Page 449 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

CURVED PIPES CONVEYING FLUID 42 1

6.2.2 The equations of motion
Consider an infinitesimal element of the pipe, contained between two cross-sections
normal to the deformed centreline, and the forces and moments acting on it, as shown in
Figure 6.2. As shown in Appendix 5.4, balance of forces and moments along the XO-, yo-
and zo-directions yields

(6.16)

YO
Figure 6.2 Forces and moments acting on a curved pipe element, expressed in the (xo, yo, ZO)
reference frame.

Here Qxo, Qyo, Q,, are components, along the axes (XO, yo, zo) of the resultant of the
transverse shear forces Qx, Qy, and of the 'combined force' Q: arising from the axial
force Q, and the external pressure force A,p,, A, being the outer cross-sectional area of