The paper by Martin Knudsen investigates the flow of gases through narrow tubes, focusing on the deviations from Poiseuille's law when the mean free path of gas molecules is not negligible compared to the tube diameter. Knudsen builds on earlier work by Kundt, Warburg, and Christiansen, who found that Poiseuille's law does not hold accurately for very narrow tubes. Christiansen also noted that Poiseuille's law for parallel walls becomes invalid when the wall separation is very small, and it aligns with Graham's law of diffusion for gases through materials like artificial graphite. Knudsen's main goal is to determine how the adiabatic flow of gases depends on tube dimensions and gas properties, and to derive laws for the transition from flow dominated by internal friction (Poiseuille's law) to molecular flow. He introduces a new theoretical framework based on Maxwell's velocity distribution and the interaction between gas molecules and a solid wall, suggesting that molecules反弹的方向完全独立于它们撞击墙壁的方向。 Knudsen presents a formula for the gas flow rate through a tube, which is valid for tubes with a width much smaller than their length and the mean free path of gas molecules: \[ Q_t = \frac{1}{V_{q_1}} \frac{p_1 - p_2}{W} \] where \( Q_t \) is the gas flow rate, \( V_{q_1} \) is the product of volume and pressure at the tube walls, \( p_1 \) and \( p_2 \) are the pressures at the两端 of the tube, and \( W \) is the resistance of the tube: \[ W = \frac{3 \sqrt{\pi}}{8 \sqrt{2}} \int_{0}^{L} \frac{o}{A^2} dl \] This formula is derived from a theoretical consideration of the interaction between gas molecules and a solid wall, and it is validated by experiments using circular cylindrical tubes. The results show that the flow rate is significantly different from Poiseuille's law, especially at low pressures. Knudsen also investigates the effects of tube radius, gas type, and temperature on the flow rate. He finds that the flow rate is directly proportional to the cube root of the specific weight of the gas and inversely proportional to the square root of the absolute temperature. The experiments confirm the validity of the theoretical framework and provide insights into the behavior of gases under various conditions.The paper by Martin Knudsen investigates the flow of gases through narrow tubes, focusing on the deviations from Poiseuille's law when the mean free path of gas molecules is not negligible compared to the tube diameter. Knudsen builds on earlier work by Kundt, Warburg, and Christiansen, who found that Poiseuille's law does not hold accurately for very narrow tubes. Christiansen also noted that Poiseuille's law for parallel walls becomes invalid when the wall separation is very small, and it aligns with Graham's law of diffusion for gases through materials like artificial graphite. Knudsen's main goal is to determine how the adiabatic flow of gases depends on tube dimensions and gas properties, and to derive laws for the transition from flow dominated by internal friction (Poiseuille's law) to molecular flow. He introduces a new theoretical framework based on Maxwell's velocity distribution and the interaction between gas molecules and a solid wall, suggesting that molecules反弹的方向完全独立于它们撞击墙壁的方向。 Knudsen presents a formula for the gas flow rate through a tube, which is valid for tubes with a width much smaller than their length and the mean free path of gas molecules: \[ Q_t = \frac{1}{V_{q_1}} \frac{p_1 - p_2}{W} \] where \( Q_t \) is the gas flow rate, \( V_{q_1} \) is the product of volume and pressure at the tube walls, \( p_1 \) and \( p_2 \) are the pressures at the两端 of the tube, and \( W \) is the resistance of the tube: \[ W = \frac{3 \sqrt{\pi}}{8 \sqrt{2}} \int_{0}^{L} \frac{o}{A^2} dl \] This formula is derived from a theoretical consideration of the interaction between gas molecules and a solid wall, and it is validated by experiments using circular cylindrical tubes. The results show that the flow rate is significantly different from Poiseuille's law, especially at low pressures. Knudsen also investigates the effects of tube radius, gas type, and temperature on the flow rate. He finds that the flow rate is directly proportional to the cube root of the specific weight of the gas and inversely proportional to the square root of the absolute temperature. The experiments confirm the validity of the theoretical framework and provide insights into the behavior of gases under various conditions.