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雷诺数

1883

Osborne Reynolds

The Reynolds number ([latex]\text{Re}[/latex]) is a dimensionless quantity in fluid 力学 used to predict flow patterns by representing the ratio of inertial forces to viscous forces. Low Reynolds numbers characterize smooth, orderly laminar flow, while high Reynolds numbers indicate chaotic, eddy-filled turbulent flow. It is crucial for determining the dynamic behavior of a fluid and for scaling experiments.

The Reynolds number is defined as [latex]\text{Re} = \frac{\rho u L}{\mu} = \frac{u L}{\nu}[/latex], where [latex]\rho[/latex] is the fluid density, [latex]u[/latex] is a characteristic velocity, [latex]L[/latex] is a characteristic linear dimension, [latex]\mu[/latex] is the dynamic 粘度, and [latex]\nu[/latex] is the 运动学 viscosity. Inertial forces are related to the momentum of the fluid, which tend to cause fluid motion to persist, while viscous forces are frictional forces that tend to resist this motion and smooth out disturbances. When viscous forces dominate (low [latex]\text{Re}[/latex]), any perturbations in the flow are damped out, resulting in a smooth, layered laminar flow. Conversely, when inertial forces dominate (high [latex]\text{Re}[/latex]), small disturbances can grow and evolve into chaotic eddies and vortices, leading to turbulence.

The transition from laminar to turbulent flow is not abrupt but typically occurs over a range of Reynolds numbers. For flow in a pipe, this transition is generally observed around [latex]\text{Re} \approx 2300-4000[/latex]. This transition is of immense practical importance; for example, turbulent flow in a pipe causes significantly higher frictional losses and requires more pumping power than laminar flow.

雷诺数最有力的应用之一是动态相似原理。如果两个几何相似的流动情况具有相同的雷诺数（以及其他相关的无量纲数），则它们的流动模式在动态上也将相似。这使得工程师能够在风洞中测试飞机的小比例模型，并通过匹配雷诺数，获得准确预测全尺寸飞机气动力的结果。