Page 161 - Aerodynamics for Engineering Students
P. 161
144 Aerodynamics for Engineering Students
From Eqns (3.77) and (3.78b) it follows that the velocity on the surface of the
sphere is given by
3
q = - Usinp
2
So that using the Bernoulli equation gives that
1 1
Po + 2 PU2 = p + pp"
Therefore the pressure variation over the sphere's surface is given by
1 9
p-po =-u2(1 --sin2p) (3.81)
2 4
Again this result is quite similar to that for the circular cylinder described in Section
3.3.9 and depicted in Fig. 3.23.
3.4.6 Flow around slender bodies
In the foregoing part of this section it has been shown that the flow around a class of
bodies of revolution can be modelled by the use of a source and sink of equal
strength. Accordingly, it would be natural to speculate whether the flow around
more general body shapes could be obtained by using several sources and sinks or a
distribution of them along the z axis. It is indeed possible to do this as first shown by
Fuhrmann.* Two examples similar to those presented by him are shown in Fig. 3.31.
Although Fuhrmann's method could model the flow around realistic-looking bodies
it suffered an important defect from the design point of view. One could calculate the
body of revolution corresponding to a specified distribution of sources and sinks, but a
designer would wish to be able to solve the inverse problem of how to choose the variation
of source strength in order to obtain the flow around a given shape. This more practical
approach became possible after Munkt introduced his slender-body theory for calculat-
ing the forces on airship hulls. A brief description of this approach is given below.
Fig. 3.31 Two examples of flow around bodies of revolution generated by (a) a point source plus a linear
distribution of source strength; and (b) two linear distributions of source strength. The source distributions
are denoted by broken lines
* Fuhrmann, G. (191 l), Drag and pressure measurements on balloon models (in German), 2. &tech., 11, 165.
Munk, M.M. (1924), The Aerodynamic Forces on Airship Hulls, NACA Report 184.
