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Related Concept Videos

General Characteristics of Pipe Flow I01:22

General Characteristics of Pipe Flow I

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Pipe flow refers to the movement of fluids within fully enclosed conduits, typically cylindrical in shape, such as water pipes or hydraulic hoses. These conduits are designed to withstand high-pressure gradients that drive fluid movement, contrasting with open-channel flows, where gravity is the primary driving force. Rectangular conduits, like air conditioning and heating ducts, generally operate at lower pressures and are less suited for high-pressure applications.
The classification of fluid...
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General Characteristics of Pipe Flow II01:24

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When fluid enters a pipe, it first passes through the entrance region, where the velocity profile adjusts due to viscous effects. In this region, a boundary layer forms along the pipe walls and grows until it fully occupies the pipe's cross-section. Once the boundary layer merges, the flow becomes fully developed, with a steady velocity profile that remains consistent along the pipe's length.
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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...
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When a fluid flows through a pipe, it experiences energy losses due to frictional resistance along the pipe walls, known as major losses. These energy losses result in a pressure drop, which varies based on the flow conditions — whether laminar or turbulent — and the specific physical properties of the fluid and pipe.
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In pipe systems, minor losses refer to energy losses arising from components such as valves, bends, fittings, expansions, and other features that disrupt the steady flow of fluid. These disturbances cause energy dissipation through turbulence and resistance, which engineers quantify to manage system efficiency effectively.
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In pipe flow analysis, problems are typically categorized into three types — Type I, Type II, and Type III — based on the known parameters and the desired outcome. Each type of problem addresses specific engineering requirements using fluid properties, pipe characteristics, and operational conditions.
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Related Experiment Video

Updated: Feb 6, 2026

Measurements of Local Instantaneous Convective Heat Transfer in a Pipe - Single and Two-phase Flow
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Measurements of Local Instantaneous Convective Heat Transfer in a Pipe - Single and Two-phase Flow

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Viscoelastic Pipe Flow is Linearly Unstable.

Piyush Garg1, Indresh Chaudhary2, Mohammad Khalid2

  • 1Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India.

Physical Review Letters
|August 8, 2018
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Summary

Researchers discovered a new linear instability in viscoelastic fluid pipe flow, explaining turbulence in polymer solutions at lower flow rates than typically seen in Newtonian fluids.

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Area of Science:

  • Fluid Dynamics
  • Rheology
  • Polymer Physics

Background:

  • Newtonian fluids are linearly stable in pipe flow across all Reynolds numbers.
  • Understanding fluid instabilities is crucial for predicting turbulence.
  • Dilute polymer solutions exhibit complex flow behaviors not fully explained by Newtonian fluid dynamics.

Purpose of the Study:

  • To identify and characterize a novel linear instability in pressure-driven pipe flow of viscoelastic fluids.
  • To investigate the role of viscoelasticity, specifically using the Oldroyd-B model, in fluid flow stability.
  • To provide a theoretical basis for experimental observations of early-stage turbulence in polymer solutions.

Main Methods:

  • Linear stability analysis of the Oldroyd-B constitutive equation for pipe flow.
  • Numerical computation of eigenvalues to determine instability growth rates.
  • Comparison of theoretical predictions with experimental data for polymer solutions.

Main Results:

  • A linear instability was identified in viscoelastic pipe flow, distinct from Newtonian flow.
  • This instability occurs at significantly lower Reynolds numbers than typically required for Newtonian turbulence.
  • The findings qualitatively align with experimental observations of turbulence in polymer solutions where Newtonian turbulence is absent.

Conclusions:

  • Viscoelasticity introduces a new pathway to turbulence in pipe flow, initiating at lower flow rates.
  • The identified instability provides the first stage in an unexplored route to turbulence in polymer solutions.
  • An analogous instability is also present in plane Poiseuille flow, suggesting broader applicability.