Poreh and Dtmant 
DISCUSSION 
Thomas T. Huang 
Naval Shtp Research and Development Center 
Bethesda, Maryland, U.S.A. 
The authors are to be congratulated on providing a most 
detailed velocity-profile model for the turbulent flows with drag re- 
duction. However, the empirical fundamental equations (equations 
(3) and (4) are applicable to poor drag reducers, for example guar 
gum, at certain concentration and shear ranges. It would be more 
appropriate to put down the limitations of these equations and to indi- 
cate that the results derived here are valid only within these limita- 
tions. I have three other comments of a minor nature. 
The maximum drag reduction asymptote stated in equation 
(3) and used to compare with the experimental result is not in good 
agreement with our experimentation. The Virk first formula agrees 
better with our data and if you use the Virk first formula (JFM 1967) 
there is very little difference between the Virk model and the present 
model, i.e. within the accuracy of experiments. 
Second, the optimal concentration to reach the maximum drag 
reduction is found by us to be a function of shear stress and thickness 
of boundary layer divided by kinematic viscosity. The effect of the 
scale does play an important role in this respect. Once drag reduc- 
tion reaches this maximum value the results arrived at here are no 
longer valid. This limitation is suggested to be stated in the paper. 
The present model does not offer any advantage for predic- 
ting drag reduction. Nevertheless, it may be more suitable for dif- 
fusion and heat transfer prediction, as authors stated. In this appli- 
cation, more definite experimental results would serve the field more 
than empirical calculation based on bold assumptions, 
1324 
