Bernoulli's Theorem ”From December 1943 Air Trails Magazine.

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.

Figure 1 - Air flow through an orificeNow 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.

Figure 2 - Airflow over an airfoilAn 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.

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.