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Related Concept Videos

General Characteristics of Pipe Flow II01:24

General Characteristics of Pipe Flow II

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.
The distance to reach a fully developed flow is called the entrance length and depends on the flow...
Turbulent Flow01:24

Turbulent Flow

Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent spots,...
General Characteristics of Pipe Flow I01:22

General Characteristics of Pipe Flow I

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...
Single Pipe Systems01:24

Single Pipe Systems

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.
In a Type I problem, fluid properties (density and viscosity), pipe characteristics (including diameter, length, and surface roughness), and the flow rate or average velocity are known. The...
Poiseuille's Law and Reynolds Number01:10

Poiseuille's Law and Reynolds Number

Any fluid in a horizontal tube can flow due to pressure differences—fluid flows from high to low pressure. The flow rate (Q) is the ratio of pressure difference and resistance through a horizontal tube. The greater the pressure difference, the higher the flow rate. The flow resistance is expressed as:
Irrotational Flow01:28

Irrotational Flow

Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:

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Related Experiment Video

Updated: Jul 8, 2026

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
09:37

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole

Published on: August 26, 2019

Instability in pipe flow.

D L Cotrell1, G B McFadden, B J Alder

  • 1Lawrence Livermore National Laboratory, Livermore, CA 94551, USA.

Proceedings of the National Academy of Sciences of the United States of America
|January 8, 2008
PubMed
Summary
This summary is machine-generated.

Linear stability analysis of pipe flow transitions is improved by accounting for wall roughness. Introducing corrugations reveals stable vortex formation and unsteady flow, with implications for fluid dynamics at high Reynolds numbers.

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Last Updated: Jul 8, 2026

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
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Published on: August 26, 2019

Magnetically Induced Rotating Rayleigh-Taylor Instability
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Area of Science:

  • Fluid dynamics
  • Turbulence theory
  • Non-linear dynamics

Background:

  • Linear stability analyses of pipe flow predict no transition, even at infinite Reynolds number.
  • This unphysical result is attributed to the use of stick boundary conditions, which neglect wall roughness effects.
  • Wall roughness introduces a crucial length scale absent in idealized models.

Purpose of the Study:

  • To investigate the impact of wall roughness on pipe flow stability using a simplified model.
  • To reconcile theoretical predictions with observed flow transitions in realistic pipe geometries.
  • To understand the role of vortex formation and dislodging in flow transitions.

Main Methods:

  • Employing linear stability analysis on a pipe flow model incorporating wall corrugations (a proxy for roughness).
  • Introducing a finite amplitude parameter to represent the corrugation's scale.
  • Analyzing flow behavior at varying Reynolds numbers and corrugation amplitudes.

Main Results:

  • Stable vortex formation occurs at low Reynolds numbers above a critical corrugation amplitude.
  • Unsteady flow and vortex dislodging are observed at higher Reynolds numbers.
  • Extrapolation to infinite Reynolds number yields a finite, consistent critical amplitude for vortex formation.

Conclusions:

  • Stick boundary conditions are insufficient for modeling pipe flow transitions due to their neglect of wall roughness.
  • Wall roughness, modeled by corrugations, is essential for predicting stable vortex formation and flow transitions.
  • A finite wall amplitude threshold exists below which vortex formation is suppressed, explaining the limitations of idealized models.