By dimensional analysis treatment, we can found that
                                      (17)
The only difference between two expressions in Eq. (17) is that the term , which is known as the "relative roughness". In commercially available pipes, the roughness is not uniform; so it is correlated with pipe diameter and the contribution forms a significant value in friction factor calculation. From tests with commercial pipes, Moody gave the values for average pipe roughness listed in Table 1