%. Would one of these situations be significantly more advantageous than the other in
terms of energy production?

Question 20

A reservoir is 1 km wide and 10 km long and has an average depth of 100