Name: linear shear between moving plates
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 22 s
Channel: JoVE

库埃特流动描述的是两平行板之间的流体运动，其中一块板静止不动，另一块板以恒定速度运动，从而形成一种稳定、层流的剪切驱动流动。
该装置简化了纳维-斯托克斯方程，这些方程可以表示为无量纲形式。
一个与压力梯度相关的无量纲参数定义了库爱特流（Couette flow）剖面的变化。
当流动方向上无压力梯度时，该参数变为零，表明两平板之间的速度呈线性变化。
两板之间的流体速度分布呈线性，从静止板处的零速度增加到运动板的速度。
库爱特流常用于模拟轻载滑动轴承中的流体行为，例如水泵中的轴承，其中一层薄薄的润滑剂将旋转轴与固定的轴承座隔开。
在这些轻载轴承中，压力效应微乎其微，因此流动特性与纯库爱特流非常相似。
润滑层的剪切应力和流量取决于轴的转速以及轴与外壳之间的间隙宽度。

库埃特流

Couette Flow

库埃特流表示两个平行板之间的流体流动，其中一个板固定，另一个板以恒定速度移动。这允许简化使用 Navier-Stokes 方程进行分析，该方程描述粘度和不可压缩条件下的流体运动。对于库埃特流，假设为稳定、层流、不可压缩的流动，流动方向上的压力梯度为零。这种流动类型有利于理解剪切驱动流动，并且与润滑和土木工程场景中的应用（例如沉积物输送和侵蚀）相关。 在库埃特流中，令 x 轴与上板的移动方向对齐，而 y 轴垂直于两个板。流动是稳定的、层流的、充分发展的，没有变化 对于库埃特流，速度分布方程由以下公式给出： <img alt="Equation 1" src="/files/ftp_upload/18064/18064_Equation_1.svg" style="text-align: center; height: 30px;"> 其中： <ol style="list-style-type: circle;"> <li>U 是上板的恒定速度，</li> <li>b 是板之间的距离，</li> <li>μ 是流体的动态粘度。</li> </ol> 以无量纲形式，将两边除以 U，我们得到： <img alt="Equation 2" src="/files/ftp_upload/18064/18064_Equation_2.svg" style="text-align: center; height: 30px;"> 其中 u/U 表示无量纲速度，y/b 表示与固定板的标准化距离。为了分析特定条件，我们将无量纲参数 P 定义为： <img alt="Equation 3" src="/files/ftp_upload/18064/18064_Equation_3.svg" style="text-align: center; height: 30px;"> 在这些条件下，当 x 方向没有压力梯度（∂p/∂x=0）时，P 变为零，从而将速度方程简化为： <img alt="Equation 4" src="/files/ftp_upload/18064/18064_Equation_4.svg" style="text-align: center; height: 26px;"> 此线性曲线表明流体速度从静止板的零线性增加到移动板的 U，从而导致流体层的剪切速率均匀。

库埃特流动描述了两种平行板之间的流体运动，其中一块板静止，另一块以恒定速度移动，从而形成稳定、...

Education

教育

JoVE Core

Civil Engineering

土木工程

Unit 1

第一单元

Differential Analysis of Fluid Flow

流体流动微分分析

KEY TERMS AND CONCEPTS

关键术语与概念

linear shear between moving plates

Linear shear between moving plates describes fluid motion in a simple channel with two parallel plates. One plate stays fixed, and the other moves at a constant speed. This setup helps show how viscosity and incompressible flow shape fluid motion under the Navier-Stokes equations.

The model uses a steady, laminar, incompressible flow with no pressure gradient in the flow direction. The x-axis points along the moving direction of the upper plate, and the y-axis is perpendicular to both plates. These assumptions make the flow fully developed and easier to analyze.

For this case, the velocity changes with distance from the stationary plate. The upper plate speed is U, the plate spacing is b, and the fluid’s dynamic viscosity is μ. In dimensionless form, the velocity is written as u/U, and the position is written as y/b.

A dimensionless parameter P is used to describe pressure effects. When there is no pressure gradient in the x-direction, P becomes zero because ∂p/∂x = 0. The velocity equation then reduces to a straight line, so the fluid speed rises from zero at the fixed plate to U at the moving plate.

This linear profile creates a uniform shear rate across the fluid layer. Shear-driven flow like this is useful for understanding lubrication and civil engineering problems. It also helps explain processes such as sediment transport and erosion.

