Question: 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

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).

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