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

Couette flow describes fluid motion between two parallel plates where one is stationary, and the other moves with constant speed, creating a steady, laminar shear-driven flow.
This setup simplifies the Navier-Stokes equations, which can be expressed in a dimensionless form.
A dimensionless parameter, related to the pressure gradient defines variations in Couette flow profiles.
When there is no pressure gradient along the flow direction, this parameter becomes zero, indicating a linear velocity variation between the two plates.
The fluid velocity profile between the plates is linear, increasing from zero at the stationary plate to the moving plate&#39;s speed.
Couette flow is commonly used to model fluid behavior in lightly loaded journal bearings, such as those in water pumps, where a thin layer of lubricant separates a rotating shaft within a fixed housing.
In these lightly loaded bearings, pressure effects are minimal, so the flow characteristics closely resemble those of pure Couette flow.
The lubricant layer&#39;s shear stress and flow rate depend on the shaft&#39;s rotational speed and the gap width between the shaft and housing.

couette-stroming

Couette Flow

Couette-stroming vertegenwoordigt de stroming van een vloeistof tussen twee parallelle platen, waarbij de ene plaat vastzit en de andere met een constante snelheid beweegt. Deze configuratie maakt een vereenvoudigde analyse mogelijk met behulp van de Navier-Stokes-vergelijkingen, die de vloeistofbeweging bepalen onder omstandigheden van viscositeit en onsamendrukbaarheid. Voor Couette-stroming omvatten de aannames een stabiele, laminaire, onsamendrukbare stroming met een nul-drukgradiënt in de stromingsrichting. Dit type stroming is nuttig voor het begrijpen van door schuifkracht aangestuurde stromingen en is relevant voor toepassingen in smeer- en civiele techniekscenario's zoals sedimenttransport en erosie. In een Couette-stromingsopstelling laat men de x-as uitlijnen met de bewegingsrichting van de bovenste plaat, terwijl de y-as loodrecht staat op beide platen. De stroming is stabiel, laminair en volledig ontwikkeld, zonder variatie in de Voor Couette-stroming wordt de snelheidsverdelingsvergelijking gegeven door: <img alt="Equation 1" src="/files/ftp_upload/18064/18064_Equation_1.svg" style="text-align: center; height: 30px;"> Waarbij: <ol style="list-style-type: circle;"> <li>U de constante snelheid van de bovenste plaat is,</li> <li>b de afstand tussen de platen is,</li> <li>μ de dynamische viscositeit van de vloeistof is.</li> </ol> In dimensieloze vorm, door beide zijden door U te delen, krijgen we: <img alt="Equation 2" src="/files/ftp_upload/18064/18064_Equation_2.svg" style="text-align: center; height: 30px;"> Waarbij u/U de dimensieloze snelheid voorstelt en y/b de genormaliseerde afstand vanaf de stationaire plaat voorstelt. Om specifieke omstandigheden te analyseren, definiëren we de dimensieloze parameter P als: <img alt="Equation 3" src="/files/ftp_upload/18064/18064_Equation_3.svg" style="text-align: center; height: 30px;"> Onder deze omstandigheden wordt P nul wanneer er geen drukgradiënt (∂p/∂x=0) in de x-richting is, waardoor de snelheidsvergelijking kan worden gereduceerd tot: <img alt="Equation 4" src="/files/ftp_upload/18064/18064_Equation_4.svg" style="text-align: center; height: 26px;"> Dit lineaire profiel geeft aan dat de vloeistofsnelheid lineair toeneemt van nul bij de stationaire plaat tot U bij de bewegende plaat, wat resulteert in een uniforme schuifsnelheid over de vloeistoflaag.

Couette-stroming

Couette flow describes fluid motion between two parallel plates where one is stationary, and the other moves with constant speed, creating a steady, ...

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Differential Analysis of Fluid Flow

Differentiële analyse van vloeistofstroming

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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

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...

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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

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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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