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

平面ポテンシャル流れは、不回転および非圧縮性の流れを仮定することにより、流体運動を単純化し、速度ポテンシャル関数と流れ場を記述するストリーム関数によって支配されます。
一様な流れでは、流体は一方向に一定の速度で移動し、直線チャネルの流量を推定するのに役立つ平行で等間隔の流線を作成します。
ソース流れとシンク流れには、ある点から半径方向の外側に移動する流体または内側に収束する流体が含まれ、対称的な流れパターンが作成されます。井戸から滲み出る地下水、または井戸に排水される地下水は、これらの流れを例示しています。
渦流は、中心点の周りの円運動を伴い、流体は中心からの距離に基づいてさまざまな速度で回転します。このタイプは、排水管を螺旋状に流れ落ちる水を管理するための余水吐の設計に関連しています。
フローネットは、流線と等電位ラインを組み合わせて、ダムの下の浸透経路などの複雑なフローパターンを視覚化するのに役立ちます。これにより、水の浸入による構造的な弱化を防ぐことができます。
これらのポテンシャルフローは、ダム、堤防、地下水系などの流体と相互作用する構造物を設計するために不可欠であり、フローパターンを予測し、水資源を効果的に管理します。

平面ポテンシャル フロー

Plane Potential Flows

平面ポテンシャル フローは、流体が非回転かつ非圧縮であると仮定することで、流体の動きを単純化します。これらの特性により、これらのフローは、特定の方向の流速を表す速度ポテンシャル関数 ϕ と、流路を視覚化するストリーム関数 ψ によって記述できます。これらは両方ともラプラス方程式によって決まります。これらのパラメーターは、さまざまな水力構造の周りのフロー パターン、速度分布、および圧力場を推定するのに役立ちます。

均一フロー

均一フローは、最も単純な形式のポテンシャル フローを表し、流体は一定の速度で直線的に移動しています。流線は直線で平行で、間隔が均等で、チャネルまたはパイプを流れる流れが一定の速度で明確に視覚化されます。このフロー タイプは、運河、パイプライン、排水システムの設計に不可欠です。これらのシステムでは、一定の速度を仮定することで、流量の推定と水力設計に役立ちます。

ソース フローとシンク フロー

ソース フローとシンク フローは、ある点から発生するか、ある点に収束する放射状対称フローを表します。ソースフローでは、流体は中心点から放射状に外側へ移動しますが、シンクフローでは内側に収束します。これらのフローは、ソースまたはシンクの強度を表す流量パラメータを使用してモデル化されます。このモデルは地下水水文学で広く使用されており、ソースフローは注入井からの地下水補給を表し、シンクフローは揚水井での地下水抽出を表します。

渦流

渦流は中心点を循環する流体を含み、自由渦と強制渦の 2 つの形式で現れます。自由渦では、粒子は外力なしで中心点の周りを円形の経路で移動し、自然の水域でよく見られる渦巻き効果を生み出します。このモデルは、詰まりや乱流を防ぐために螺旋状の水流を管理する放水路や排水システムを設計するために使用されます。強制渦では、外力によって流体の回転が駆動され、流体が剛体として回転するシナリオが作成されます。強制渦は、沈殿タンクや、均一な回転が沈殿物の分離と流体の混合に役立つ特定の油圧装置で使用されます。

フロー ネット

フロー ネットでは、流線が流体の流路を表し、等電位線が等しい水力ポテンシャルの点を示します。これらの線は垂直に交差し、構造物の周囲の圧力分布と潜在的な浸透経路を識別するのに役立つグリッド パターンを作成します。フロー ネットは、土壌または多孔質媒体の浸透を評価するために構築されます。浸透率は、これらの線の間隔と方向を慎重に分析し、侵食または構造的弱点の可能性のある領域を特定することで推定されます。

平面ポテンシャル流れは、速度ポテンシャル関数と流れによって支配される非回転および非圧縮性の流れを仮定することにより、流体運動を簡素化します...

Education

JoVE Core

Civil Engineering

土木工学

Unit 1

ユニット1

Differential Analysis of Fluid Flow

流体流れの微分解析

KEY TERMS AND CONCEPTS

主要用語と概念

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 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

Plane Potential Flow Patterns and Models

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