595 



obtain a constant value of — tw, it is necessary to make b independent 

 of §, in other words to distribute the vortices uniformly over the 

 breadlli of the current. However, it is obvious tiiat the vortices cannot 

 pass througli the walls of the channel; hence we must take: 



6 = constans, ifÜ<^g<^l — 1) 



6 = , if § < or ^ > 1 — L> ' ' ' ^ ^^ 



Consequently the quantity — uv will have a constant value in the 

 region defined by: D<^y<^\ — D only; in the two remaining 

 strips it decreases to zero. 



With the omission of a constant factoi-, the following expressions 

 for — uv are found : 



a) if y<CD: 



y yID 



— wf = I d% 'f i -j~ ]—^\ '^^ 'f' ^') = 



b) if i»<j/<l — X>: 



(33) 



y 1 



630 



y-D 



c) if y ]> 1 — D: in the expression given under a) y has to 

 be replaced by 1 — y. 



By means of these formulae we find: 

 1 



D 



■J 







dyuv=z (\—D) 



^ 630^ 



,z.Y 







hence: 



T = 0,828 D \ (34) 



All vortices being of the same dimensions, equation (30) gives 



immediately : 



294 

 « = ^ ......... (35) 



Inserting these values into equation (17): 



1 294 



fl = .... .... (36) 



• 0,828 -D22 u,828X»'fl'' ^ ' 



39* 



