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雷諾數計算器
根據流速或流量計算雷諾數。提供層流/過渡/湍流的視覺指示器。入口長度計算與常見流體預設值。
結果
雷諾數
雷諾數是流動流體中慣性力與黏滯力之比：
- v — 流速 (m/s)
- D — 管道內徑 (m)
- ν — 運動黏度 (m²/s)；1 cSt = 10⁻⁶ m²/s
- ρ — 流體密度 (kg/m³)
- μ — 動力黏度 (Pa·s)
流動狀態閾值
| 雷諾數範圍 | 流態 | 特性 |
|---|---|---|
| Re < 2,300 | 層流 | 平滑、有序的層流；摩擦係數 f = 64/Re；可預測 |
| 2,300 – 4,000 | 過渡配合 | 不穩定；間歇性湍流；設計時應避免此範圍 |
| Re > 4,000 | 湍流 | 混亂；摩擦較高；使用 Colebrook-White 公式計算 f |
水力入口長度
從管入口到流速分佈完全發展所需的距離：
常見流體黏度
| 流體 | 溫度 | ν (cSt) | ρ (kg/m³) |
|---|---|---|---|
| 水 | 20°C | 1.004 | 998 |
| 水 | 40°C | 0.658 | 992 |
| 水 | 80°C | 0.365 | 972 |
| 液壓油 ISO VG 32 | 40°C | 32 | 870 |
| 液壓油 ISO VG 46 | 40°C | 46 | 870 |
| 液壓油 ISO VG 68 | 40°C | 68 | 880 |
| 空氣 | 20°C, 1 atm | 15.6 | 1.204 |
| 引擎油 SAE 30 | 40°C | 100 | 880 |
實務範例
已知： v = 2 m/s, D = 25 mm, 40°C 時的 ISO VG 32 液壓油 (ν = 32 cSt)
Re = 2 × 0.025 / (32 × 10⁻⁶) = 1,563
流動狀態： 層流 (Re < 2300)
入口段長度：Le = 0.06 × 1563 × 0.025 = 2.34 m
Re = 2300 時的臨界流速：v_crit = 2300 × 32 × 10⁻⁶ / 0.025 = 2.94 m/s
💡 提示： 在油液（ν = 30–100 cSt）的液壓系統中，由於黏度高，流動幾乎總是層流。水系統通常為紊流，因為 ν ≈ 1 cSt。
The Reynolds number Re = vD/ν is a dimensionless number that compares inertial forces to viscous forces in a flowing fluid. It predicts whether flow will be laminar (smooth) or turbulent (chaotic).
Named after Osborne Reynolds who demonstrated the transition in his famous 1883 experiment using dye in a glass tube.
For pipe flow, the critical thresholds are:
- Re < 2,300: Laminar — fluid moves in smooth parallel layers
- 2,300 – 4,000: Transition — flow is unstable, may switch between laminar and turbulent
- Re > 4,000: Turbulent — chaotic mixing, eddies, higher energy loss
These thresholds are for circular pipes. For open channels and other geometries, different critical values apply.
Kinematic viscosity ν = μ/ρ, where μ is dynamic viscosity and ρ is density.
Units: m²/s or cSt (centistokes). 1 cSt = 10⁻⁶ m²/s.
Common values: water at 20°C ≈ 1 cSt; hydraulic oil VG 32 at 40°C ≈ 32 cSt; air at 20°C ≈ 15.6 cSt (much higher than water due to low density despite low dynamic viscosity).
When fluid enters a pipe, the velocity profile is initially flat (uniform). As viscous effects propagate from the wall, the profile gradually develops into the fully-developed shape (parabolic for laminar).
The entry length is the distance needed:
- Laminar: Le ≈ 0.06 × Re × D (can be very long at high Re)
- Turbulent: Le ≈ 4.4 × Re1/6 × D (relatively short, 10–60 diameters)
Temperature strongly affects viscosity, especially for oils. Hydraulic oil viscosity drops approximately 50% for every 20°C increase.
Example: ISO VG 46 oil is ~46 cSt at 40°C but ~200 cSt at 0°C and ~15 cSt at 80°C. This dramatically changes the Reynolds number — cold-start conditions may have very different flow regimes than operating temperature.
Water viscosity changes less dramatically: ~1.8 cSt at 0°C, ~1 cSt at 20°C, ~0.3 cSt at 80°C.
本頁所述的操作流程由 Vibromera 團隊使用 Balanset-1A（一款用於現場轉子平衡的便攜式雙通道動平衡儀及振動分析儀）開發並經過實地測試。
專業現場動平衡校正儀器與軟體。已在 50 多個國家使用。
Nikolai Shelkovenko
Nikolai Shelkovenko是一名振動分析工程師，也是Vibromera的創辦人兼執行長。 15年多來，他一直在現場——而非在試驗台上——為旋轉設備進行動平衡校正：粉碎機、工業風機、破碎機、離心機、軸與主軸。正是這些實際工作催生了Balanset系列儀器——它們被設計為一種專業人員可以隨身攜帶到機器旁、在現場獨立使用的工具，而非實驗室設備。 Vibromera成立於2017年，自2023年起總部設於葡萄牙波爾圖。Balanset系列產品的研發、組裝與支援均在此完成。旗艦產品是Balanset-1A，一款用於單平面及雙平面動平衡校正與振動診斷的可攜式分析儀。 Nikolai親自參與客戶支援工作，處理各種棘手的動平衡校正案例，並參與軟體開發。他以任何語言為全球客戶提供服務。
