“…see Nikuradse (1933), Perry, Schofield & Joubert (1969), Perry, Lim & Henbest (1987), Schlichting (1955), Ligrani & Moffat (1986), Jimenez (2004), Shockling, Allen & Smits (2006) and Schultz & Flack (2007). These studies have shown that surface roughness has a direct effect on the inner region of the Luker et al (2000) M = 2.7, Square roughness, Latin & Bowersox (2000) M = 2.7, 2D Bar roughness, Latin & Bowersox (2000) M = 0, Smooth, Klebanoff (1954) law of the wall and is often described by the single roughness Reynolds number parameter. Nikuradse (1933) demonstrated that for low-speed flows, sand-grain generated roughness increased the velocity defect and skin friction, and shifted the velocity law of the wall plot downward.…”