fluid_mechanics

12.2 Basic Energy Considerations 649
(a)
Blade motion
W 2
U 2
V 2
W 1
U 1
(1)
(2)
V 1
ω
(1)
(2)
(b)
F I G U R E 12.4 Idealized flow through a windmill: (a) windmill;
(b) windmill blade geometry; (c) absolute velocity, V; relative velocity, W; and blade
velocity, U; at the inlet and exit of the windmill blade section.
(c)
different directions. For this to happen, the blades must have pushed up on the fluid—opposite to the
direction of blade motion. Alternatively, because of equal and opposite forces 1actionreaction2
the fluid must have pushed on the blades in the direction of their motion—the fluid does work on
the blades. This extraction of energy from the fluid is the purpose of a turbine.
These examples involve work transfer to or from a flowing fluid in two axial-flow turbomachines.
Similar concepts hold for other turbomachines including mixed-flow and radial-flow configurations.
F l u i d s i n t h e N e w s
Current from currents The use of large, efficient wind turbines to
generate electrical power is becoming more commonplace throughout
the world. “Wind farms” containing numerous turbines located
at sites that have proper wind conditions can produce a significant
amount of electrical power. Recently, researchers in the United
States, the United Kingdom and Canada have been investigating the
possibility of harvesting the power of ocean currents and tides by using
current turbines that function much like wind turbines. Rather
than being driven by wind, they derive energy from ocean currents
that occur at many locations in the 70% of the earth’s surface that
is water. Clearly, a 4-knot (2.5 ms) tidal current is not as fast as
a 40-mph (70 kmhr) wind driving a wind turbine. However,
since turbine power output is proportional to the fluid density, and
since seawater is more than 800 times as dense as air, significant
power can be extracted from slow, but massive, ocean currents.
One promising configuration involves blades twisted in a helical
pattern. This technology may provide electrical power that is both
ecologically and economically sound. (See Problem 12.6.)