Upgrading of the modified Knudsen equation and its verification for calculating the gas flow rate through cylindrical tubes

The modified Knudsen equation was developed to calculate the gas flow rate through a cylindrical tube with arbitrary length-to-diameter ratio in any flow regime including molecular flow, viscous laminar flow, turbulent flow, critical flow, subcritical flow, and their intermediates in our laboratory. Here, it is upgraded for better agreement with literature data, and the upgraded version is compared with 83 literature sources including 31 gas flow equations to verify its reliability. For Kn > 10(-5), the modified Knudsen equation mostly agrees with the literature data to within 20%, except for orifice flows with p(d)/p(u) approximate to 1.