Flows with Drag Reductton (Veloetty and Frictton) 
CONCLUSIONS 
It has been shown that the effect of linear macromolecules in 
dilute solutions on the flow in the wall region, can be described by 
van Driest's mixing length model with a variable damping parameter 
At, If the Reynolds number of the flow R* is large, the constant 
shear approximation used by van Driest can be used. When Rt/At is 
not large, it is necessary to take into consideration the variation of 
the shear stress with the distance from the wall. The velocity distri- 
bution in the outer region is modified in this case using Coles' Wake 
Function multiplied by a factor. The factor decreases as the damping 
action of the molecules increases. Although the model does not ex- 
plain the damping mechanism it suggests a similarity between flows 
with and without polymers, which is not present in the elastic sublayer 
model. The model does not explain the nature of the maximum drag 
reduction asymptote either, however, it is pointed out that the maximum 
drag reduction curves for a given polymer might be associated with a 
maximum value of the damping parameter At. 
REFERENCES 
[1] COLES, D.J., of Appl. Math. & Physics. (ZAMP), Vol. 5 
No. 3,,1954. 
[2] ELATA, C., LEHRER, J. & KAHANOVITZ, 1966, ISRAEL, J. 
Tech. 4, 87. 
[3] McMILLAN, M.L., HERSHEY, H.C. & BAXTER, R.A.,1971, 
"Drag reduction’, Chem. Eng. Prog. Symposium Series, 111, 
67, 27: 
[4] ME VER OW AS, 1960, Aoi Ch. By t2, S22. 
[5] POREH, M. & PAZ, U. 1968, Inter. J. Heat Mass Transfer, 
11, 805. 
[6 ] TOMIPA, Y., 1970, Bull, JS, M.E. 13, 995. 
[7 ] VAN DRIEST, E.R. 1965,’ 5, Aero. Sci. 23,..1007- 
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