Page 234 - Fluid Mechanics and Thermodynamics of Turbomachinery

Centrifugal Pumps, Fans and Compressors 215

FIG. 7.9. Flow model for Stodola slip factor.

A number of more refined (mathematically exact) solutions have been evolved
of which the most well known are those of Busemann, discussed at some length
by Wislicenus (1947) and Stanitz (1952) mentioned earlier. The volume of mathe-
matical work required to describe these theories is too extensive to justify inclusion
here and only a brief outline of the results is presented.
Busemann’s theory applies to the special case of two-dimensional vanes curved
as logarithmic spirals as shown in Figure 7.10 Considering the geometry of the vane
element shown it should be an easy task for the student to prove that,

0

D tan ˇ ln.r 2 /r 1 / (7.17a/

0
FIG. 7.10. Logarithmic spiral vane. Vane angle ˇ is constant for all radii.