Flows with Drag Reductton (Veloctty and Frictton) 
as well as near (Ret 12) cp » Where a smooth transition from the 
Newtonian curve to the polymer solution curve is observed. 
The effect of the transition region between the viscous sub- 
layer and the log region, was first considered by Poreh and Paz(1968) 
The velocity in this zone was approximated by the following log law 
t a +, + + 
ee allie oid’ AOL ie dae kr (6) 
a ; : 
where Sie 3 the ''thickness'' of the viscous sublayer, was assumed to 
be proportional to the ''thickness"' me in the two-layer model 
+ 
Pos 0. 43 i oe 
and the value of y:* was determined by the intersection of Eqs. (1) 
and (2). When Au’= 0 and Var = 11.6Eq. (6) reduces to 
+ 
Hie, (sion eee is "SAGs (8) 
which had been used by von Karman to describe the buffer zone in 
Newtonian flows, The model has been used successfully to relate heat 
transfer characteristics to friction losses in dilute polymer solutions. 
The effect of the buffer zone on the friction coefficient was found, 
however, to be negligible. 
Recently, Virk (1971) proposed a new 3-layer model to de- 
scribe the velocity distribution in drag reducing fluids. He termed the 
transition between the viscous sublayer and the log region - elastic 
sublayer and proposed to describe it by a universal logarithmic law 
ae 
Bourn ky Seri Bas (9) 
where Ay ~11.7 and B,=- 17.0. The "edge" of the viscous sub- 
layer y,t is given by the intersection of Eqs.(1) and (9). The "edge" 
of the elastic sublayer, is given by the intersection of Eqs.(9) and 
(2). The relation between Au and the thickness of the elastic layer 
is given by 
A + 
Ae fe) ey ee (10) 
+ 
Thus, when Au becomes small the elastic sublayer deminishes. 
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