| Nearly
every model airplane builder knows that the cambered upper surface
of an airfoil produces lift by creating a low-pressure area above
the airfoil. However, comparatively few know why this low-pressure
area exists. This low-pressure area on an airfoil, the curved flight
of a spinning ball, the operation of an air-speed indicator, and
even the operation of a atomizer (spray bottle) are but a few of
the many things explained by Bernoulli’s theorem.
The principle behind
Bernoulli’s theorem is the law of conservation of energy.
It states that energy can be neither created nor destroyed, but
merely changed from one form to another. To illustrate how this
applies, let us consider Figure I. which represents a horizontal
pipe with air flowing through it. The air in the pipe has two forms
of available energy. One is potential energy, which is in the form
of air pressure. The other is kinetic energy which the air has by
virtue of its motion. Now, notice that the pipe is constricted at
(B). Supposing the cross-sectional area at (B) is one half the cross-sectional
area at (A): the air will have to move about twice as fast past
(B), in order to allow the same amount of air by in the same time.
This is analogous to a nozzle on a hose, where you obtain a high-velocity
stream of water by passing the water through a small orifice.
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| Figure
1 - Air flow through an orifice |
Now since the air is
going faster past (B), it must have more kinetic energy when passing
(B). Recalling the law of conservation of energy, we realize that
we must have converted some of the potential energy in order to
have more kinetic energy. Since the only potential energy available
in this set-up is in the form of air pressure, there will be a low-pressure
area in the construction of the pipe at (B). In short, we may say
that if air is flowing, other factors being equal, an increase in
velocity will result in a decrease in pressure; and conversely,
a decrease in velocity will result in an increase in pressure. It
should be noted that the pressure and velocity at (C) are the same
as at (A).
Now consider Figure
II. This represents an airfoil in a wind tunnel. Notice how the
streamlines close in over the top of the airfoil. The closing in
of the streamlines constricts the air flow just as (B) of Figure
1 did. As a result there is an increase in air velocity over the
top of the airfoil and a resulting low-pressure area.
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| Figure
2 - Airflow over an airfoil |
An interesting experiment
which beautifully illustrates Bernoulli’s theorem can easily
be performed. Obtain a light cardboard mailing tube and wrap a strip
of cloth about two feet long around its center. Set the tube on
the floor so that the strip of cloth unwinds from the low side of
the tube. Now give the cloth a brisk horizontal pull and the tube
will soar into the air. Figure 3 explains why. The rotation of the
tube, coupled with skin friction, causes an increase in relative
air velocity above the tube arid a decrease in relative air velocity
below the tube. This, of course, will create a low-pressure area
above the tube, a high pressure area below the tube and the result
is lift. A similar set-up causes a spinning ball to curve in flight.
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| Figure
3 - Airflow over a rotating tube (or a baseball) |
I said that Bernoulli’s
theorem explains the operation of an atomizer. When you squeeze
the bulb the air moves through a narrow passage at a high velocity.
This high velocity is, of course, accompanied by a low pressure.
The atmospheric pressure on the surface of the liquid in the bottle
then forces the liquid up a tube into the low-pressure area where
the high- velocity air sprays the liquid out. Aspirators and many
carburetor jets work in a similar manner.
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