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

Un ingegnere deve progettare una conduttura per trasportare il petrolio da un serbatoio di stoccaggio a un impianto di lavorazione.
Data la viscosità, la densità e il raggio dell'oleodotto, l'obiettivo è mantenere una portata costante dell'olio attraverso un tubo circolare, garantendo al contempo un flusso laminare per ridurre al minimo l'attrito e la perdita di pressione.
Utilizzando la legge di Hagen-Poiseuille, la caduta di pressione richiesta attraverso la tubazione viene calcolata considerando fattori come la lunghezza del tubo, il raggio, la viscosità dell'olio e la portata desiderata.
Questo calcolo mostra la caduta di pressione necessaria per raggiungere la portata specificata sulla lunghezza del tubo.
Per garantire che il flusso rimanga laminare, viene controllato il numero di Reynolds, che dipende dalla velocità, dalla densità e dalla viscosità dell'olio.
Un numero di Reynolds inferiore a 2100 conferma il flusso laminare, rendendo applicabile la legge di Hagen-Poiseuille.
Inoltre, viene stimata la velocità massima al centro del tubo verificando che il progetto soddisfi i requisiti operativi.
Questo esempio evidenzia l'importanza del raggio del tubo nella determinazione della portata, poiché anche piccole regolazioni possono influire in modo significativo sui requisiti di pressione e sull'efficienza del flusso nella progettazione delle tubazioni.

esempio di progettazione: flusso di petrolio attraverso tubi circolari

Design Example: Flow of Oil Through Circular Pipes

Comprendere il comportamento del flusso di un fluido attraverso i tubi è fondamentale nella meccanica dei fluidi, specialmente in applicazioni come il trasporto di petrolio tramite oleodotti. La legge di Hagen-Poiseuille fornisce una soluzione precisa, derivata dalle equazioni di Navier-Stokes per il flusso stazionario, incomprimibile e laminare all'interno di un tubo circolare. La legge di Hagen-Poiseuille aiuta a determinare la caduta di pressione necessaria attraverso una sezione di condotta, determinando parametri come lunghezza del tubo, raggio, viscosità dell'petrolio e portata volumetrica desiderata.

La legge di Hagen-Poiseuille descrive la caduta di pressione (ΔP) richiesta per sostenere una portata specifica in un tubo circolare in condizioni laminari. La legge è espressa come:

<img alt="Equation 1" src="/files/ftp_upload/18066/18066_Equation_1.svg" style="text-align: center; height: 30px;">

Dove:

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
 <li>μ è la viscosità dinamica dell'olio,</li>
 <li>L è la lunghezza della condotta</li>
 <li>Q è la portata volumetrica desiderata e</li>
 <li>r è il raggio interno del tubo.</li>
</ul>

Questa relazione evidenzia il ruolo del raggio del tubo nel determinare la caduta di pressione. Poiché il raggio è elevato alla quarta potenza, piccole modifiche al diametro del tubo possono influenzare profondamente la pressione richiesta per mantenere una determinata portata.

Per garantire un flusso laminare è necessario calcolare il numero di Reynolds (Re), che valuta se il movimento del fluido sarà regolare (laminare) o caotico (turbolento). Il numero di Reynolds è dato da:

<img alt="Equation 2" src="/files/ftp_upload/18066/18066_Equation_2.svg" style="text-align: center; height: 30px;">

Dove:

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
 <li>⍴ è la densità dell'olio,</li>
 <li>v è la velocità media dell'olio,</li>
 <li>D è il diametro del tubo (il doppio del raggio) e</li>
 <li>μ è la viscosità dinamica.</li>
</ul>

Il flusso è considerato laminare per numeri di Reynolds inferiori a 2100, rendendo applicabile la legge di Hagen-Poiseuille. Se il numero di Reynolds supera questa soglia, potrebbero essere necessarie delle regolazioni, come ridurre la portata o aumentare il diametro del tubo per mantenere condizioni laminari.

La legge di Hagen-Poiseuille può determinare le dimensioni ottimali dei tubi per soddisfare requisiti di flusso e vincoli di pressione specifici, sia nella distribuzione dell'acqua, nella gestione delle acque reflue o nel trasporto di petrolio. La selezione del raggio corretto dei tubi assicura un movimento efficiente dei fluidi, riduce al minimo la perdita di energia e riduce i costi operativi, migliorando le prestazioni complessive dei sistemi infrastrutturali.

Esempio di Progettazione: Flusso di Petrolio attraverso Tubi Circolari

Un ingegnere deve progettare una conduttura per trasportare il petrolio da un serbatoio di stoccaggio a un impianto di lavorazione.
Data la viscosità, la densità e il ...

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

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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...

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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...

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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.

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Pressure Drop in Oil Pipe Design

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