Bernoulli Effect

The Bernoulli effect provides that, when a gas such as air flows, its pressure drops. This is the basis for how aircraft wings work: The cross-sectional shape of the wing, called an aerofoil (or airfoil), forces air to follow a longer path over the top of the wing, thereby speeding it up and creating a net upward force called lift.

Figure F.5 illustrates the Bernoulli effect for the case of a reservoir at constant pressure (``mouth pressure'') driving an acoustic tube. Any flow inside the ``mouth'' is neglected. Within the acoustic channel, there is a flow with constant particle velocity . To conserve energy, the pressure within the acoustic channel must drop down to . That is, the flow kinetic energy subtracts from the pressure kinetic energy within the channel.

For a more detailed derivation of the Bernoulli effect, see, e.g., [182]. Further discussion of its relevance in musical acoustics is given in [144,200].

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.