ASSIGNMENT HYDROPOWER
1. Micro-Hydropower. You have a cabin in the Colorado 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 25 feet and that water would flow through the system
at a rate of 50 cubic feet per minute. The simple inexpensive hydro turbo-generator (turbine
mated with electric generator) that you intend to buy has a working efficiency of 60%. Answer
the following (show your work):
a.
b.
c.
How much power can you generate with this system? (1.06 kW)
How many 100 watt light bulbs can you power with this hydro setup? (10 bulbs)
What type of turbine would you expect to find in your turbo-generator? Why?
Hint
First convert to metric measurements
o
1 meter = 3.28 feet
o
1 cubic meter (m3) = 35.31 cubic feet. (ft3)
o
You might want to check on the web for easy measurement conversion sites such
as http://www.convert-me.com/en/
2. Macro-Hydropower. The Glen Canyon Dam in Arizona dams the Colorado River creating Lake
Powell behind it. The dam has a height of 710 feet. Total nameplate (maximum continuous)
generating capacity for the power plant at the dam is about 1 GW (1 million kW). Assume an
effective head of 700 feet and generating efficiency of 95%.
a. At maximum capacity, what flow is required through the dam’s turbines to generate its
nameplate power? Express flow in cubic meters. (493.3 m3/s, g = 10 m/s2)
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.). (5.26 TWh)
c. How many people should this energy support, assuming average community consumption of
3000 kWh per year per person? (1,752,117 persons)
d. How much coal would be required in a coal-burning power plant to generate the equivalent
amount of energy as the Glen Canyon Dam generates in a year? Assume that the dam
generates 5 billion kWh hours (5×10 9 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? (1.62 MT; 17,814 cars/year; 369.4 km)
The energy content of coal is 8,142 kWh/tonne (1 tonne = 2,206 pounds)
The energy efficiency of a typical coal-burning power plant is about 38%
A railroad coal car carries about 100 tons (90.72 tonnes) of coal and is about 75 feet
(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 Glen Canyon Dam generates in a year? How many
Goodyear blimps of natural gas does this represent? (10.07 x 109 m3/year; 1,778,210 blimps/
year)
The energy content of natural gas is about 0.95 kWh/m3
The efficiency of a modern gas-fired power plant is about 55%
The Goodyear blimp holds about 200,000 ft3 (5,663 m3) of gas.
3. Pumped Storage. Consider a pumped hydro system that is used for energy storage. During offpeak 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 m above the hydro turbine/pump units and the
hydraulic turbine can accommodate up to 650 l/s (liters per second) of flow.
a. How much area would the pumped storage reservoir need to be to store 1000 MWh of hydro
energy if its average depth were 10 m? Express your answer in acres. Is this
reasonable?(91.06 acres)
The potential energy of water in the reservoir can be calculated as gH, where is the
density of water, g is gravitational acceleration, and H is the effective head of the system.
First calculate the total volume of water required in meters, then the surface area of the
reservoir if it is 10m deep on average. Then convert to acres.
b. Estimate the theoretical power (assume 100% efficiency) produced during the times that
electricity is generated. (637.9 kW)
c. If the round-trip efficiency of the pumped storage unit is 75% (i.e., energy out / energy in),
how much water (m3) must the reservoir hold to store the same 1000 MWh of
energy?(4.89x106 m3 )
Hints
density of water is 1000 kg/m3 (or 1.0 kg/liter)
acceleration of gravity g is 9.8 m/s2
1 acre = 4,047 m2