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

Die Couette-Strömung beschreibt die Fluidbewegung zwischen zwei parallelen Platten, von denen eine stationär ist und die andere sich mit konstanter Geschwindigkeit bewegt, wodurch eine stetige, laminare, schergetriebene Strömung entsteht.
Dieser Aufbau vereinfacht die Navier-Stokes-Gleichungen, die in dimensionsloser Form ausgedrückt werden können.
Ein dimensionsloser Parameter, der sich auf den Druckgradienten bezieht, definiert Schwankungen in den Strömungsprofilen der Couette.
Wenn es keinen Druckgradienten entlang der Strömungsrichtung gibt, wird dieser Parameter zu Null, was auf eine lineare Geschwindigkeitsvariation zwischen den beiden Platten hinweist.
Das Geschwindigkeitsprofil der Flüssigkeit zwischen den Platten ist linear und steigt von Null an der stationären Platte bis zur Geschwindigkeit der sich bewegenden Platte.
Die Couette-Strömung wird häufig verwendet, um das Verhalten von Flüssigkeiten in leicht belasteten Gleitlagern zu modellieren, wie z. B. in Wasserpumpen, bei denen eine dünne Schmiermittelschicht eine rotierende Welle innerhalb eines festen Gehäuses trennt.
Bei diesen leicht belasteten Lagern sind die Druckeinwirkungen minimal, so dass die Strömungseigenschaften denen der reinen Couette-Strömung sehr ähnlich sind.
Die Scherspannung und die Durchflussrate der Schmierschicht hängen von der Drehzahl der Welle und der Spaltweite zwischen Welle und Gehäuse ab.

couette-strömung

Couette Flow

Die Couette-Strömung stellt den Flüssigkeitsfluss zwischen zwei parallelen Platten dar, wobei eine Platte fixiert ist und sich die andere mit konstanter Geschwindigkeit bewegt. Diese Konfiguration ermöglicht eine vereinfachte Analyse mithilfe der Navier-Stokes-Gleichungen, die die Flüssigkeitsbewegung unter Bedingungen von Viskosität und Inkompressibilität regeln. Für die Couette-Strömung umfassen die Annahmen eine stetige, laminare, inkompressible Strömung mit einem Nulldruckgradienten in Strömungsrichtung. Dieser Strömungstyp ist hilfreich für das Verständnis von schergetriebenen Strömungen und ist für Anwendungen in Schmier- und Tiefbauszenarien wie Sedimenttransport und Erosion relevant.

Lassen Sie in einem Couette-Strömungsaufbau die x-Achse mit der Bewegungsrichtung der oberen Platte übereinstimmen, während die y-Achse senkrecht zu beiden Platten steht. Die Strömung ist gleichmäßig, laminar und voll entwickelt, ohne Variation in

Für die Couette-Strömung lautet die Geschwindigkeitsverteilungsgleichung:

<img alt="Equation 1" src="/files/ftp_upload/18064/18064_Equation_1.svg" style="text-align: center; height: 30px;">


Wobei:

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
 <li>U ist die konstante Geschwindigkeit der oberen Platte,</li>
 <li>b ist der Abstand zwischen den Platten,</li>
 <li>μ ist die dynamische Viskosität der Flüssigkeit.</li>
</ul>

In dimensionsloser Form erhalten wir durch Division beider Seiten durch U:

<img alt="Equation 2" src="/files/ftp_upload/18064/18064_Equation_2.svg" style="text-align: center; height: 30px;">


Wobei u/U die dimensionslose Geschwindigkeit darstellt und y/b den normalisierten Abstand von der stationären Platte. Um bestimmte Bedingungen zu analysieren, definieren wir den dimensionslosen Parameter P wie folgt:

<img alt="Equation 3" src="/files/ftp_upload/18064/18064_Equation_3.svg" style="text-align: center; height: 30px;">


Unter diesen Bedingungen wird P Null, wenn in x-Richtung kein Druckgradient (∂p/∂x=0) vorliegt, wodurch sich die Geschwindigkeitsgleichung auf Folgendes reduziert:

<img alt="Equation 4" src="/files/ftp_upload/18064/18064_Equation_4.svg" style="text-align: center; height: 26px;">

Dieses lineare Profil zeigt an, dass die Flüssigkeitsgeschwindigkeit linear von Null an der stationären Platte auf U an der beweglichen Platte ansteigt, was zu einer gleichmäßigen Schergeschwindigkeit über die Flüssigkeitsschicht hinweg führt.

Couette-Strömung

Die Couette-Strömung beschreibt die flüssige Bewegung zwischen zwei parallelen Platten, von denen eine stationär ist und die andere sich mit konstanter Geschwindigkeit bewegt, wodurch eine stetige, ...

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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

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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.

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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...

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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.

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Linear Shear Between Moving Plates

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