2.0 Drag reduction in curved
pipes
Virk [28] published an extensive
review on drag reduction in straight pipes. The paper highlighted some
important aspects of drag reduction such as mechanism of polymer drag
reduction, turbulence structure and velocity profile. The work also
pioneered the concepts of maximum drag reduction (MDR) and drag
reduction envelop. The Virk’s envelop for polymer drag reduction in
straight pipes is shown in Fig. 1 on the Prandtl-Karman coordinates.
Eqs. (6) – (8) give the equations for laminar flow, turbulent flow and
maximum drag reduction asymptote. The maximum drag reduction law holds
irrespective of polymer specie used, its concentration or molecular
weight [29].
\(\frac{1}{\sqrt[f]{}}=\frac{N_{\text{Re}}\sqrt[f]{}}{16}\) (6)
\(\frac{1}{\sqrt[f]{}}=4N_{\text{Re}}\sqrt[f]{}\ -0.4\) (7)
\(\frac{1}{\sqrt[f]{}}=19N_{\text{Re}}\sqrt[f]{}\ -3.24\) (8)