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A note on “critical roughness height” and “transitional roughness”

An unrigorous but plausible analysis suggests that the concept of a critical roughness height, below which roughness does not affect a turbulent wall flow, is erroneous. The Oseen approximation implies that the effect of roughness on the additive constant in the logarithmic law of the wall should vary as the square of the roughness Reynolds number (specifically the roughness height in “wall units”). This is an important point in determining whether surfaces used in experiments at high unit Reynolds number can be regarded as hydraulically smooth. Attention is also called to the qualitative difference between Nikuradse’s measurements of friction factor in pipe flow with uniform-size sand-grain roughness in the “transitional” range of Reynolds number and the data correlation in the Moody chart of 1944; the latter was derived from tests on miscellaneous real-life rough surfaces in the 1930s. Nearly all textbooks on elementary fluid dynamics present, but practically none discuss, this difference. Nikuradse’s m...