It is clear by comparing Figs. 6.12b and 6.13 that the effects of sand roughness and commercial (manufactured) roughness are not quite the same. Take the special case of commercial roughness ratio ε /d = 0.001 in Fig. 6.13, and replot in the form of the wall law shift ΔB (Fig. 6.12a) versus the logarithm of ε+ = ε u∗/ν. Compare your plot with Eq. (6.45).