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## 9.12. Infinite hyperbolic horn (hypex) [12]

### Theoretical considerations

The equation describing the cross-sectional area S(x) as a function of the distance x along the axis is
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(9.51)
where S T is the area of the throat, which is located at x   =   0 and 0     α     1. We can vary the parameter α to create any profile between hyperbolic (α   =   0) and exponential (α   =   1). In the steady state, the Helmholtz equation for the hyperbolic horn is obtained by inserting S(x) from Eq. (9.51) into Eq. (2.27) to yield
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