Name: plane potential flow patterns and models
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 23 s
Channel: JoVE

평면 전위 흐름은 비회전 및 비압축성 흐름을 가정하여 유체 움직임을 단순화하며, 유동장을 설명하기 위해 속도 전위 함수와 스트림 함수에 의해 제어됩니다.
균일한 흐름에서 유체는 한 방향으로 일정한 속도로 이동하여 직선 채널에서 유속을 추정하는 데 유용한 평행하고 균일한 간격의 유선을 생성합니다.
소스 및 싱크 흐름은 유체가 점에서 방사상 바깥쪽으로 이동하거나 안쪽으로 수렴하여 대칭적인 흐름 패턴을 만드는 것을 포함합니다. 우물에서 스며들거나 우물로 배수되는 지하수는 이러한 흐름을 잘 보여줍니다.
와류 흐름은 중심점을 중심으로 한 원형 운동을 포함하며, 여기서 유체는 중심으로부터의 거리에 따라 다양한 속도로 회전합니다. 이 유형은 배수구를 따라 소용돌이치는 물을 관리하기 위한 배수로를 설계하는 것과 관련이 있습니다.
유전망은 유선과 등전위선을 결합하여 댐 아래의 누출 경로와 같은 복잡한 흐름 패턴을 시각화하는 데 도움이 됩니다. 이는 물 침투로 인한 구조적 약화를 방지하는 데 도움이 됩니다.
이러한 잠재적 흐름은 흐름 패턴을 예측하고 수자원을 효과적으로 관리함으로써 댐, 제방 및 지하수 시스템과 같은 유체와 상호 작용하는 구조를 설계하는 데 필수적입니다.

평면 잠재 유동

Plane Potential Flows

평면 잠재 유동은 유체가 비회전적이고 비압축성이라고 가정하여 유체 운동을 단순화합니다. 이러한 특성으로 인해 이러한 유동은 주어진 방향의 유동 속도를 나타내는 속도 잠재 함수 ϕ와 유동 경로를 시각화하는 스트림 함수 ψ로 설명할 수 있으며, 둘 다 라플라스 방정식에 의해 지배됩니다. 이러한 매개변수는 다양한 유압 구조 주변의 유동 패턴, 속도 분포 및 압력장을 추정하는 데 도움이 됩니다.

균일 유동

균일 유동은 유체가 일정한 속도로 직선으로 움직이는 가장 단순한 형태의 잠재 유동을 나타냅니다. 유선은 직선이고 평행하며 균일한 간격을 두고 있어 일정한 속도로 채널이나 파이프를 가로지르는 유동을 명확하게 시각화합니다. 이 유동 유형은 일정한 속도의 가정이 유량 추정 및 유압 설계에 도움이 되는 운하, 파이프라인 및 배수 시스템을 설계하는 데 필수적입니다.

원천 및 싱크 유동

원천 및 싱크 유동은 지점에서 시작하거나 지점으로 수렴하는 방사형 대칭 유동을 설명합니다. 소스 흐름에서 유체는 중앙 지점에서 방사형으로 바깥쪽으로 이동하는 반면 싱크 흐름에서는 안쪽으로 수렴합니다. 이러한 흐름은 소스 또는 싱크의 강도를 나타내는 유량 매개변수를 사용하여 모델링됩니다. 이 모델은 지하수 수문학에서 널리 사용되며, 소스 흐름은 주입 우물에서와 같은 지하수 재충전을 나타내고 싱크 흐름은 펌핑 우물에서 지하수 추출을 나타냅니다.

와류 흐름

와류 흐름은 중앙 지점을 순환하는 유체를 포함하며 자유 및 강제의 두 가지 형태로 나타납니다. 자유 와류에서 입자는 외부 힘 없이 중앙 지점 주위를 원형 경로로 이동하여 자연 수역에서 종종 관찰되는 소용돌이 효과를 생성합니다. 이 모델은 막힘이나 난류를 방지하기 위해 나선형 물 흐름을 관리하는 방류로 및 배수 시스템을 설계하는 데 사용됩니다. 강제 와류에서 외부 힘이 유체의 회전을 구동하여 유체가 강체로 회전하는 시나리오를 생성합니다. 강제 와류는 침전조와 특정 유압 장치에서 사용되며, 균일한 회전은 침전물 분리와 유체 혼합에 도움이 됩니다.

유동망

유동망에서 유선은 유체 흐름 경로를 나타내는 반면 등전위선은 동일한 유압 잠재력의 지점을 표시합니다. 이러한 선은 수직으로 교차하여 구조물 주변의 압력 분포와 잠재적 침투 경로를 식별하는 데 도움이 되는 격자 패턴을 만듭니다. 유동망은 토양이나 다공성 매체의 침투를 평가하기 위해 구성됩니다. 침투율은 이러한 선의 간격과 방향을 신중하게 분석하고 잠재적인 침식 또는 구조적 약점 영역을 식별하여 추정합니다.

평면 전위 흐름은 속도 전위 함수와 흐름에 의해 제어되는 비회전 및 비압축성 흐름을 가정하여 유체 운동을 단순화합니다.

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

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 simplest potential flow. The fluid moves in a straight line at a constant velocity. Its streamlines are straight, parallel, and evenly spaced. This model helps in canal, pipeline, and drainage system design because a constant-velocity assumption can support flow rate estimation and hydraulic design.

Source and sink flows show radial motion around a point. In a source flow, fluid moves outward from the center. In a sink flow, fluid moves inward toward the center. A flow rate parameter gives the strength of the source or sink. These flows are used in groundwater hydrology, where a source can represent groundwater recharge, such as from an injection well, and a sink can represent groundwater extraction from a pumping well.

Vortex flow describes fluid that circulates around a center point. It appears as a free vortex or a forced vortex. In a free vortex, particles move in circular paths without an external force, like a whirlpool in natural water. This model helps in spillway and drainage system design to reduce clogging or turbulence. In a forced vortex, an external force causes the fluid to rotate as a rigid body. Forced vortices are used in sedimentation tanks and some hydraulic devices, where steady rotation helps with sediment separation and fluid mixing.

Flow nets combine streamlines and equipotential lines. Streamlines show the path of the fluid, while equipotential lines mark points with equal hydraulic potential. These lines cross at right angles and form a grid pattern. Flow nets are used to study seepage in soil or porous media and to estimate seepage rates. They also help identify pressure distributions, possible seepage paths, and areas where erosion or structural weakness may occur.

Plane Potential Flow Patterns and Models

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 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...

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 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

Explore plane potential flow patterns, including uniform, source, sink, and vortex flows, plus flow nets used to study seepage and pressure fields.

Plane Potential Flow Patterns and Models | 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

Plane Potential Flow Patterns and Models

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