Download power in a water wave

Energy, Power, and Climate Change
8.8 Wave Power
WAVES
Common water waves are produced by the sun-driven
winds passing over the water's surface.
The height of the waves depends on the following three
factors:
The speed of the wind
The duration of the wind
The fetch
FYI: The
FETCH is thePower,
length of the
waterClimate
over which the
wind passes.
Energy,
and
Change
FYI: A NNE wind on Lake8.8
Michigan
produces
a much larger amplitude...
Wave
Power
than a west wind.
FETCH
FYI: The course of the Edmund Fitzgerald on Lake Superior.
Energy, Power, and Climate Change
8.8 Wave Power
POWER IN A WATER WAVE
A
L

The power of a water wave is complicated to calculate,
so we'll simplify it some.
Think of the crest as storage of potential energy, and
the falling water as conversion into kinetic energy.
FYI: The
AVERAGE HEIGHT
of theand
water Climate
is A / 2.
Energy,
Power,
Change
FYI: This much potential 8.8
energyWave
is converted
into kinetic energy each
Power
period T.
POWER IN A WATER WAVE
FYI: Power is energy per time:
U
FYI: Power is proportional to the SQUARE of the AMPLITUDE A.
U
Power is proportional to the WAVE SPEED V.
Power is porportional to the LENGTH of the WAVEFRONT L.
U
U
A
= mgh
= mgA/2
= VgA/2
= LAgA/2
A/2
L
U = LgA2/2

 = VT
K = LgA2/2
K =
VTLgA2/2
P =
gVLA2
2
Power Generated By A Wave
3.
FYI: The
mass densityPower,
of water is 1000
Energy,
andkg/m
Climate
Change
8.8 Wave Power
POWER IN A WATER WAVE
Waves having an amplitude of 2 m roll onto a beach at a
rate of one every 8 seconds. The wave crests are 75
meters apart.
(a) What is the wave velocity?
V = d/t = /T
= 75/8 = 9.75 m/s
(b) How much wave power is there, per unit length?
P =
gVLA2
2
2
2

gVA
(1000)(10)(9.75)2
P / L =
= 195 kW/m
=
2
2
(c) How much wave power is there along 25 km of beach?
P = (195 kW/m)L
P = (195 kW/m)(25000 m)
P = 4875 MW
Energy, Power, and Climate Change
8.8 Wave Power
POWER GENERATION FROM A WATER WAVE
THE OSCILLATING WATER COLUMN
Air Column - Compressed
and rarefied by rising and
falling wave.
Wind Turbine
Generator
Turbine generates
both ways
FYI: A pelamis
can generate
750 kW
of power.
Energy,
Power,
and
Climate
Change
8.8 Wave Power
POWER GENERATION FROM A WATER WAVE
THE PELAMIS
The pelamis is named after the sea snake for
obvious reasons.
Each of four sections is hinged to the previous
one.
Fluid inside moves back and forth.
The moving fluid drives a generator.