The Bernoulli Principle

1. The Bernoulli Principle • Magan Fowler

2. Daniel Bernoulli • 1700-1782 • Bernoulli was a Swiss mathematician and physicist. • He discovered this principle while conducting experiments about the conservation of energy. • His results were published in Hydrodynamica (1738). • Leonhard Euler (1707-1783), a German mathematician, generalized Bernoulli’s findings into what we know know as the Bernoulli principle.

3. Bernoulli’s Principle • “In a fluid-flow situation (such as water or air) the pressure in the moving fluid is lower at places where the speed of flow is greater than at places where the flow is slower.” (p. 166) • In other words, as the velocity of a fluid increases, the pressure exerted by that fluid decreases.

4. Why does pressure decrease with velocity? • Pressure= Force exerted per area (P=F/A) • While the fluid as a whole moves with any certain velocity, the atoms that make up that fluid also move around, or “jostle.” This jostling of the atoms creates pressure. (Think of water in a container. While the water is not moving, the atoms that make up the water are jostling around within the container. As the atoms move and collide with the sides of the container, they exert force on the container which creates pressure.) • Running example- This is why pressure decreases with velocity.

5. Examples • Chimney: When air moves across the top of a chimney, it has a higher velocity than the air at the bottom of the chimney (in the fireplace). This means that there is a lower pressure above the chimney than there is in the fireplace, so the smoke is drawn out of the chimney to the area with the lower pressure (you could think of it as if the higher pressure in the fireplace forces the smoke out of the chimney).

6. Paper demonstration: When you blow between two sheets of paper, the air moving between them has a higher velocity than the air on the outside of the sheets of paper. This means that there is a lower pressure between the sheets of paper than there is on the outside. The higher pressure on the outside of the sheets of paper push them inward, causing the sheets of paper to move closer together.

7. How does this apply to the voice? • When you speak or sing, a stream of air is moving through your vocal folds from your lungs. Since the air has a high velocity, an area of low pressure is created between your vocal folds.

8. The vocal folds are pulled inward because of this drop in pressure (now the pressure from outside of the vocal tract is greater than the pressure between the folds and pushes the folds together). Immediately the folds are forced open again by the air stream that is still coming from your lungs. This again causes a Bernoulli effect, and this cycle continues. The repetition of this cycle happens so quickly that it creates the vibrations that create your voice.

9. How does this apply to wind instruments? • For a reed instrument, the Bernoulli principle acts on the reed and the mouth piece. The velocity of the air from the musician’s breath creates a low pressure between the reed and the mouth piece, which causes the reed to vibrate onto the mouth piece. • For a brass instrument, the Bernoulli principle acts on the musician’s lips, causing them to vibrate similarly to the vocal folds.

10. Resources • The Physics of Sound • http://www.voicesource.co.uk/article/151 • http://www.scienceclarified.com/everyday/Real-Life-Chemistry-Vol-3-Physics-Vol-1/Bernoulli-s-Principle.html#ixzz12kTVoSQs • http://home.earthlink.net/~mmc1919/venturi_discuss_nomath.html • http://www.voicewize.com/information_center • http://www.gosh.nhs.uk/gosh_families/information_sheets/encouraging_healthy_voice/encouraging_healthy_voice_children.html