Rheology of Drag Reducing Fluids by Aroon Shenoy

Author:Aroon Shenoy
Language: eng
Format: epub, pdf
ISBN: 9783030400453
Publisher: Springer International Publishing

(2.78)

For Newtonian fluids , it is clear (Fenter, 1959) that the expression for FN in the fully rough regime can be given exactly by

(2.79)

Combining Eqs. (2.78) and (2.79) gives

(2.80)

Combining Eqs. (2.76) and (2.80) gives the conventional Newtonian form for the velocity profile in the rough pipe s as

(2.81)

This is because in the fully rough regime all the drag reduction effectiveness of the additive is annulled by the pipe roughness, and hence, the velocity profile can be expected to be no different from the Newtonian case. In very rough pipes , it was found (White, 1967) that there was insignificant change in the frictional characteristics with drag reducing agents even at very large Reynolds numbers. Same conclusion was drawn (Brandt, McDonald, & Boyle, 1969) that drag reducers had little or no effect on flow in fully rough regimes, but they tended to delay the onset of this regime.

In the fully rough regime, though Eq. (2.81) would represent the velocity profile for drag reducing fluids, it again suffers from the limitation of not being able to predict the velocity gradient as zero at the centerline. An expression similar to Eq. (2.22) can be easily derived as follows. A modified form of Eq. (2.22) can be written as

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