Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren

Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren

1875 | Martin Knudsen
The text discusses the molecular and internal friction flows of gases through tubes, focusing on the behavior of gas molecules under different conditions. It begins by noting that Poiseuille's law applies when the mean free path of gas molecules is much smaller than the tube diameter. However, deviations from this law occur when the tube is narrow enough that the mean free path is not negligible compared to the diameter. These deviations led to the development of theories regarding the movement of gases near solid walls, with Christiansen showing that Poiseuille's law is modified for very narrow channels and that the flow rate aligns with Graham's law of diffusion. The study presents a new theory based on Maxwell's distribution of molecular speeds and the interaction between gas molecules and solid walls. It concludes that gas flow through narrow tubes is governed by a different law than Poiseuille's, which accounts for molecular motion rather than viscous flow. The derived formula for the flow rate $ Q_t $ is given by $ Q_t = \frac{1}{\sqrt{\rho_1}} \frac{p_1 - p_2}{W} $, where $ \rho_1 $ is the specific weight of the gas, $ p_1 $ and $ p_2 $ are the pressures at the ends of the tube, and $ W $ is the resistance of the tube, dependent on its dimensions. The text also describes experimental setups and measurements using glass tubes and McLeod gauges to determine the flow rates of various gases under different pressures and temperatures. The results show that the flow rate depends on the tube dimensions, the gas type, and the temperature. The experiments confirm that the derived formula for molecular flow is valid, and that the flow rate is inversely proportional to the square root of the gas's specific weight. The study further explores the transition between molecular flow and viscous flow, showing that a complex law governs the flow when the mean free path is neither very large nor very small compared to the tube dimensions. The results indicate that the flow rate reaches a minimum when the mean free path is about five times the tube radius, and increases again at higher pressures. The experiments also validate Maxwell's speed distribution law and the theory of molecular interactions with solid walls, demonstrating the applicability of the derived formulas for low-pressure gas flows. The findings contribute to understanding gas flow in narrow channels and have implications for the measurement of small pressure differences and the study of dissociation phenomena.The text discusses the molecular and internal friction flows of gases through tubes, focusing on the behavior of gas molecules under different conditions. It begins by noting that Poiseuille's law applies when the mean free path of gas molecules is much smaller than the tube diameter. However, deviations from this law occur when the tube is narrow enough that the mean free path is not negligible compared to the diameter. These deviations led to the development of theories regarding the movement of gases near solid walls, with Christiansen showing that Poiseuille's law is modified for very narrow channels and that the flow rate aligns with Graham's law of diffusion. The study presents a new theory based on Maxwell's distribution of molecular speeds and the interaction between gas molecules and solid walls. It concludes that gas flow through narrow tubes is governed by a different law than Poiseuille's, which accounts for molecular motion rather than viscous flow. The derived formula for the flow rate $ Q_t $ is given by $ Q_t = \frac{1}{\sqrt{\rho_1}} \frac{p_1 - p_2}{W} $, where $ \rho_1 $ is the specific weight of the gas, $ p_1 $ and $ p_2 $ are the pressures at the ends of the tube, and $ W $ is the resistance of the tube, dependent on its dimensions. The text also describes experimental setups and measurements using glass tubes and McLeod gauges to determine the flow rates of various gases under different pressures and temperatures. The results show that the flow rate depends on the tube dimensions, the gas type, and the temperature. The experiments confirm that the derived formula for molecular flow is valid, and that the flow rate is inversely proportional to the square root of the gas's specific weight. The study further explores the transition between molecular flow and viscous flow, showing that a complex law governs the flow when the mean free path is neither very large nor very small compared to the tube dimensions. The results indicate that the flow rate reaches a minimum when the mean free path is about five times the tube radius, and increases again at higher pressures. The experiments also validate Maxwell's speed distribution law and the theory of molecular interactions with solid walls, demonstrating the applicability of the derived formulas for low-pressure gas flows. The findings contribute to understanding gas flow in narrow channels and have implications for the measurement of small pressure differences and the study of dissociation phenomena.
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[slides] Die Gesetze der Molekularstrmung und der inneren Reibungsstrmung der Gase durch Rhren | StudySpace