Page 450 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

422 SLENDER STRUCTURES AND AXIAL FLOW

the pipe and pe the external pressure;t Aw, Aye, A, are components around the axes
(xo, yo, zo) of the resultant of the bending moments Ax and Ay and the twisting couple
&;Mu is the added mass per unit length, and c the coefficient of viscous damping due
to the surrounding fluid, associated with transverse motions; MA and c' play similar roles
for longitudinal motion; R,,, R,, R,, are the components of the reaction force per unit
length arising from the internal flow, and Gxo, G,, G, are the components of the effective
gravity force, including buoyancy effects.
From the relation between the systems (xo, yo, ZO) and (x, y, z) given by equation (6.1),
one can obtain

where
Q,* = Qz +Aope. (6.18)
Substituting equations (6.17) and the values of K,, K: and to from (6.2) into (6.16), the
equations of motion for the pipe may be written in the form
av au
(g + $) Qx - Qy] -cat

(6.19)
av
]
2 [ eY + $ex + e; - c - + R, + Gyo -
as
at

+The pipe is assumed to be immersed in a fluid of generally nonuniform pressure (e.g. in a hydrostatic
environment). Hence, pe is not absorbed within the internal fluid pressure pi simply by defining the latter as
'measured above the ambient pressure' as in Chapter 3.