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

エンジニアは、貯蔵タンクから処理施設に石油を輸送するためのパイプラインを設計する必要があります。
オイルの粘度、密度、およびパイプラインの半径を考慮すると、目標は、摩擦と圧力損失を最小限に抑えるために層流を確保しながら、円形パイプを通るオイル流量を安定させることです。
ハーゲン・ポアズイユの法則を使用して、パイプの長さ、半径、オイルの粘度、目的の流量などの要素を考慮して、パイプライン全体で必要な圧力損失を計算します。
この計算は、パイプの長さにわたって指定された流量を達成するために必要な圧力損失を示しています。
流れが層流に保たれるように、オイルの速度、密度、粘度に依存するレイノルズ数がチェックされます。
2100未満のレイノルズ数は層流を確認し、ハーゲン・ポアズイユの法則が適用されます。
さらに、パイプの中心での最大速度が推定され、設計が運用要件を満たしていることが確認されます。
この例では、わずかな調整でもパイプライン設計の圧力要件と流量効率に大きな影響を与える可能性があるため、流量を決定する際のパイプ半径の重要性を強調しています。

設計例: 円形パイプを通るオイルの流れ

Design Example: Flow of Oil Through Circular Pipes

パイプを通る流体の流れの挙動を理解することは、流体力学において、特にパイプラインを通るオイル輸送のような用途では重要です。ハーゲン・ポアズイユの法則は、円形パイプ内の定常、非圧縮、層流の流れに対するナビエ・ストークス方程式から導かれる正確な解を提供します。ハーゲン・ポアズイユの法則は、パイプの長さ、半径、オイルの粘度、および望ましい体積流量などのパラメータを決定することで、パイプラインセクション全体で必要な圧力降下を決定するのに役立ちます。

 ハーゲン・ポアズイユの法則は、層流条件下で円形パイプ内で特定の流量を維持するために必要な圧力降下 (ΔP) を説明します。この法則は次のように表されます:

<img alt="Equation 1" src="/files/ftp_upload/18066/18066_Equation_1.svg" style="text-align: center; height: 30px;">

 ここで:

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
 <li>μ はオイルの動粘度、</li>
 <li>L はパイプラインの長さ、</li>
 <li>Q は望ましい体積流量、</li>
 <li>r はパイプの内半径です。</li>
</ul>

 この関係は、圧力降下を決定するパイプ半径の役割を強調しています。半径は 4 乗されるため、パイプの直径を少し変更するだけで、特定の流量を維持するために必要な圧力に大きく影響する可能性があります。

 層流を確実にするには、流体の動きが滑らか (層流) になるか無秩序 (乱流) になるかを評価するレイノルズ数 (Re) を計算する必要があります。レイノルズ数は次のように求められます。

<img alt="Equation 2" src="/files/ftp_upload/18066/18066_Equation_2.svg" style="text-align: center; height: 30px;">

 ここで:

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
 <li>⍴ はオイルの密度、</li>
 <li>v はオイルの平均速度、</li>
 <li>D はパイプの直径 (半径の 2 倍)、</li>
 <li>μ は動粘度です。</li>
</ul>

 レイノルズ数が 2100 未満の場合は流れが層流と見なされ、ハーゲン・ポアズイユの法則が適用されます。レイノルズ数がこのしきい値を超える場合は、流量を減らしたり、層流状態を維持するためにパイプの直径を大きくしたりするなどの調整が必要になる場合があります。

 ハーゲン・ポアズイユの法則は、給水、廃水管理、石油輸送など、特定の流量要件と圧力制約を満たす最適なパイプ寸法を決定できます。適切なパイプ半径を選択すると、効率的な流体移動が保証され、エネルギー損失が最小限に抑えられ、運用コストが削減され、インフラシステムの全体的なパフォーマンスが向上します。

エンジニアは、貯蔵タンクから処理施設に石油を輸送するためのパイプラインを設計する必要があります。
オイルの粘度、密度、そして...

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

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

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 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

Pressure Drop in Oil Pipe Design

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