Desai and Lieber 



The measurements of the drag on a circular cylinder made by Tritton are 

 the most recent experiments and extend down to the lowest value — 0.416 — 

 of the Reynolds number, based on diameter, as yet attempted. The results of 

 Wieselsberger [71] and Relf [72] are in agreement with Tritton' s. Those of 

 Fage [73,74,75], Schiller and Linke [76], Roshko [77], and Humphreys [78] cover 

 the range of high Reynolds numbers and hence are not useful for comparison 

 with the present work. The results obtained by Thom [66], Kawaguti [65], and 

 Apelt [79] by numerical integration of the exact Navier-Stokes equations are in 

 agreement with Tritton' s results. Allen and Southwell's [48], and Southwell and 

 Squire's [24] results are somewhat higher than Tritton' s. Since Tritton' s paper 

 gives a comparison of these other works with its own results, it is considered 

 sufficient to compare our results with Tritton' s. For this purpose, Tritton' s 

 drag v/s Re curve is plotted in Figs. lA, IB, and IC. From them it can be seen 

 that the first and second iteration results behave asymptotically in the same 

 fashion as Tritton' s, but that these curves for higher Re lie above those of 

 Tritton' s. The values of the first iteration drag are lowered by the negative 

 contributions of the second iteration results for Re < 4. We expressly state 

 that the second iteration drag results for Re > 4 are not very accurate and that 

 they should be considered indicative of what the second iteration leads to rather 

 than as conclusive. 



Figure 2A shows that the ratio of the first iteration pressure drag to the 

 viscous drag remains essentially equal to 1. The divergence with increasing 

 Re may be an indication of decreasing accuracy of computation, though this has 

 not been ascertained in the present work. By comparing these results with 

 those which may be obtained by computation with multiple precision, we can de- 

 cide on this issue. It is interesting that, like Oseen's theory, this ratio has 

 turned out to be unity. However, this is not the ratio of the total pressure drag 

 to the total viscous drag obtained by considering both the first and the second 

 iterations together. The results of the second iteration show that the ratio will 

 be different from unity. Kawaguti's [65] and Thorn's work [66] show that this is 

 indeed the case. 



Definition of points of separation similar to the one we have given have 

 been used by Van Dyke, Proudman and Pearson, and Yamada. These first two 

 authors have correctly pointed out that the results of Tomotika and Aoi are 

 seriously in error as far as the determination of points of separation is con- 

 cerned. Figure 2B gives the angle of separation determined with first iteration 

 as well as first and second iterations together. It shows the general behavior 

 found in experiments by Grove et al. [47], Thom [66], Homann [80,81], and 

 Taneda [82]. It shows asymptotic behavior with increasing Reynolds number. 

 At Re = 0.75 the angle a^ is zero, which implies that according to the results 

 of the first iteration separation begins at Re = 0.75. On the other hand, aj is 

 zero at Re = 2.3, showing that the separation begins at Re = 2.3 when two itera- 

 tions are taken into account. Nisi and Porter [83,84] estimate the Reynolds 

 number at which the separation begins to be 1.6. Homann [80,81] gives a value 

 of 6.0. Taneda [82] estimates it to be 2.5, and this recent value is close to the 

 theoretical Re = 2.3 predicted by the present work. Experimental values must 

 be slightly higher than theoretical values, because a vortex and separation 

 associated with the former cannot be discerned until after they have reached 

 a finite size which can be observed. Theoretical values, on the other hand, 



586 I 



