The Reynolds number ([latex]\text{Re}[/latex]) is a dimensionless quantity in 流体力学 雷诺数用于预测流动模式,它表示惯性力与粘性力的比值。低雷诺数表征平滑有序的层流,而高雷诺数则表明混乱、充满涡流的湍流。雷诺数对于确定流体的动力学行为和进行尺度实验至关重要。

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The Reynolds number ([latex]\text{Re}[/latex]) is a dimensionless quantity in 流体力学 雷诺数用于预测流动模式,它表示惯性力与粘性力的比值。低雷诺数表征平滑有序的层流,而高雷诺数则表明混乱、充满涡流的湍流。雷诺数对于确定流体的动力学行为和进行尺度实验至关重要。
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 viscosity, and [latex]\nu[/latex] is the kinematic 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.
层流到湍流的转变并非突变,通常发生在一定的雷诺数范围内。对于管道内的流动,这种转变通常发生在雷诺数约为 2300-4000 的范围内。这种转变具有极其重要的实际意义;例如,管道内的湍流比层流会产生显著更高的摩擦损失,需要更大的泵送功率。
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。
雷诺数
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