57:020 Fluid Mechanics
15
Analytical Fluid Dynamics
•Example: turbulent flow in rough pipe
2001_August_a4_f3
Three regimes of flow depending on k+ 
1.K+<5, hydraulically smooth (no effect of roughness)
2.5 < K+< 70, transitional roughness (Re dependent)
3.K+> 70, fully rough (independent Re)
Both laminar sublayer and overlap layer
are affected by roughness
Inner layer:
•
Outer layer: unaffected
•
Overlap layer:
Friction factor:
For 3, using EFD data to adjust constants:
constant