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🔬 努森数Knudsen Number Calculator
Kn = λ / L：分子平均自由程 λ 与特征长度 L 之比。Kn < 0.01 连续介质，0.01-0.1 滑移流，0.1-10 过渡区，> 10 自由分子流。本地处理。Kn = λ / L: mean free path λ over characteristic length L. Kn < 0.01 continuum, 0.01-0.1 slip, 0.1-10 transition, > 10 free-molecular. Processed locally.
使用说明与常见问题How-to & FAQ
「努森数」是什么？What is the Knudsen Number Calculator tool?
Kn = λ / L：分子平均自由程 λ 与特征长度 L 之比。Kn < 0.01 连续介质，0.01-0.1 滑移流，0.1-10 过渡区，> 10 自由分子流。本地处理。Kn = λ / L: mean free path λ over characteristic length L. Kn < 0.01 continuum, 0.01-0.1 slip, 0.1-10 transition, > 10 free-molecular. Processed locally.
如何使用「努森数」？How do I use the Knudsen Number Calculator tool?
填写平均自由程和特征长度，即可得到克努森数 Kn = λ ÷ L 以及所属的流动区域；不知道平均自由程时可留空，并填写温度、压力和分子直径来估算。结果会随输入实时更新。Enter the mean free path and the characteristic length to get the Knudsen number Kn = λ ÷ L and its flow regime; if you don't know the mean free path, leave it blank and give the temperature, pressure and molecular diameter to estimate it. The result updates as you type.
真空中？In vacuum?
低压下 λ 变大，微通道中即使常压也可能进入滑移流。At low pressure λ grows; even at ambient pressure microchannels can enter slip flow.
能举个计算实例吗？Can you show a worked example?
例如在「努森数」中填 特征长度 m = 1e-6，温度 K（估算用） = 300，压力 Pa（估算用） = 101325，分子直径 m（估算用） = 3.7e-10，结果区显示：平均自由程 λ：6.72078×10⁻⁸ m；努森数 Kn：0.0672078；流态：滑移流For example, entering Characteristic length m = 1e-6, Temperature K (for estimate) = 300, Pressure Pa (for estimate) = 101325, Molecular diameter m (for estimate) = 3.7e-10 in the Knudsen Number Calculator gives: Mean free path λ: 6.72078×10⁻⁸ m; Knudsen number Kn: 0.0672078; Regime: slip flow
哪些输入会被检查？Which inputs are validated?
「努森数」会检查这些输入——「平均自由程 m（或留空按气体估算）」：可留空；「特征长度 m」、「温度 K（估算用）」、「压力 Pa（估算用）」、「分子直径 m（估算用）」：必须填写，须大于 0；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Knudsen Number Calculator checks its inputs — "Mean free path m (or blank to estimate)": optional; "Characteristic length m", "Temperature K (for estimate)", "Pressure Pa (for estimate)", "Molecular diameter m (for estimate)": required, must be greater than 0; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「努森数」的设置：「平均自由程 m（或留空按气体估算）」可留空；「特征长度 m」默认 1e-6；「温度 K（估算用）」默认 300；「压力 Pa（估算用）」默认 101325；「分子直径 m（估算用）」默认 3.7e-10。每次生成结果都按当前设置处理。Settings in the Knudsen Number Calculator — "Mean free path m (or blank to estimate)" optional; "Characteristic length m" default 1e-6; "Temperature K (for estimate)" default 300; "Pressure Pa (for estimate)" default 101325; "Molecular diameter m (for estimate)" default 3.7e-10. The result always uses the current settings.
计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?
「努森数」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Knudsen Number Calculator uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.
「努森数」免费吗？需要注册吗？Is the Knudsen Number Calculator free? Do I need an account?
「努森数」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Knudsen Number Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.