The Bernoulli Principle
Magan Fowler
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.
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.
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.
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).
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.
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.
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.
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.
Resources
The Physics of Sound
http://www.voicesource.co.uk/article/151
http://www.scienceclarified.com/everyday/Real-Life-Chemistry-Vol-3-PhysicsVol-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