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: Illustration of the Bernoulli effect in an acoustic tube.

Figure F.5 illustrates the Bernoulli effect for the case of a reservoir at constant pressure $p_m$ (``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 $u$. To conserve energy, the pressure within the acoustic channel must drop down to $p_m - \rho u^2/2$. 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].