Name: irrotational flow near boundaries
Uploaded: 2025-02-13T15:43:25.000Z
Duration: 1 min 28 s
Channel: JoVE

비회전 흐름(Irrotational flow)은 흐름 경로를 따라 회전하지 않는 유체 입자의 이동을 말하며, 컬이 없고 소용돌이가 없는 속도 필드를 특징으로 합니다.
속도의 0이 아닌 구성 요소인 상수 u=U가 하나만 있는 균일한 흐름은 속도 구배가 없기 때문에 비회전 흐름의 예입니다.
솔리드 물체가 균일한 흐름에 도입되면 흐름은 경계 근처를 제외하고는 비회전 상태로 유지됩니다.표면 근처에서는 속도가 0에서 급격히 증가하여 가파른 경사와 상당한 전단 응력이 생성됩니다.
실제로 점성이 없는 흐름의 경우, 흐름은 경계를 지나 미끄러지듯 지나가면서 비회전 운동을 보존합니다. 그러나 실제 유체에서는 점도가 고정된 표면 근처에 경계층을 형성하여 회전 효과를 일으키고 때로는 다운스트림 분리를 유발합니다.
파이프 흐름에서 입구 영역은 처음에는 균일한 흐름을 가진 회전 코어를 나타내지만 파이프 벽을 따라 경계층이 형성되고 두꺼워짐에 따라 점성력이 지배하는 완전히 개발된 영역으로 전환됩니다.
흐름이 비회전적이고, 압축할 수 없고, 안정적이고, 점성이 없다고 가정하면 Bernoulli의 방정식을 흐름장에 적용할 수 있습니다.

비회전 유동

Irrotational Flow

비회전 유동은 입자가 축을 중심으로 회전하지 않는 유체 운동으로 특징지어지며, 그 결과 와도가 0이 됩니다. 유동이 비회전이 되려면 속도장의 컬이 0이어야 합니다. 이는 속도 기울기에 특정 조건을 부과합니다. 예를 들어, z축을 중심으로 회전을 0으로 유지하려면 기울기 조건:

<img alt="Equation 1" src="/files/ftp_upload/18059/18059_Equation_1.svg" style="text-align: center; height: 27px;">

을 충족해야 하며, 다른 축에 대한 유사한 조건도 충족해야 합니다.

<img alt="Equation 2" src="/files/ftp_upload/18059/18059_Equation_2.svg" style="text-align: center; height: 27px;">

u가 일정하고 v와 w가 모두 0인 균일 유동은 이러한 조건을 충족하며 비회전 유동의 간단한 예가 됩니다. 그러나 고체 물체가 도입되면 비회전성은 물체에서 멀리 떨어진 곳에서만 지속됩니다. 경계 근처에서 속도는 0(미끄럼 없음 조건으로 인해)에서 자유 흐름 값으로 급격히 증가하여 점성 유체에서 상당한 전단 응력과 경계층을 생성합니다.

유체가 대형 저수조에서 파이프로 유입되면 초기 흐름은 거의 균일하여 속도 분포가 평평한 비회전 코어가 생성됩니다. 유체가 하류로 이동하면 점성으로 인해 파이프 벽을 따라 경계층이 형성되어 속도 프로파일이 궁극적으로 완전히 발달된 포물선 프로파일로 이어지는 기울기를 개발합니다. 이 완전히 발달된 영역에서 회전 효과는 벽 근처에서 우세하지만 중앙 코어는 대략 비회전 상태로 유지될 수 있습니다.

파이프 흐름의 초기 비회전 영역에서 베르누이 방정식

<img alt="Equation 3" src="/files/ftp_upload/18059/18059_Equation_3.svg" style="text-align: center; height: 27px;">

은 비압축성, 비점성 흐름 및 비회전성의 조건이 유지되므로 유선을 따라 지점 사이에 적용될 수 있습니다. 그러나 경계층이 커지고 벽 근처에서 회전 효과가 중요해짐에 따라 베르누이 방정식의 가정은 무너집니다. 즉, 베르누이 방정식은 입구 영역과 비회전 코어에만 적용되고 점성 효과가 지배적인 완전히 발달된 회전 영역에는 적용되지 않습니다.

비회전 흐름(Irrotational flow)은 흐름 경로를 따라 회전하지 않는 유체 입자의 이동을 말하며, 0 curl 및 ...

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

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 far from the object. Near the surface, the fluid speed rises sharply from zero because of the no-slip condition. This creates strong shear stress and a boundary layer in viscous fluids.

A similar change happens when fluid enters a pipe from a large reservoir. At first, the flow is nearly uniform, so the center region forms an irrotational core with a flat velocity profile. Farther downstream, viscosity causes boundary layers to grow along the pipe walls.

As the flow continues, the velocity profile develops more gradient and becomes fully developed and parabolic. In that region, rotational effects are strongest near the walls, while the center may still be approximately irrotational. Bernoulli's equation can apply in the entrance region and in the irrotational core, where the flow is incompressible, inviscid, and irrotational. It no longer applies well in the fully developed region, where viscosity and rotation dominate.

Irrotational Flow Near Boundaries

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 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

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 irrotational flow behaves near solids and in pipe entrance flow, including boundary layers, rotational effects, and when Bernoulli's equation applies.

Irrotational Flow Near Boundaries | 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

Irrotational Flow Near Boundaries

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