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相关概念视频

Navier–Stokes Equations01:28

Navier–Stokes Equations

449
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...
449
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

154
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.
154
Steady, Laminar Flow in Circular Tubes01:23

Steady, Laminar Flow in Circular Tubes

172
Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is...
172
Couette Flow01:22

Couette Flow

233
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...
233
Velocity Potential01:20

Velocity Potential

358
In steady, incompressible flow through a long, straight pipe with a uniform cross-section, the flow in the central region (far from the pipe walls) is irrotational. This irrotational nature means that fluid particles do not rotate around their axes, and a scalar function called the velocity potential, represented by ϕ, can be used to describe their movement. In irrotational flows, the velocity field V is defined as the gradient of the velocity potential:
358
Newtonian Fluid: Problem Solving01:18

Newtonian Fluid: Problem Solving

207
Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
207

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相关实验视频

Updated: Jun 14, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K

通过Navier-Stokes/Allen-Cahn系统对粘性不压缩流体的经典两相流程进行近似分析.

Helmut Abels1, Julian Fischer2, Maximilian Moser2

  • 1Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany.

Archive for rational mechanics and analysis
|September 6, 2024
PubMed
概括

这项研究表明,纳维尔-斯托克斯/艾伦-卡恩系统汇聚到两相流体流动的利接口模型. 在特定的移动条件下,使用相对法提供错误估计.

科学领域:

  • 多相流动动力学 多相流动力学
  • 部分微分方程部分微分方程.
  • 流体力学的流体力学

背景情况:

  • 在粘性,不可压缩的流体中建模双相流动对于理解复杂的流体行为至关重要.
  • 艾伦-卡恩方程经常用于模拟接口,但它与利的接口模型的连接需要严格的分析.
  • 将分散接口模型 (如艾伦-卡恩) 与利接口模型 (如纳维尔-斯托克斯) 结合起来,是流体动力学的一个关键挑战.

研究的目的:

  • 为了确定纳维尔-斯托克斯/艾伦-卡恩系统与经典利接口模型的数学收.
  • 分析两个粘性,不可压缩的流体的两相流动,在一个有限的域内具有相同的粘度.
  • 为了推导出误差估计量化近似准确度.

主要方法:

  • 使用相对法来分析数学收.
  • 证明纳维尔-斯托克斯/艾伦-卡恩系统的解决方案与扰乱的两相流量问题保持接近.
  • 分析艾伦-卡恩移动性参数的行为,因为它倾向于以次临界方式为零.

主要成果:

  • 已经证明了纳维尔-斯托克斯/艾伦-卡恩系统的合,以实现双相流动的利接口模型.
  • 使用相对法获得的对收的误差估计.
  • 确定在Allen-Cahn移动性参数的特定亚临界条件下,收保持.

更多相关视频

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

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Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids
10:28

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids

Published on: January 3, 2014

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相关实验视频

Last Updated: Jun 14, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K
Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

8.7K
Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids
10:28

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids

Published on: January 3, 2014

13.6K

结论:

  • 纳维尔-斯托克斯/艾伦-卡恩系统在特定条件下准确地近似了两相流动的利接口模型.
  • 相对法对于在这种流体动力学模型中推导误差估计是有效的.
  • 这些发现为使用扩散接口模型模拟两相流程提供了严格的数学基础.