A,20 • FLOW BETWEEN ROTATING CYLINDERS 



system is not observed. To avoid disturbing secondary flows produced at 

 the end walls, the ratio of height to width of annulus must be as great 

 as 40, according to Wendt's measurements. The observed values of 

 Uoiro - r^lv vary from about 2000 for 2{r, - r)/{r, + r-:) = 0.016 to 

 about 65,000 for 2{r, - ri)/(ro + r,) = 0.3 as shown in Fig. A,20. The 

 velocity distribution indicates the presence of boundary layers at the 

 surfaces of the cylinders, and it is probable that the transition mecha- 

 nism is somewhat similar to that of the boundary layer on a plate. As 

 2(ro — rO/Cfo + n) increases, the boundary layers occupy a smaller and 



10* 



10^ 



> 10^ 



103 



102 



10-4 10-3 10-2 



2 (ro - ri) 



To -I- Ti 



10-' 



10° 



Fig. A,20. Transition Reynolds numbers for flow between rotating cylinders. 



smaller fraction of the width of the annulus, and thus a transition 

 Reynolds number based on the width of the annulus increases. 



In the general case in which both cylinders rotate there are certain 

 ranges of variables in which transition does not occur even at the highest 

 Reynolds numbers. Here the stabilizing action of the centrifugal field is 

 sufficient to prevent transition. The available data are not inconsistent 

 with Prandtl's criterion that in such cases {du/dr)/{u/r) should He be- 

 tween — 1 and +2. Since this ratio varies across the annulus, there are 

 undoubtedly many cases in which the flow is partly laminar and partly 

 turbulent, and it is not possible to state that the experiments yield pre- 

 cisely -f-2 as the limiting value. 



<51 > 



