Experimental Investigation Into the Relationship Between the Roughness Height in Use With Nikuradse or Colebrook Roughness Functions and the Internal Wall Roughness Profile for Commercial Steel Pipes

The relationships between the sand grain roughness height (k_s) in use with Nikuradse or Colebrook correlations for the roughness function (RF) and the internal pipe wall roughness element described by the root-mean-square (RMS) of the roughness profile (R_q) for turbulent flow in pipes are experimentally examined. Flow tests were conducted on a total of 13 commercial steel pipes of two sizes: 168.3 mm and 114.3 mm outer diameter (OD). The aim was to provide further insight into relationship between k_s and R_q, for use with either RF correlations. The tests were conducted on high-pressure pipeline quality natural gas in the range of Reynolds number (based on pipe internal diameter) of 9 × 10⁶–16 × 10⁶. For commercial carbon steel pipes, the relationship between k_s and R_q was found in the form $ks=1.306 Rq+0.078 Rq2$ and $ks=2.294 Rq$ (both k_s and R_q in μm), for use with Colebrook and Nikuradse RF correlations, respectively. These correlations cover a wide range of R_q from 2.7 μm to 12.5 μm which is typically found in commercial carbon steel pipes. For stainless steel (SS) pipes, preliminary results indicate that other surface roughness profile parameters need to be employed to better define the values of k_s for these types of commercial steel pipes.