Name: pressure and velocity in inviscid flow
Uploaded: 2025-02-13T15:43:25.000Z
Duration: 1 min 28 s
Channel: JoVE

움직이는 유체에서는 점도로 인해 전단 응력이 발생합니다. 점도가 낮은 물의 경우 이러한 효과는 무시할 수 있으므로 유체 모션 해석이 단순화됩니다.
전단 응력이 무시할 수 있는 경우 유체는 점성이 없거나 마찰이 없는 것으로 간주됩니다. 점성이 없는 유체에서 수직 응력은 모든 방향에서 동일하며, 이는 압력이 응력 방향과 무관하다는 것을 의미합니다.
압력은 수직 응력의 음수이며, 압축 응력이 양수 압력 값을 생성하도록 합니다.
오일러 방정식(Euler's equations)으로 알려진 점성 흐름에 대한 일반 운동 방정식은 운동량 보존을 설명합니다. 이 방정식은 유체 요소에 적용되는 뉴턴의 두 번째 법칙을 나타내며, 유체에 작용하는 힘과 속도 변화를 관련시킵니다.
오일러 방정식은 압력 구배, 중력과 같은 물체 힘, 유체 속도의 변화를 주도하는 국소 및 대류 가속도를 설명합니다.
그들은 점성력을 무시하고 해석을 단순화하지만 편미분 방정식의 비선형 속도 항으로 인해 해결하기가 여전히 어렵습니다.
유선을 따라 오일러 방정식을 통합하면 베르누이 방정식이 파생되어 점성 흐름의 압력, 속도 및 고도 변화에 대한 통찰력을 제공하여 유체 역학의 핵심 도구가 됩니다.

오일러의 운동 방정식

Euler&#39;s Equations of Motion

유체 역학에서 전단 응력은 변형에 대한 유체의 내부 저항을 나타내는 점성에서 발생합니다. 물과 같은 저점성 유체의 경우 이러한 응력은 최소화되어 유체를 비점성 또는 마찰이 없는 것으로 처리할 수 있어 흐름 분석이 간소화됩니다. 비점성 유체에서는 전단 응력이 없고 유체 요소에 수직으로 작용하는 수직 응력만 남습니다. 특히, 수직 응력의 음수로 정의되는 압력은 다른 방향에서 균일하게 유지되고 응력의 방향에 영향을 받지 않습니다.

비점성 유체의 운동은 유체 역학에 적용된 뉴턴의 제2 법칙에서 파생된 오일러 방정식에 의해 지배됩니다. 이러한 방정식은 속도 변화율을 유체 요소에 작용하는 힘과 연관시켜 운동량 보존을 설명합니다. 비점성 유체의 경우 관련 힘에는 압력 구배와 중력과 같은 체적력이 포함됩니다. 오일러 방정식은 점성 항을 제외한 이러한 힘의 균형을 다음과 같이 표현합니다.

<img alt="Equation 1" src="/files/ftp_upload/18057/18057_Equation_1.svg" style="text-align: center; height: 30px;">

여기서 ρ는 유체 밀도, v는 속도 벡터, p는 압력, g​는 중력 가속도를 나타냅니다.

오일러 방정식은 점성을 무시하지만 유체 입자의 대류 가속도를 설명하는 비선형 항 때문에 복잡합니다. 유선을 따라 적분하면 이러한 방정식은 베르누이 방정식을 생성하는데, 이는 유체 역학에서 기본적인 관계를 설명하며, 무점성 흐름에 대한 압력, 속도 및 고도를 연결합니다. 베르누이 방정식은 유체 흐름 내의 에너지 분포를 분석하고 유체 수송, 공기 역학 및 유체 역학의 응용 프로그램을 지원하는 강력한 도구입니다.

움직이는 유체에서는 점도로 인해 전단 응력이 발생합니다. 점도가 낮은 물의 경우 이러한 효과는 무시할 수 있으며 유체 움직임을 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

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 same in different directions and does not depend on how the stress is oriented.

Euler's equations come from Newton's second law applied to fluid motion. They describe momentum conservation by linking the change in velocity to the forces on a fluid element. For inviscid flow, those forces are pressure gradients and body forces such as gravity. The equations include density, velocity, pressure, and gravitational acceleration, but they leave out viscous terms.

Even without viscosity, Euler's equations are still nonlinear. That means they are complex because they include convective acceleration, which follows the motion of fluid particles. When the equations are integrated along a streamline, they lead to Bernoulli's equation. Bernoulli's equation connects pressure, velocity, and elevation in inviscid flows and is useful for fluid transport, aerodynamics, and hydrodynamics.

Pressure and Velocity in Inviscid Flow

euler&#39;s equations of motion

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 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 pressure, velocity, and gravity shape inviscid fluid motion through Euler's equations, and how they lead to Bernoulli's equation along a streamline.

Pressure and Velocity in Inviscid Flow | 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

Pressure and Velocity in Inviscid Flow

Description

Transcript