Page 127 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: LINEAR DYNAMICS I 109

1 .OO

0.75
0 -
-
s
0.50
-
s
2

0.25

0.7030 \
0 I I I I
(a) 0 0.2 0.4 0.6 !

&+3
I
1
I
I

I I I I I I I
/-4f
/ I I
I
1 I
I I
I
I
I
0.7030
I I
0.4 0.6

Figure 3.25 (a) The ratio of %e(S2,)/%e(S21)o as a function of the dimensionless
flow velocity U/BL = u/(n[j3(f + 7r2)]1/2] for a tensioned and pressurized pipe with
([f - li’(1 - 2u)]/[f + 7r2])’’2/n 0.0636 and j3 = 0.4338 at u = 0 and IJ = 0.312; (b) the phase
=
difference in the displacement at 6 = 0.175 and 6 = 0.815 during vibration as a function of U/aL.
+, Experiment; -, theory with pressurization and resulting dilatation of the pipe ignored:
__- . theory with these effects taken into account (Naguleswaran & Williams 1968).

Another set of experiments was conducted by Liu & Mote (1974), aiming to study
the effects of flow and tensioning on the dynamics of the system. They used small-
diameter vertical aluminium pipes (0, = 6.375 mm, h = 0.559 mm), 1.829 m (6 ft) long,
conveying an oil-water emulsion circulated with the aid of a gear pump. The apparatus
involved a shaker to excite the pipe and strain gauges to measure the vibration. The fluid