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In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution...
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Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
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Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
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Updated: Aug 2, 2025

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
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Method for estimating pulsatile wall shear stress from one-dimensional velocity waveforms.

J C Muskat1, C F Babbs1, C J Goergen1

  • 1Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana, USA.

Physiological Reports
|April 17, 2023
PubMed
Summary
This summary is machine-generated.

Simplified models underestimate blood flow's impact on artery health. Our new open-source method accurately calculates wall shear stress (WSS) using non-invasive data, revealing critical details of pulsatile blood flow.

Keywords:
Womersley solutionflow-mediated dilationreduced-order modelshear ratevelocity profile

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Area of Science:

  • Cardiovascular Physiology
  • Biomedical Engineering
  • Fluid Dynamics

Background:

  • Wall shear stress (WSS) regulates endothelial function but is often estimated using simplified Poiseuille flow models.
  • Pulsatile blood flow significantly impacts flow-mediated dilation (FMD), yet clinical adoption of accurate Womersley-based models is limited due to measurement challenges.

Purpose of the Study:

  • To develop an open-source method for reconstructing unsteady, Womersley-derived velocity profiles and WSS in conduit arteries.
  • To provide a clinically applicable tool for accurate WSS assessment using non-invasive data.

Main Methods:

  • Developed an open-source computational method requiring only time-averaged vessel diameter and Doppler ultrasound velocity data.
  • Validated the method against subject-specific computational fluid dynamics (CFD).
  • Applied the method to synthetic velocity waveforms in major conduit arteries (carotid, brachial, femoral).

Main Results:

  • The Poiseuille model significantly underestimates peak WSS (38.5%-55.1%) during systolic acceleration/deceleration.
  • The Poiseuille model also underestimates or misses retrograde WSS, which is crucial for endothelial function.
  • Accurate WSS calculation is essential, as oscillatory shear influences vasodilator production.

Conclusions:

  • The developed method enables accurate, non-invasive WSS assessment in conduit arteries using Womersley flow principles.
  • Simplified flow models lead to systematic underestimation of WSS, potentially misrepresenting the biological effects of pulsatile blood flow.
  • This tool can improve understanding of endothelial function and cardiovascular health.