UCCS PES/ENSC 2500
Chapter 11 Hydroelectric Energy
name: _________________________
Problem 11.1
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?
One cubic meter of water has a mass of: ___________________________
Its potential energy at a height of 100 m is:
E = mgh = ______________________________J
From equation (8.12) the change in temperature is
ΔT = E / (mC)
Specific heat for water C = __________________________ J/(kg °C), so
T = T0 + ΔT = ____________________________°C
Problem 11.2
The Three Gorges Dam is rated at: 22.5 GWe maximum output.
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?
If the output is: 22.5 GWe then the mechanical energy is:
22.5 GW e/ 0.9 = _______________________GW.
E = mgh
Power is: P = E / t = mgh / t
Solving for: m / t gives:
2
Note that J = kg m /s
2
2
3
so W = kg m /s
2
2
and W s /m = kg/s
Problem 11.3
3
Water falls from a head of 100 m at a rate of: 1 m /s, and this energy is converted into electrical energy at an
efficiency of: 90%.
How many typical single-family homes can this provide with electricity?
4
From Chapter 2 the average electrical need per household is: 1.2 × 10 kWh per year, for an average power
requirement over the year of
4
(1.2 × 10 kWh) / (8760 h/y) = _____________________________ kW
3
The energy associated with: 1 m
of water at a height of: 100 m is
E = mgh = ______________________________ J
If this water fall through this distance in: 1 s then the average power generated is
P = E / t = _______________________________ kW
If this power is converted to electricity with an efficiency of 90%, then the electrical power available is
_________________________________ kWe
This is sufficient to power:
______________________________ homes with cats.
Problem 11.7
A reservoir is: 1 km wide and 10 km long and has an average depth of: 100 m.
Every hour, 0.1% of the reservoir's volume drops through a vertical height of: 100 m and passes through
turbines to produce electricity with an efficiency of: 92%.
What is the electrical power output of this facility?
The mass of the water is:
m = ___________________________________ kg
The potential energy associated with: 0.1% of this water at a height of: 100 m is:
E = ___________________________________ J
If this passes through a turbine with: 92% efficiency every hour (i.e. 3600 s) then the average power generated
would be:
P = _________________________________ W