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

Couette akışı, birinin sabit olduğu ve diğerinin sabit hızla hareket ettiği iki paralel plaka arasındaki sıvı hareketini tanımlar ve sabit, laminer kesme tahrikli bir akış oluşturur.
Bu kurulum, boyutsuz bir biçimde ifade edilebilen Navier-Stokes denklemlerini basitleştirir.
Basınç gradyanı ile ilgili boyutsuz bir parametre, Couette akış profillerindeki varyasyonları tanımlar.
Akış yönü boyunca basınç gradyanı olmadığında, bu parametre sıfır olur ve iki plaka arasında doğrusal bir hız değişimini gösterir.
Plakalar arasındaki akışkan hızı profili doğrusaldır ve sabit plakadaki sıfırdan hareketli plakanın hızına kadar artar.
Couette akışı, ince bir yağlayıcı tabakasının sabit bir mahfaza içinde dönen bir şaftı ayırdığı su pompalarındakiler gibi hafif yüklü muylu rulmanlardaki sıvı davranışını modellemek için yaygın olarak kullanılır.
Bu hafif yüklü rulmanlarda basınç etkileri minimum düzeydedir, bu nedenle akış özellikleri saf Couette akışına çok benzer.
Yağlayıcı tabakasının kayma gerilimi ve akış hızı, milin dönme hızına ve mil ile gövde arasındaki boşluk genişliğine bağlıdır.

couette akışı

Couette Flow

Couette akışı, bir plakanın sabit ve diğerinin sabit bir hızla hareket ettiği iki paralel plaka arasındaki akışkan akışını temsil eder. Bu yapılandırma, viskozite ve sıkıştırılamazlık koşulları altında akışkan hareketini yöneten Navier-Stokes denklemlerini kullanarak basitleştirilmiş bir analize olanak tanır. Couette akışı için varsayımlar, akış yönünde sıfır basınç gradyanı olan sabit, laminer, sıkıştırılamaz bir akışı içerir. Bu akış türü, kayma kaynaklı akışları anlamak için faydalıdır ve tortu taşınması ve erozyon gibi yağlama ve inşaat mühendisliği senaryolarındaki uygulamalarla ilgilidir.

Bir Couette akış düzeneğinde, x ekseni üst plakanın hareket yönü ile hizalanırken y ekseni her iki plakaya dik olsun. Akış sabit, laminer ve tam gelişmiştir,

Couette akışı için hız dağılım denklemi şu şekilde verilir:

<img alt="Equation 1" src="/files/ftp_upload/18064/18064_Equation_1.svg" style="text-align: center; height: 30px;" />

Burada:

<ol style="list-style-type: circle;">
	<li>U üst plakanın sabit hızıdır,</li>
	<li>b plakalar arasındaki mesafedir,</li>
	<li>μ sıvının dinamik viskozitesidir.</li>
</ol>

Boyutsuz formda, her iki tarafı U'ya bölerek şunu elde ederiz:

<img alt="Equation 2" src="/files/ftp_upload/18064/18064_Equation_2.svg" style="text-align: center; height: 30px;" />

Burada u/U boyutsuz hızı, y/b ise sabit plakadan normalize edilmiş mesafeyi temsil eder. Belirli koşulları analiz etmek için boyutsuz parametre P'yi şu şekilde tanımlıyoruz:

<img alt="Equation 3" src="/files/ftp_upload/18064/18064_Equation_3.svg" style="text-align: center; height: 30px;" />

Bu koşullar altında, x yönünde basınç gradyanı olmadığında (∂p/∂x=0) P sıfıra iner ve hız denklemi şu şekilde azalır:

<img alt="Equation 4" src="/files/ftp_upload/18064/18064_Equation_4.svg" style="text-align: center; height: 26px;" />

Bu doğrusal profil, akışkan hızının sabit plakadaki sıfırdan hareketli plakadaki U'ya doğrusal olarak arttığını ve bunun da akışkan tabakası boyunca düzgün bir kayma hızıyla sonuçlandığını gösterir.

Couette Akışı

Couette akışı, birinin sabit olduğu ve diğerinin sabit hızla hareket ettiği iki paralel plaka arasındaki sıvı hareketini tanımlar ve sabit bir ...

Education

JoVE Core

Civil Engineering

İnşaat Mühendisliği

Unit 1

Ünite 1

Differential Analysis of Fluid Flow

Akışkan Akışının Diferansiyel Analizi

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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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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

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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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