25 



Furthermore, the variation of V with respect to ar is also substantially linear along the after 

 end or 



fJ -U, x-x 



^.-^e -e--, 



[82] 



Inserting these linear relations, Equations [81] and [82], into momenium equation [80] gives 



'*" Ar,., -^] 'Illli!. 



[83] 



fi„ = fi. 



S el 



(A + 3) f/j' + ^ - (A + 4) V^ f/ ^ + 3 ^ f;^A +4 



or nondimensionally 



L2 L2 



WnTJ \l)LA 



[l-(^|]seca 



'gVP'^ /g 



lU V*^ IV V \ 



The initial position g of tha tail portion of the boundary layer may be taken at 0.8 of the 

 length of the body. An average value of A = 1.4 over the tail portion is appropriate in view of 

 the value of A = 1.42 found on the Mark 13 Torpedo.^^ 



In the region of the boundary layer near the tail, it is useful to establish relations be- 

 tween 6 and D, S* and A*, and A and H. A power law is assumed for the velocity profile or 





[85] 



Substituting this expression into Equation [32] and performing the indicated integration 



results in 



