As mentioned in Section 2.2 and reviewed in Virk (1975), polymeric additives can greatly reduce the resistance in turbulent pipe flow. That is manifested by a decrease in f at a given Re. At the small concentrations used (typically tens to hundreds of ppm by weight), μ is very close to that of the solvent and non- Newtonian behavior such as shear thinning is not evident. Laminar flow is unaffected. In turbulent flow, decreases in f occur for 

The threshold shear stress

decreases with increasing polymer molecular weight, but is independent of polymer concentration and solvent viscosity. Once 

is exceeded, increases in the concentration or molecular weight of the additive lead to greater reductions in f. However, the “maximum drag reduction” appears to be insensitive to the identity and concentration of the polymer and is described by (Virk, 1975)

This is compared with the laminar result and the Prandtl–Kármán correlation in Fig. P2.7.

For the oil pipeline in Example 2.3-2, how much might the pressure drop be reduced by use of a polymeric additive?

Transcribed Image Text:

Tw τ Μ