Page 161 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: LINEAR DYNAMICS I 143

Figure 3.50 Continuation of the comparison as in Figure 3.49, for pipes with B = 0.485 and
0.645 (Paidoussis 1970).

Table 3.4 Comparison of experimental results with theory for hanging cantilevers conveying air
(Pa'idoussis 1970).
B x 103 Y Values of uCf Values of w~,
Theory Exp't Theory Theory Exp't Theory
p=o p =0.02 p =o = 0.02
0.23 61.1 6.15 6.33 6.33 21.3 18.0 19.7
2.03 42.4 5.62 6.05 5.79 19.5 19.5 18.1

Cantilevers of intermediate length, while unstable by buckling at zero and small flow
velocities, were stable at a higher flow range. Thus, if the cantilever was supported
and the flow increased to a certain point, upon release the cantilever retained its straight.
undeformed shape. Further increase of flow, nevertheless, eventually resulted in the devel-
opment of oscillatory instability.
Clearly these observations agree with the theoretically predicted behaviour of standing
cantilevers, if one interprets increasing length as increasing negative y.
Experimental results for standing cantilevers are shown, and compared with theory (B =
1.1 x = 0.02), in Figure 3.51. It is noted that measurements with y < -22.8