Renewable Energy Systems EENV 3327
Homework #2: Hydropower
Instructors: Dr. Mazen Abualtayef
Eng. Alaa Hassan
Homework #2
Hydropower
1. Micro-Hydropower. You have a cabin in wilderness far away from civilization and
want to install a small hydro generator to provide electricity. A stream runs down a
hill behind your cabin where you can construct a simple run-of-river hydro
installation. You calculate that the effective head of the installation is 8.0 meters and
that water would flow through the system at a rate of 1.40 cubic meters per minute.
The simple inexpensive hydro turbo-generator that you intend to buy has a working
efficiency of 65%. Answer the following (show your work):
a.
b.
c.
How much power can you generate with this system?
How many 32 watt PL light can you power with this hydro setup?
What type of turbine would you expect to find in your turbo-generator?
2. Macro-Hydropower. A dam has a height of 220 meters. Total generating capacity
for the power plant at the dam is about 1 GW (1 million kW). Assume an effective
head of 215 meters and generating efficiency of 90%.
a. At maximum capacity, what flow is required through the dam’s turbines to
generate its power?
b. If the dam operates at 60% of capacity on average, how much energy does it
produce in a year? Express your answer in watts (e.g., W, kW, MW, GW, etc.).
c. How many people should this energy support, assuming average community
consumption of 1000 kWh per year per person?
d. How much coal would be required in a coal-burning power plant to generate the
equivalent amount of energy as the Dam generates in a year? Assume that the
dam generates 5 billion kWh hours (5×109 kWh or 5 terra-watt hours) of energy
annually. How many coal cars would be required to carry this coal? How long
would a train of these cars be?
 The energy content of coal is 8,142 kWh/ton
 The energy efficiency of a typical coal-burning power plant is about 38%
 A railroad coal car carries about 100 tons of coal and is about 22.86 m in
length
e. How much natural gas would be required in a gas-fired power plant to generate
the equivalent amount of electrical energy as the Dam generates in a year?
 The energy content of natural gas is about 10.83 kWh/m3
 The efficiency of a modern gas-fired power plant is about 55%
Renewable Energy Systems EENV 3327
Homework #2: Hydropower
Instructors: Dr. Mazen Abualtayef
Eng. Alaa Hassan
3. US Energy Consumption. The total electrical energy consumption of the US in 2003 is
estimated to be 3.66×1012 kWh (CIA World Factbook).
a. How many dams would be required to supply all of the electrical needs of the
United States?
 Assume that the dam generates 5 billion kWh (5×109 kWh or 5 terra-watt
hours) of energy annually.
b. How much land area would be inundated by these dams (in square kilometers)?
 Assume that water flows through the dam at a rate of 500 m3/sec when it is
generating at its rated power.
Hints
 The average depth of lake behind the dam is 40 meters.
4. Pumped Storage. Consider a pumped hydro system that is used for energy storage.
During off-peak hours, excess electricity is used to pump water up to a storage
reservoir. During peak demand periods, the flow is reversed and electric power is
generated by flowing the water through a hydraulic turbine. The storage reservoir is
100 meters above the hydro turbine/pump units and the hydraulic turbine can
accommodate up to 0.65 m3/s of flow.
a. How much area would the pumped storage reservoir need to store 1000 MWh of
hydro energy if its average depth was 10 meters? Express your answer in dunums.
Is this reasonable?
 First calculate the total volume of water required in m3, then the surface area
of the reservoir if it is 10 meters deep on average. Then convert to dunums.
b. Estimate the theoretical power (assume 100% efficiency) produced during the
times that electricity is generated.
c. If the round-trip efficiency of the pumped storage unit is 75%, how much water
(m3) must the reservoir hold to store the same 1000 MWh of energy?
Hints
 density of water is 1000 kg/m3
 acceleration of gravity g is 9.81 m/s2

1 dunum = 1,000 m2
Ton of coal equivalent
Ton of oil equivalent
Cubic meters of natural gas
= 8,142
= 11,630
= 10.83
kWh
kWh
kWh