In Discovery AIM, the formulas proposed by Cebeci and Bradshaw based on Nikuradse’s data are adopted to compute the wall roughness effect. (ref: T. Cebeci and P. Bradshaw. Momentum Transfer in Boundary Layers. Hemisphere Publishing Corporation, New York. 1977.)
The inputs required here are Roughness Height and Roughness Constant that helps in computing the roughness function which ultimately quantifies the downward shift (deltaB in image attached below) of logarithmic mean velocity distribution near the rough walls.
Roughness Height: The default roughness height is zero, which corresponds to smooth walls. For the roughness to take effect, a non zero value must be specified. For a uniform sand-grain roughness, the height of the sand-grain can simply be taken as roughness height . For a non-uniform sand-grain, however, the mean diameter would be a more meaningful roughness height. In case the distribution data is not available but Ra (surface Roughness) value is known, Roughness height is calculated as:
Roughness Height = 2*Ra.
Roughness constant: Choosing a proper roughness constant is again dependent on the type of distribution and has experimental evidence. The default roughness constant (0.5) was determined so that, it reproduces Nikuradse’s resistance data for pipes roughened with tightly-packed, uniform sand-grain roughness. One needs to adjust the roughness constant when the roughness to be modeled departs much from uniform sand-grain.For instance, there is some experimental evidence that, for non-uniform sand-grains, ribs, and wire-mesh roughness, a higher value (0.5-1) is more appropriate. Unfortunately, a clear guideline for choosing this constant for arbitrary types of roughness is not available.It is an empirical constant that can only be computed experimentally and there is no equation for calculating this value.
To summarize, roughness height is calculated based on the grain size distribution of the wall and as long as the distribution is uniform, a roughness constant of 0.5 is experimentally observed to be a good input value. Any deviation of grain structure to non uniform, would require to use roughness constant = 0.5-1 but there are no guidelines/formula available for choosing the most appropriate value and it remains an empirical constant.
With the calculation approach of Discovery AIM known, I hope I was able to answer your question.
Thanks & Regards,