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

工程师需要设计一条管道，将石油从储罐输送至加工设施。
根据油的黏度、密度以及管道的半径，目标是保持圆形管道中油的稳定流速，同时确保层流状态，以尽量减少摩擦和压力损失。
根据哈根-泊肃叶定律，通过考虑管道长度、半径、油的黏度以及期望的流速等因素，计算管道两端所需的压降。
该计算展示了在管道长度上实现指定流速所需的压力降。
为了确保流动保持层流状态，需检查雷诺数，该数值取决于油的流速、密度和黏度。
雷诺数低于2100表明流动为层流，此时可应用哈根-泊肃叶定律。
此外，通过估算管道中心的最大流速，验证设计是否满足运行要求。
该示例强调了管道半径在确定流量方面的重要性，因为即使对管道半径进行微小调整，也会显著影响管道设计中的压力需求和流动效率。

设计示例：油通过圆形管道的流动

Design Example: Flow of Oil Through Circular Pipes

了解流体通过管道的流动行为对流体力学至关重要，尤其是在通过管道输送石油等应用中。哈根-泊肃叶定律提供了纳维-斯托克斯方程的一个精确解，适用于圆形管道内稳定、不可压缩的层流。通过确定管道长度、半径、油粘度和所需体积流速等参数，哈根-泊肃叶定律可确定管道部分所需的压降。 哈根-泊肃叶定律描述了层流条件下维持圆形管道中特定流速所需的压降 (ΔP)。该定律表示为： <img alt="Equation 1" src="/files/ftp_upload/18066/18066_Equation_1.svg" style="text-align: center; height: 30px;"> 其中： <ol style="list-style-type: circle;"> <li>μ 是油的动态粘度，</li> <li>L 是管道的长度</li> <li>Q 是所需的体积流速，</li> <li>r 是管道的内半径。</li> </ol> 这种关系突出了管道半径在确定压降方面的作用。由于半径是四次方，管道直径的微小变化会极大地影响维持给定流速所需的压力。 确保层流需要计算雷诺数 (Re)，它可以评估流体运动是平稳的（层流）还是混乱的（湍流）。雷诺数由以下公式给出： <img alt="Equation 2" src="/files/ftp_upload/18066/18066_Equation_2.svg" style="text-align: center; height: 30px;"> 
Where:
其中： <ol style="list-style-type: circle;"> <li>⍴ 是油的密度，</li> <li>v 是油的平均速度，</li> <li>D 是管道直径（半径的两倍），</li> <li>μ 是动态粘度。</li> </ol> 雷诺数低于 2100 时，流动被视为层流，因此适用哈根-泊肃叶定律。如果雷诺数超过此阈值，则可能需要进行调整，例如降低流速或增加管道直径以保持层流条件。 哈根-泊肃叶定律可以确定最佳管道尺寸，以满足特定的流量要求和压力限制，无论是在供水、废水管理还是石油运输中，选择正确的管道半径可确保高效的流体流动，最大限度地减少能量损失，降低运营成本，从而提高基础设施系统的整体性能。

一名工程师需要设计一条管道，将石油从储油罐输送至加工设施。  
根据石油的黏度、密度以及……

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

Education

教育

JoVE Core

Civil Engineering

土木工程

Unit 1

第一单元

Differential Analysis of Fluid Flow

流体流动微分分析

KEY TERMS AND CONCEPTS

关键术语与概念

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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