Relating pressure (p) and velocity (v) at any two points of height y within a continuous tube of flow, the Bernoulli equation is given by
where is fluid density and g is the acceleration of gravity. This expression is based on continuity of volume flow and conservation of energy.
An approximate reed orifice geometry.
For the reed geometry as approximated in Fig. 9, the upstream cavity is viewed as a large tank of constant or slowly varying pressure pu and essentially zero volume flow uu.
Application of the Bernoulli equation, assuming no appreciable change in height, leads to an expression for the flow through the reed orifice of the form
where w and x are the width and height of the reed channel, respectively, and the sign function is
An example flow curve determined using Eqs. (22) is shown in Fig. 10.
Flow characteristic through the reed orifice.
Although the flow expression of Eq. (22) is derived for steady flow, its use is generally assumed to be valid under oscillating conditions as well. The validity of this assumption has been questioned by results of da Silva et al. (2007).
The acoustic resistance to flow presented by the orifice is inversely proportional to the slope of the flow curves in Fig. 10 (Fletcher and Rossing, 1991). For low values of , the resistance is given by a small positive value. At very high pressure differences, the reed is blown closed against the mouthpiece facing and all flow ceases.
The threshold blowing pressure, which occurs at the flow peak, can be determined from Eqs. (22) and (20) and is roughly equal to 1/3 the closure pressure. Between the threshold and closure pressures, the flow resistance is negative and the reed mechanism functions as an acoustic generator.