Impact of neglecting the variations in the relative surface roughnesses of capillary tubes on the accuracy of a capillary tube model

Published by lahde on


Existing capillary tube models rely heavily on friction factor correlations, which enable the specification of the relative surface roughness. However, measuring the surface roughnesses of capillary tubes is a time consuming task, which requires specialized equipment. In this research we have developed a friction factor correlation, which does not require that the surface roughness is measured and has a comparable accuracy to existing correlations.


Capillary tube models frequently rely on friction factor correlations, which are functions of the Reynolds number, and the tube’s relative surface roughness. However, this study shows that explicitly correlating the friction factor with the relative surface roughness is unnecessary, at least when the latter is lower than 0.0025. To test this a correlation was fitted directly onto friction factor measurements obtained in an adiabatic flow of R600a, through nine capillary tubes from three manufacturers. The friction factor was correlated exclusively as a function of the Reynolds number, meaning that the impacts of the relative surface roughnesses on the friction factor were averaged, and included only implicitly. This correlation, and an existing correlation, which allows the specification of the relative surface roughness, were then implemented in a capillary tube model. The accuracy of the capillary tube model, using either the developed or existing correlation was then evaluated by comparing the results to experimental data. No significant decrease in the accuracy of the model was observed when the relative surface roughnesses, ranging from 0.0012 to 0.0025, were not individually specified for each capillary tube. To further verify this, the procedure was repeated on a larger database of friction factor and mass flow rate measurements, which also consisted of data from independent studies. Similar conclusions were drawn, as the average accuracy of the model differed only by 1 to 3% among different studies, and not always in favor of the correlation where the relative surface roughnesses could be specified.