Pa'idoussis 



Q +i^5x 



ax 



^ dx 



\ T + !I 



Sx 



F„ 5x + F-Bx 

 N A 



Fig. 1(b) Forces and moments acting on an element 

 (r(x) of the body- 



Taking force balances in the x- and y-directions and a moment 

 balance we obtain 



II +F +F ^= 0, 



99-F +-L(T^)+F-^-F -mA =0. 



8x 9x 



ax 



at' 



ax 



(1) 



(2) \ 



(3) 



where the inertia forces in the x-direction have been neglected. 



We next consider the functional form of the forces. The 

 lateral inviscid force F. 6x represents the reaction on the body of 

 the force required to accelerate the fluid around it, and may be 

 written as 



F. = [(a/at) + u(a/ax)](Mv), 



(4) 



as discussed by Lighthill [ 28] , [ 29] , where v is the lateral relative 

 velocity between the body and the fluid flowing past it, and M is the 

 virtual mass of the fluid. Here the effects of sideslip have been 

 neglected, effectively assuming that each cross section of the body is 



984 