Linear Shear Between Moving Plates

euler&#39;s equations of motion

Pressure and Velocity in Inviscid Flow

Pressure and velocity in inviscid flow are linked by Euler's equations of motion. In fluid mechanics, viscosity creates shear stress, which is a force that acts along a surface. For low-viscosity fluids like water, these shear stresses are very small. That lets the fluid be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent. Only normal stresses remain, and these act perpendicular to a fluid element. Pressure is the negative of the normal stress. It stays the...

stream function

Stream Function for Incompressible Flow

The stream function helps describe two-dimensional incompressible flow. In this type of flow, the continuity equation keeps mass conserved. That means fluid entering a region must be balanced by fluid leaving it. For incompressible flow, the density stays constant. The continuity requirement then becomes a zero-divergence condition for the velocity field. In two dimensions, the horizontal and vertical velocity components are usually written as u and v. A stream function, written as ψ, is used...

irrotational flow

Irrotational Flow Near Boundaries

Irrotational flow is fluid motion in which particles do not spin around their own axes. It has zero vorticity, which means the curl of the velocity field is zero. That condition places limits on the velocity gradients in the flow. A simple example is uniform flow. In this case, the velocity u stays constant, while v and w are both zero. This satisfies the irrotational conditions and gives a basic model of non-rotating flow. When a solid object is added, irrotational flow usually remains only...

velocity potential

Velocity Potential in Pipe Flow

Velocity potential in pipe flow describes the motion of fluid in the central region of a long, straight pipe with a uniform cross-section. In this region, the flow is steady, incompressible, and irrotational. Irrotational means the fluid particles do not spin around their own axes. A scalar function called the velocity potential, written as φ, is used to describe this motion. The velocity field V is defined as the gradient of φ. Because the curl of a gradient is always zero, this form of V...

plane potential flows

Plane Potential Flow Patterns and Models

Plane potential flows describe fluid motion using simple flow patterns and models. They assume the fluid is irrotational and incompressible. These assumptions let the flow be written with a velocity potential function, φ, which gives the flow speed in a direction, and a stream function, ψ, which shows the flow path. Both are governed by Laplace's equation and are useful for estimating flow patterns, velocity distributions, and pressure fields around hydraulic structures. Uniform flow is the...

navier&#8211;stokes equations

Fluid Stress and Flow Equations

Fluid stress and flow equations describe how incompressible Newtonian fluids move under pressure, shear, and gravity. In these fluids, density stays constant, and stress changes linearly with the rate of deformation. The main stress types are normal stress and shear stress. Normal stress depends on pressure acting on the fluid and on deformation rate in specific directions. Shear stress acts along the surface of a fluid layer. It shows how neighboring layers slide past one another, so velocity...

steady, laminar flow between parallel plates

steady-laminar-flow-between-parallel-plates

Laminar Flow Profile Between Parallel Plates

Laminar flow between parallel plates shows how fluid moves through a narrow, flat channel. This model helps describe flow in water conveyance and drainage systems, where the space is limited and the motion stays orderly. It is also useful for analyzing flow in rectangular channels used in many engineering settings. The flow is studied with the Navier-Stokes equations, which govern fluid motion. These equations are often difficult to solve because they are nonlinear. In this case, the problem...

couette flow

Linear shear between moving plates describes fluid motion in a simple channel with two parallel plates. One plate stays fixed, and the other moves at a constant speed. This setup helps show how viscosity and incompressible flow shape fluid motion under the Navier-Stokes equations. The model uses a steady, laminar, incompressible flow with no pressure gradient in the flow direction. The x-axis points along the moving direction of the upper plate, and the y-axis is perpendicular to both plates.

steady, laminar flow in circular tubes

Parabolic Flow in Circular Tubes

Parabolic flow in circular tubes describes the steady, incompressible motion of a viscous fluid through a tube with a constant radius. This Hagen-Poiseuille flow is a classic example of laminar flow. It is often used to study fluid transport in narrow channels, including capillaries. Cylindrical coordinates are used to describe the tube. The radial direction is r, the angular direction is θ, and the axial direction is z. In this flow, the velocity is purely axial. That means the fluid moves...

design example: flow of oil through circular pipes

design-example-flow-of-oil-through-circular-pipes

Pressure Drop in Oil Pipe Design

Pressure drop in oil pipe design depends on pipe size, oil properties, and the flow rate needed through a circular pipe. For steady, incompressible, laminar flow, Hagen-Poiseuille's law gives an exact solution from the Navier-Stokes equations. It is used to find the pressure difference needed to keep oil moving through a pipeline section. The pressure drop equation uses the oil's dynamic viscosity, the pipeline length, the desired volumetric flow rate, and the pipe's inner radius. This...

key terms and concepts

Learn how fluid moves between two parallel plates when one plate is fixed and the other moves. See the linear velocity profile, shear rate, and key assumptions.

Linear Shear Between Moving Plates | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Linear Shear Between Moving Plates

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