The paradoxical nature of pulmonary pressure-flow relationships

Most equations proposed to describe pulmonary pressure-flow relationships are inadequate because the "constants" that contain the airway geometry are not, in fact, constant but vary as the distribution of Reynold's number Re varies with flow or gas density. However, even when the normalized pressure drop is plotted against Re (Moody diagram), different relationships are found for different gas mixtures. Thus the normalized pressure drop is a function of one or more variables in addition to Re. As long as this variable or variables remain unknown, the pulmonary pressure-flow relationships will remain paradoxical.