The other boundary condition is obtained at the array (x = L), 

 where we must have: 



M 





du 



ES ^ 



o X 





1 







c)\^ 



Su 



+ 





(K.p 



A 









2 







dt 



S t 



x=L 



where: 



(8) 



M = Dynamic mass of the array. In general, it will 

 be composed of three parts: the actual mass of 

 the materials of the array, an apparent mass due 

 to the motion of the array in water, and the mass 

 of any water trapped in the array and having to 

 move with it . 



a = Drag coefficient of the array. This is a function 

 of the Reynolds number, and for certain array 

 configurations such as cylindrical or spherical, 

 its value can be found in the literature . 



A = Area of the array projected in the direction of 

 motion. 



Notice that a quadratic form has been taken for the hydrodynamic 

 drag. (The two vertical bars in the first velocity factor mean "absolute value 

 of," and they are necessary since the drag must always oppose the motion). 

 This is absolutely necessary because the Reynolds numbers involved are high. 



Let us define the following two parameters: 



P SL 

 c 



M 



B = 



gpA 



2M 



(9) 



Notice that u is the ratio of the mass of the cable to the mass of 

 the array. Equation 8 can then be put in the following form: 



ht" 



+ u 



S_u 



ax' 



+ B 



B_u 

 dt' 



a_u 



St' 



= 



(10) 



x' = 1 



12 



Arthur m.lLittleJnf. 



S-7001-0307 



