Name: laminar flow profile between parallel plates
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 17 s
Channel: JoVE

두 개의 평행 플레이트 사이의 꾸준한 층류는 단순 유체 시스템을 모델링하는 데 자주 사용되는 좁고 제한된 채널에서의 유체 이동을 설명합니다.
두 개의 고정된 플레이트 사이의 흐름의 경우 Navier-Stokes 방정식은 속도가 흐름 방향을 따라 가속도 없이 플레이트에 수직으로만 변하므로 단순화됩니다.
이것은 유체가 중심에서 가장 빠르게 움직이고 마찰로 인해 플레이트에서 0으로 느려지는 포물선 속도 프로파일로 이어지며, 이를 미끄럼 방지 조건으로 합니다.
플레이트 사이의 유속은 압력 구배, 유체 점도 및 플레이트 분리에 따라 달라집니다. 갭을 넓히거나 압력 구배를 증가시키면 흐름이 향상됩니다.
평균 유속은 압력 강하와도 관련이 있으며, 채널 중심의 최대 속도는 평균 속도의 1.5배입니다.
이 분석은 층류 조건을 나타내는 낮은 레이놀즈 수에 대해서만 유효하며 난류가 높고 레이놀즈 수가 높은 흐름에 대해서는 실패합니다.
이 분석의 응용 분야에는 층류 조건이 존재하는 수처리 공장의 관개 수로, 지하수 흐름 및 침전조가 포함됩니다.

평행판 사이의 정상, 층류

Steady, Laminar Flow Between Parallel Plates

평행판 사이의 정상, 층류를 이해하는 것은 다양한 물 수송 및 배수 시스템에서 일반적으로 발견되는 좁은 직사각형 채널의 흐름을 분석하고 설계하는 데 필수적입니다. 나비에-스토크스 방정식은 유체 운동을 지배하며 일반적으로 비선형성으로 인해 풀기 어렵습니다. 그러나 평행판 사이의 정상 층류와 같이 특정한 경우에는 단순화가 가능합니다. 이 시나리오에서는 정상, 비압축성, 층류를 가정합니다.

x축을 따라 정렬되고 y축이 판에 수직인 거리 '2h'만큼 떨어진 두 개의 수평 판을 고려할 때 유체 운동은 평행하다고 가정합니다. 여기서 연속 방정식은 x축을 따라 속도 변화가 없음을 나타내고, 나비에-스토크스 방정식은 다음과 같이 축소됩니다.

<img alt="Equation 1" src="/files/ftp_upload/18063/18063_Equation_1.svg" style="text-align: center; height: 30px;">

y 및 z 방향의 방정식은 이러한 축을 따라 압력 기울기가 없음을 나타내므로 압력은 y 방향으로 정수압적으로 변하여 적분을 통해 다음을 얻을 수 있습니다.

<img alt="Equation 2" src="/files/ftp_upload/18063/18063_Equation_2.svg" style="text-align: center; height: 12px;">

x축을 따라 압력 기울기가 있는 평행판의 경우 방정식은 다음과 같이 간소화됩니다.

<img alt="Equation 3" src="/files/ftp_upload/18063/18063_Equation_3.svg" style="text-align: center; height: 30px;">

두 번 적분하고 경계 조건(y = +h 및 y = -h에서 u = 0)을 적용하면 다음을 얻습니다.

<img alt="Equation 4" src="/files/ftp_upload/18063/18063_Equation_4.svg" style="text-align: center; height: 30px;">

이 표현식은 판 사이의 간격을 가로지르는 속도 프로파일이 포물선이며, 판 사이의 중간인 y = 0에서 최대 속도를 나타냅니다. 판의 단위 폭을 통한 체적 유량은 간격을 가로지르는 속도 프로파일을 통합하여 얻습니다.

평행 판 사이의 층류를 이해하는 것은 지하수 흐름, 폐수 처리 및 윤활에 실제적으로 적용됩니다. 예를 들어, 이 모델은 물이 판 사이의 흐름처럼 토양 입자 사이를 이동하는 토양층의 흐름을 근사할 수 있습니다. 유량과 속도 분포를 알면 엔지니어가 효율적인 배수 시스템을 설계하고 지하수 이동을 예측하는 데 도움이 됩니다.

두 개의 평행 플레이트 사이의 꾸준한 층류는 단순 유체 시스템을 모델링하는 데 자주 사용되는 좁고 제한된 채널에서의 유체 이동을 설명합니다.
때문에...

steady-laminar-flow-between-parallel-plates

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

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 becomes simpler because the flow is steady, incompressible, and laminar. Two horizontal plates are placed along the x-axis, and the gap between them is 2h. The y-axis is perpendicular to the plates, and the fluid moves parallel to the plates.

With these assumptions, the continuity equation shows that the velocity does not change along the x-axis. The Navier-Stokes equations also simplify in the y and z directions. They show no pressure gradient along those axes, so pressure changes hydrostatically in the y-direction. After integration, the x-direction equation includes the pressure gradient along the plates.

Solving that equation requires integrating twice and applying the no-slip boundary conditions, where u = 0 at y = +h and y = -h. The result is a parabolic velocity profile across the gap. The fluid moves fastest at y = 0, the midpoint between the plates. The volumetric flow rate for a unit width of the plates is then found by integrating the velocity profile across the space.

This flow model has practical uses in groundwater flow, wastewater treatment, and lubrication. It can also represent water moving through soil layers, where the flow resembles movement between plates. Engineers use the velocity distribution and flow rate to help design drainage systems and predict groundwater movement.

Laminar Flow Profile Between Parallel Plates

laminar-flow-profile-between-parallel-plates

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steady, laminar flow 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...

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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.

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key terms and concepts

Learn how steady laminar flow between parallel plates leads to a parabolic velocity profile, pressure-gradient behavior, and flow-rate calculations.

Laminar Flow Profile Between Parallel 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

Laminar Flow Profile Between Parallel Plates

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