Hoyt and Fabula 



Reynolds Number Correlation 



Data from poly(ethylene oxide) of 4 million molecular weight has been cor- 

 related on a pipe flow Reynolds number basis using the viscosity of pure water. 

 At a concentration of 100 wppm, drag reduction reaches a maximum of 78 - 79% 

 at a Reynolds number of about 10.^ At a lower concentration (30 wppm) the ef- 

 fect falls off at higher Reynolds numbers. A possible explanation for the fall-off 

 is rapid shear degradation of the polymer at the higher flow velocities. 



The envelope of maximum drag reduction shown on Fig. 19 is the maximum 

 effect obtained for any polymer in pipe flow as a function of Reynolds number. 

 Thus it is an empirical relationship for pipe flow corresponding to that given for 

 rotating disks in Fig. 8. These pipe flow data are consistent in general with 

 those reported in Ref. 11. 



To further demonstrate the validity of Fig. 8, Table 3 gives some concentra- 

 tions of materials required to attain the maximum drag reduction of 67% at a 

 pipe flow Reynolds number of 14,000. 



Table 3 

 Concentrations (wppm) of Material Required to 

 Achieve 67% Drag Reduction in Pipe Flow at 

 Re = 14,000 



*Source of polymer: Stein, Hall and Co. 

 Source of other materials listed in Table 1. 



OTHER EXPERIMENTS 



The drag reduction phenomena has been suggested [12] as a possible expla- 

 nation of certain erratic fluctuations of measured resistance in some towing 

 tanks. ^ Frictional drag measurements on the same model in the same towing 

 tank are known to be subject in some tanks to considerable variation, always 

 down from the "standard," and as much as 14%, with no other complete explana- 

 tion than a "change in resistance characteristics of the water." Since it is 

 known that many algae and marine organisms secrete mucous or slime, it is 

 conceivable that these may act in the same manner as the conjpounds studied 

 above. 



^Data taken by the Western Co. under U. S. Navy contract. 



^It appears that these fluctuations are reduced in tanks where the water is 

 chemically purified. 



954 



