Bernoulli's Principle and Airplane Wings

Bernoulli’s Principle and airplane wing

Bernoulli's principle states that if you increase the velocity of a incompressible fluid, i.e. liquid, then the pressure exerted perpendicular to the velocity decreases. Bernoulli arrived at his principle studying the flow of water. Instead of pressure exerted perpendicular to the flow one could consider it as a decrease in the liquid’s potential energy perpendicular to its flow.

To some Bernoulli’s principle is a form of conservation of energy whereby the kinetic, potential and internal energies are summed up and considered constant along a given streamline of a fluid. Another way of viewing this is the fluids speed increase results in an increase in its dynamic pressure, which results in a decrease of its static pressure.

Really and truly such conceptualizations are better for liquids wherein cohesive forces bind the liquid, thus as the liquid’s velocity increases along a streamline, then those liquid molecules pull upon their neighbouring molecules, along the streamline. And it is this pulling that best explains the static pressure drop.

Most of us are taught that the Bernoulli equation also explains why an airplane wing has lift. The reasoning being the shape of the wing forces the air above the wing to move faster than the air below the wing. Hence based upon Bernoulii’s principle the static pressure above the wing is decreased. Viewing the airflow around a wing in Fig 1, this means that the pressure above the wing is less than that below.

The above sounds good until one considers that the cohesive forces between air molecules is small, so small that one cannot envision how the neighbouring air molecules are pulled along the streamline. The reality is that Bernoulli’s principle does not apply to air in the same manner as it would cohesively bound liquids. If you are in disagreement then try to explain how an airplane wings works when a plane is upside down. Certainly planes tend to be more efficient when upright but the fact remains that planes can fly upside down, and yes some planes do this better than others.

The reason that Airplane wings have lift has more to do with the angle of attack and the wings shape. One must remember that our atmosphere’s gas molecules are moving in all directions, as is depicted in Fig 2. Accordingly the force exerted is similar in all directions. Note although fig 2 only shows one molecule, its arrows represent the motions of an ensemble of molecules is approximately equal in all directions.

Now consider a moving wing at some angle of attack as illustrated in Fig 3. Basically the moving wing (at a proper angle of attack) collides with the atmosphere’s gaseous molecules knocking them forward and downward. The greater the attack angle the more molecules are knocked downwards by the wing’s underside.

Thus some of the gas molecules that would (in the future seconds or fractions thereof) impinge on the top of the wing are knocked forward and downward. The result is fewer gas molecules actually hit the top of a moving wing than the bottom of that wing, as is illustrated in Fig.4. Accordingly, more gaseous molecules hit the underside of the wing than the topside, thus providing lift. And that is the major reason that airplanes can fly.