ea wmwBB g gg taaa namaemmecm K nxntmrvnvmv-**,-. 



wfot >3 > .M*-im*^ **ttt* im *»««»« 



The solution of Equation (.18) is given by Gieoing and Smith" 

 potential function is divided into three parte as 



4>(x,z) - <J) 1 + r(4- 2 + (^3). 



The velocity 



(21) 



The velocity potential <£>. is due to sources and sinks which are distributed on 

 each section of the control plane. 4'o is the velocity potential due to a vortex 

 of unit strength which is located at the inside of a section. The vortex is 

 introduced to calculate the life force around the section. <J>,, the last term of 

 Equation (21) is the velocity potential due to sources and sinks of unit 

 strength distributed on the section. This velocity potential cancels the normal 

 velocity generated by fy~. If we substitute Equation (21) into Equation (20), 

 the following conditions are given 



and 



Hi 



on 



0*2 

 5n 



» Un, 



0*3 

 "on - 



(22) 



(23) 



These three velocity potentials are expressed as 



(1^(10 - ~ % I Cj(q)G (p,q)dl(q) for 1-1 and 3 



(24) 



and 



4, 2 (P) - Re{ -jjj- ln[x-a + i(z-b)] - •§£ In [(x-a) + i(z+b)] 



-ik[x-a + i(z-f-b)] ,. r . ., ...1 



/- 5 . I dk + 2 *i e " ik ol^ ♦ Kz+b)J 



-2pv 



k - k r 



