Consider a supersonic flow with an upstream Mach number of \(M_{\infty}\). This flow moves over the same wavy wall as first shown in Fig. 9.5 and as given in Example 9.1. For small \(h\), use linear theory to derive an equation for the velocity potential and surface pressure coefficient.

Figure 9.5:

Data From Example 9.1:

Consider a subsonic flow with an upstream Mach number of \(M_{\infty}\). This flow moves over a wavy wall with a contour given by \(y_{w}=h \cos (2 \pi x / l)\), where \(y_{w}\) is the ordinate of the wall, \(h\) is the amplitude, and \(l\) is the wavelength. Assume that \(h\) is small. Using the small perturbation theory of this chapter, derive an equation for the velocity potential and the surface pressure coefficient.

Transcribed Image Text:

Wavelength Amplitude, h,