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

쿠엣 흐름은 하나는 고정되어 있고 다른 하나는 일정한 속도로 이동하여 안정적인 층류 전단 구동 흐름을 생성하는 두 개의 평행 판 사이의 유체 운동을 설명합니다.
이 설정은 무차원 형식으로 표현할 수 있는 Navier-Stokes 방정식을 단순화합니다.
압력 구배와 관련된 무차원 매개변수는 Couette 흐름 프로파일의 변화를 정의합니다.
흐름 방향을 따라 압력 구배가 없으면 이 매개변수는 0이 되어 두 플레이트 사이의 선형 속도 변화를 나타냅니다.
플레이트 사이의 유체 속도 프로파일은 선형이며 고정 플레이트의 0에서 움직이는 플레이트의 속도까지 증가합니다.
쿠엣 흐름은 일반적으로 워터 펌프와 같이 부하가 가벼운 저널 베어링에서 유체 거동을 모델링하는 데 사용되며, 얇은 윤활층이 고정된 하우징 내에서 회전축을 분리합니다.
이러한 경하중 베어링에서는 압력 효과가 최소화되므로 흐름 특성은 순수 Couette 흐름의 특성과 매우 유사합니다.
윤활층의 전단 응력과 유속은 샤프트의 회전 속도와 샤프트와 하우징 사이의 갭 폭에 따라 달라집니다.

쿠에트 유동

Couette Flow

쿠에트 유동은 한 판은 고정되어 있고 다른 판은 일정한 속도로 움직이는 두 평행 판 사이의 유체 흐름을 나타냅니다. 이 구성은 점도 및 비압축성 조건에서 유체 운동을 제어하는 ​​나비에-스토크스 방정식을 사용하여 단순화된 분석을 허용합니다. 쿠에트 유동의 경우 가정에는 유동 방향에 압력 기울기가 0인 안정적이고 층류이며 비압축성 유동이 포함됩니다. 이 유동 유형은 전단 구동 유동을 이해하는 데 유용하며 퇴적물 이동 및 침식과 같은 윤활 및 토목 공학 시나리오의 응용 프로그램과 관련이 있습니다.

쿠에트 유동 설정에서 x축은 상부 판의 이동 방향과 일치하고 y축은 두 판에 수직이 되도록 합니다. 흐름은 안정적이고 층류이며 완전히 발달되어 있으며,

쿠엩 흐름의 경우 속도 분포 방정식은 다음과 같습니다.

<img alt="Equation 1" src="/files/ftp_upload/18064/18064_Equation_1.svg" style="text-align: center; height: 30px;">

여기서:

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
 <li>U는 상부 판의 일정 속도,</li>
 <li>b는 판 사이의 거리,</li>
 <li>μ는 유체의 동적 점도입니다.</li>
</ul>

무차원 형태로 양변을 U로 나누면 다음과 같습니다.

<img alt="Equation 2" src="/files/ftp_upload/18064/18064_Equation_2.svg" style="text-align: center; height: 30px;">

여기서 u/U는 무차원 속도를 나타내고 y/b는 고정 판으로부터의 정규화된 거리를 나타냅니다. 특정 조건을 분석하기 위해 무차원 매개변수 P를 다음과 같이 정의합니다.

<img alt="Equation 3" src="/files/ftp_upload/18064/18064_Equation_3.svg" style="text-align: center; height: 30px;">

이러한 조건에서 x 방향으로 압력 기울기(∂p/∂x=0)가 없을 때 P는 0이 되어 속도 방정식을 다음과 같이 줄입니다.

<img alt="Equation 4" src="/files/ftp_upload/18064/18064_Equation_4.svg" style="text-align: center; height: 26px;">

이 선형 프로파일은 유체 속도가 고정 플레이트의 0에서 이동 플레이트의 U까지 선형적으로 증가하여 유체 층 전체에 균일한 전단 속도가 발생함을 나타냅니다.

Couette flow는 하나는 고정되어 있고 다른 하나는 일정한 속도로 이동하여 안정되고 ...

Education

교육

JoVE Core

Civil Engineering

토목공학

Unit 1

제1단원

Differential Analysis of Fluid Flow

유체 흐름의 미분 분석

KEY TERMS AND CONCEPTS

핵심 용어 및 개념

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 offers a foundational exploration of essential construction materials such as bricks, stones, steel, wood, and concrete, along with fluid mechanics topics like flow over immersed bodies, open channel flow, and dimensional modeling. It also covers key surveying concepts, including leveling, traverse adjustments, curve design, topographic mapping, and geospatial technologies (GPS & GIS). Science-in-action videos showcase laboratory research on materials, fluids, and surveying practices in real-world engineering systems.

civil engineering

Linear Shear Between Moving Plates

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