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Related Concept Videos

Steady, Laminar Flow in Circular Tubes01:23

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Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is...
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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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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:
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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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Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
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Laminar flow represents a smooth, orderly fluid motion where particles move along parallel paths, resulting in minimal mixing between layers. Streamlined particle paths characterize this flow regime and occur under conditions where viscous forces dominate over inertial forces. The distinction between laminar, transitional, and turbulent flow is primarily determined by the Reynolds number, a dimensionless quantity calculated as:
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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Hydrodynamic-dissipation relation for characterizing flow stagnation.

Seth Davidovits1, E Kroupp2, E Stambulchik2

  • 1Lawrence Livermore National Laboratory, Livermore, California 94550, USA.

Physical Review. E
|July 17, 2021
PubMed
Summary
This summary is machine-generated.

Researchers developed a new method to analyze hydrodynamic stagnation, which converts flow energy into internal energy. This technique reveals a key lengthscale in the energy conversion process for implosions.

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Area of Science:

  • Plasma Physics
  • Fluid Dynamics
  • Energy Conversion

Background:

  • Hydrodynamic stagnation is a critical process in various physical phenomena, including inertial confinement fusion.
  • Understanding the conversion of kinetic energy to internal energy during stagnation is essential for controlling these processes.
  • Current methods for analyzing hydrodynamic dissipation lack direct measurement of the energy conversion lengthscale.

Purpose of the Study:

  • To develop a novel technique for direct analysis of hydrodynamic dissipation.
  • To identify and quantify the lengthscale associated with the conversion of flow energy to internal energy.
  • To demonstrate the technique's utility in theoretical and experimental implosion studies.

Main Methods:

  • Development of a new analytical technique to probe hydrodynamic stagnation.
  • Calculation of a characteristic lengthscale for energy conversion.
  • Application of the technique to theoretical implosion models.
  • Validation using Z-pinch implosion experimental data.

Main Results:

  • A direct method for analyzing hydrodynamic dissipation and energy conversion is established.
  • A quantifiable lengthscale characterizing the flow energy to internal energy conversion is determined.
  • The technique successfully identifies and compares stagnation dynamics in different implosion scenarios.

Conclusions:

  • The developed analysis provides direct insight into the hydrodynamic-dissipation process.
  • The identified lengthscale is a crucial parameter for understanding implosion dynamics.
  • This method offers a valuable tool for both theoretical modeling and experimental analysis of implosions.