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相关概念视频

Euler's Equations of Motion01:28

Euler's Equations of Motion

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In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains...
422
Navier–Stokes Equations01:28

Navier–Stokes Equations

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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
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Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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Laminar and Turbulent Flow01:07

Laminar and Turbulent Flow

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Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the...
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Viscosity of Fluid01:19

Viscosity of Fluid

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Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
335
Couette Flow01:22

Couette Flow

203
Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
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相关实验视频

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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从线性博尔兹曼方程和粘度-毛细体平衡中获得严格的水力学.

Florian Kogelbauer1, Ilya Karlin1

  • 1Department of Mechanical and Process Engineering, <a href="https://ror.org/05a28rw58">ETH Zurich</a>, CH-8092 Zurich, Switzerland.

Physical review. E
|December 18, 2024
PubMed
概括

这项研究严格地从博尔兹曼运动方程中推导出精确的水力动力学方程,揭示了纯消散的修改,并将其应用于通道流现象.

科学领域:

  • 流体动力学 流体动力学
  • 统计力学就是统计力学.
  • 动力学理论 动力学理论

背景情况:

  • 从动力学理论中推导出准确的水力动力学方程是具有挑战性的.
  • 现有的模型往往缺乏严格的理由或范围有限.
  • 了解分散和非局部效应对于复杂的流体行为至关重要.

研究的目的:

  • 从线性博尔兹曼方程中严格推导出水力动力学变量的确切闭包.
  • 开发一种独特的,最优的相位空间在平衡点附近的减少方法.
  • 调查对水力动力学系统中改和消散的影响.

主要方法:

  • 光谱理论和自身向量属性的分析.
  • 对于相位空间缩小的慢变形体理论.
  • 在水力动力学上受制约的系统中,的改变.

主要成果:

  • 定义了一个独特的,最优的相位空间在平衡点附近的减少.
  • 建立了一个修改后的,确保在水力动力学分流体上纯净的消散.
  • 在道流动中使用Knudsen最小悖论来示例导出方程.

结论:

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  • 这项研究为从动力学理论中获得的水力动力学方程提供了严格的基础.
  • 这些发现提供了科尔特韦格理论的非局部变体,将粘度和毛细体联系起来.
  • 这种方法成功地解释了诸如克努森最小悖论之类的复杂现象.