Smith 



relation between the values of a on the elements. On each element one point is 

 selected where Eq. (5) is required to hold; i.e., one point is selected where the 

 normal velocity is required to vanish. That requirement gives a number of linear 

 equations equal to the number of unknown values of cr . Once they are solved, flow 

 velocities may be calculated at any point, on or off the body surface, by summing 

 the contributions of the surface elements and the contribution of the onset flow. 

 Usually, velocities and pressures on the body surface are of greatest interest. 

 Because of the way in which the body surface is approximated, these must be 

 evaluated at the same points where the normal velocity was made to vanish. 



Approximation of the Body Surface 



Figure 3 shows the surface elements used to approximate various types of 

 bodies. Three-dimensional body surfaces are approximated by plane quadrilat- 

 eral elements, axisymmetric bodies by frustums of cones, and two-dimensional 

 bodies by infinite plane strips. In three-dimensional cases, the body is specified 

 by the coordinates of a set of points distributed over the body surface. These 

 points are used to form quadrilateral elements. For two-dimensional or axisym- 

 metric bodies, only a single-profile curve is specified by points. These points 

 are connected by straight-line segments, which are then the traces of the infinite 

 plane strips or the frustums of cones in the plane of the profile curve. 



Fig. 3 - Approximation of the body surface by elements (a) two- 

 dimensional and axisymmetric bodies, (b) three-dimensional bodies 



If the body surface is axisymmetric, it is not necessary that the flow itself 

 also be symmetric about the same axis. If the flow is axisymmetric, it is inde- 

 pendent of circumferential location about the axis of symmetry, and thus the sur- 

 face source density is truly constant over each frustum element. It is only neces- 

 sary that the flow vary with the circumferential location in a known way. The 



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