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

An engineer needs to design a pipeline to transport oil from a storage tank to a processing facility.
Given the oil&#39;s viscosity, density, and the pipeline&#39;s radius, the goal is to maintain a steady oil flow rate through a circular pipe while ensuring laminar flow to minimize friction and pressure loss.
Using Hagen-Poiseuille&#39;s law, the required pressure drop across the pipeline is calculated by considering factors like pipe length, radius, oil viscosity, and the desired flow rate.
This calculation shows the pressure drop needed to achieve the specified flow rate over the pipe&#39;s length.
To ensure the flow remains laminar, the Reynolds number, which depends on the oil&#39;s velocity, density, and viscosity, is checked.
A Reynolds number below 2100 confirms laminar flow, making Hagen-Poiseuille&#39;s law applicable.
Additionally, the maximum velocity at the center of the pipe is estimated verifying that the design meets operational requirements.
This example highlights the significance of pipe radius in determining the flow rate, as even minor adjustments can significantly impact pressure requirements and flow efficiency in pipeline design.

design example: flow of oil through circular pipes

Design Example: Flow of Oil Through Circular Pipes

Understanding fluid flow behavior through pipes is critical in fluid mechanics, especially in applications like oil transportation through pipelines. Hagen-Poiseuille's law provides an exact solution derived from the Navier-Stokes equations for steady, incompressible, and laminar flow within a circular pipe. Hagen-Poiseuille's law helps determine the necessary pressure drop across a pipeline section by determining parameters like pipe length, radius, oil viscosity, and the desired volumetric flow rate.
Hagen-Poiseuille's law describes the pressure drop (&#916;P) required to sustain a specific flow rate in a circular pipe under laminar conditions. The law is expressed as:
<img alt="&#916;P=8&#956;LQ/&#960;R&#8308; equation; fluid dynamics, pressure drop, Hagen-Poiseuille formula, physics study." src="/files/ftp_upload/18066/18066_Equation_1.svg" style="text-align: center; height: 30px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
Where:
<ol style="list-style-type: circle;">
	<li>&#956; is the dynamic viscosity of the oil,</li>
	<li>L is the length of the pipeline</li>
	<li>Q is the desired volumetric flow rate, and</li>
	<li>R is the pipe's inner radius.</li>
</ol>
This relationship highlights the role of pipe radius in determining pressure drop. Because the radius is raised to the fourth power, minor changes to the pipe's diameter can profoundly affect the pressure required to maintain a given flow rate.
Ensuring laminar flow requires calculating the Reynolds number (Re), which assesses whether the fluid motion will be smooth (laminar) or chaotic (turbulent). The Reynolds number is given by:
<img alt="Reynolds number equation Re=&#961;vD/&#956;, formula for fluid flow analysis, educational diagram." src="/files/ftp_upload/18066/18066_Equation_2.svg" style="text-align: center; height: 30px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
Where:
<ol style="list-style-type: circle;">
	<li>&#9076; is the density of the oil,</li>
	<li>v is the mean velocity of the oil,</li>
	<li>D is the pipe diameter (twice the radius), and</li>
	<li>&#956; is the dynamic viscosity.</li>
</ol>
Flow is considered laminar for Reynolds numbers below 2100, making Hagen-Poiseuille's law applicable. If the Reynolds number exceeds this threshold, adjustments may be necessary, such as reducing the flow rate or increasing pipe diameter to maintain laminar conditions.
Hagen-Poiseuille's law can determine the optimal pipe dimensions to meet specific flow requirements and pressure constraints, whether in water distribution, wastewater management, or oil transport. Selecting the correct pipe radius ensures efficient fluid movement, minimizes energy loss, and reduces operational costs, enhancing infrastructure systems' overall performance.

An engineer needs to design a pipeline to transport oil from a storage tank to a processing facility.
Given the oil&#39;s viscosity, density, and the ...

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

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Differential Analysis of Fluid Flow

KEY TERMS AND CONCEPTS

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

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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...

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.

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Pressure Drop in Oil Pipe Design

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