601 



— =, or the best ordered arrangement with all vortices along the 



walls and C equal to a (high) constant value). 



For the sake of comparison the formulae (39), (47) and (46) have 

 been represented together in fig. 4 at a logarithmic scale. 



^ 7. Motion of a fluid between two fixed parallel walls. 



The motion of a fluid between two fixed parallel walls may be 

 treated according to the same scheme as has been used for the 

 motion between a fixed and a moving wall. As the former case 

 has somewiiat more resemblance to the t.ypes of motion occurring 

 usually in |)ractical cases, the principal features of the calculation 

 will be mentioned here. 



The distance of the walls will be taken equal to A; (he mean 

 velocity of the current is denoted by V ; the pressure gradient 

 — dp/dx will be denoted by J. — Rkynolds' characteristic number 

 becomes: R= Vho/n; (he coefficient of the resistance formula is 

 written C ^ JI>/qV'. Equation (8) of |)aragraph 2 has to be replaced 

 by the following equation governing the principal motion: 



d*U d — 



dy dy 



A first integration of this formula gives: 



dU — f h \ 



^Ty -^"^'^•^(^T -.yj . • . • . . (49) 



The constant of the integration is determined by observing that 

 on account of the symmetry of the arrangement both quantities 

 dU/dy and uv vanish for y ^ h/2. On integrating a second and a 

 third time, and observing that f/ ^ at both walls, we get: 



h 



liVh = — Jh' — j rfi 



dy Qy uv (50) 





 This equation replaces formula (11). Condition (9) which expresses 

 the dependance of the relative motion on the principal motion, 

 retains its form. Now firstly, using (49), we eliminate dU/dy from 

 (9); then using (50), we eliminate J and we obtain: 



A k 



-Jdy ip' {l^y + fi'S^; -^fj dy Qy ^J 

 f*^ 



-= --— . . (51) 



I dy (}y uv 



T> 



