Name: pressure drop in oil pipe design
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 25 s
Channel: JoVE

엔지니어는 저장 탱크에서 처리 시설로 오일을 운송하기 위한 파이프라인을 설계해야 합니다.
오일의 점도, 밀도 및 파이프라인의 반경을 감안할 때 목표는 원형 파이프를 통해 일정한 오일 유량을 유지하면서 층류를 보장하여 마찰과 압력 손실을 최소화하는 것입니다.
Hagen-Poiseuille의 법칙을 사용하여 파이프 길이, 반경, 오일 점도 및 원하는 유속과 같은 요소를 고려하여 파이프라인 전체에 필요한 압력 강하를 계산합니다.
이 계산은 파이프 길이에 걸쳐 지정된 유량을 달성하는 데 필요한 압력 강하를 보여줍니다.
흐름이 층류로 유지되도록 하기 위해 오일의 속도, 밀도 및 점도에 따라 달라지는 레이놀즈 수를 확인합니다.
레이놀즈 수가 2100 미만이면 층류가 확인되므로 Hagen-Poiseuille의 법칙이 적용됩니다.
또한 파이프 중앙의 최대 속도를 추정하여 설계가 운영 요구 사항을 충족하는지 확인합니다.
이 예는 유속을 결정하는 데 있어 파이프 반경의 중요성을 강조하며, 사소한 조정조차도 파이프라인 설계에서 압력 요구 사항과 흐름 효율성에 큰 영향을 미칠 수 있기 때문입니다.

설계 사례: 원형 파이프를 통한 oil 흐름

Design Example: Flow of Oil Through Circular Pipes

파이프를 통한 유체 흐름 거동을 이해하는 것은 유체 역학에서 매우 중요하며, 특히 파이프라인을 통한 석유 수송과 같은 응용 분야에서 더욱 그렇습니다. 하겐-푸아줄의 법칙은 원형 파이프 내에서 정상, 비압축성 및 층류 흐름에 대한 나비에-스토크스 방정식에서 파생된 정확한 솔루션을 제공합니다. 하겐-푸아줄의 법칙은 파이프 길이, 반경, 오일 점도 및 원하는 체적 유량과 같은 매개변수를 결정하여 파이프라인 구간에서 필요한 압력 강하를 결정하는 데 도움이 됩니다.

하겐-푸아줄의 법칙은 층류 조건에서 원형 파이프에서 특정 유량을 유지하는 데 필요한 압력 강하(ΔP)를 설명합니다. 이 법칙은 다음과 같이 표현됩니다.

<img alt="Equation 1" src="/files/ftp_upload/18066/18066_Equation_1.svg" style="text-align: center; height: 30px;">

여기서:

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
 <li>μ는 오일의 동적 점도,</li>
 <li>L은 파이프라인의 길이,</li>
 <li>Q는 원하는 체적 유량,</li>
 <li>r은 파이프의 내부 반경입니다.</li>
</ul>

이 관계는 압력 강하를 결정하는 데 있어 파이프 반경의 역할을 강조합니다. 반경이 4제곱으로 증가하기 때문에 파이프 직경의 사소한 변화가 주어진 유량을 유지하는 데 필요한 압력에 큰 영향을 미칠 수 있습니다.

층류를 보장하려면 유체 운동이 매끄러울지(층류) 아니면 혼란스러울지(난류) 평가하는 레이놀즈 수(Re)를 계산해야 합니다. 레이놀즈 수는 다음과 같습니다.

<img alt="Equation 2" src="/files/ftp_upload/18066/18066_Equation_2.svg" style="text-align: center; height: 30px;">

여기서:

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
 <li>⍴는 오일의 밀도,</li>
 <li>v는 오일의 평균 속도,</li>
 <li>D는 파이프 직경(반경의 두 배),</li>
 <li>μ는 동적 점도입니다.</li>
</ul>

레이놀즈 수가 2100 미만인 경우 흐름은 층류로 간주되므로 하겐-푸아줄의 법칙이 적용됩니다. 레이놀즈 수가 이 임계값을 초과하면 층류 조건을 유지하기 위해 유량을 줄이거나 파이프 직경을 늘리는 등 조정이 필요할 수 있습니다.

하겐-푸아세유의 법칙은 물 분배, 폐수 관리 또는 석유 수송 여부에 관계없이 특정 흐름 요구 사항과 압력 제약을 충족하는 최적의 파이프 치수를 결정할 수 있습니다. 올바른 파이프 반경을 선택하면 효율적인 유체 이동이 보장되고 에너지 손실이 최소화되며 운영 비용이 줄어들어 인프라 시스템의 전반적인 성능이 향상됩니다.

설계 사례: 원형 파이프를 통한 OIl 흐름

엔지니어는 저장 탱크에서 처리 시설로 오일을 운송하기 위한 파이프라인을 설계해야 합니다.
오일의 점도, 밀도 및 ...

design-example-flow-of-oil-through-circular-pipes

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 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 relationship shows why pipe radius matters so much. Because radius is raised to the fourth power, even a small change in diameter can greatly change the pressure needed to maintain the same flow rate.

To know whether Hagen-Poiseuille's law applies, engineers calculate the Reynolds number. The Reynolds number uses the oil's density, mean velocity, pipe diameter, and dynamic viscosity. Flow is considered laminar when Reynolds number is below 2100, which means the motion stays smooth instead of becoming chaotic or turbulent.

If the Reynolds number is too high, the design may need changes. A lower flow rate or a larger pipe diameter can help keep the flow laminar. This method is useful in oil transport and also in systems such as water distribution and wastewater management, where the goal is efficient fluid movement, less energy loss, and lower operating cost.

Pressure Drop in Oil Pipe Design

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 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

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 Hagen-Poiseuille's law and Reynolds number help design oil flow in circular pipes by linking pipe radius, viscosity, pressure drop, and laminar flow.

Pressure Drop in Oil Pipe Design | 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 Drop in Oil Pipe Design

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