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Energy Conservation and Bernoulli's Equation01:16

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Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
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In the middle of the nineteenth century, it was observed that two trains passing each other at a high relative speed get pulled towards each other. The same occurs when two cars pass each other at a high relative speed. The reason is that the fluid pressure drops in the region where the fluid speeds up. As the air between the trains or the cars increases in speed, its pressure reduces. The pressure on the outer parts of the vehicles is still the atmospheric pressure, while the resultant...
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The study of external flow is essential for creating structures and objects that interact efficiently and safely with moving fluids, such as air or water. When a body is immersed in a flowing fluid, it experiences two primary forces: drag, which opposes motion along the flow direction, and lift, which acts perpendicular to the flow. The shape, size, and orientation of the object influence these forces.Streamlined and Blunt Bodies in External FlowObjects in fluid flow are classified as...
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Energy dissipation in flows through curved spaces.

J-D Debus1, M Mendoza1, S Succi2

  • 1ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Str. 27, HIT, CH-8093 Zürich, Switzerland.

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Fluid dynamics in curved spaces causes energy loss due to intrinsic curvature, not just obstacles. This curvature-induced viscosity leads to significant energy dissipation in various physical systems.

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Area of Science:

  • Fluid dynamics
  • General Relativity
  • Biophysics

Background:

  • Fluid motion in curved geometries is common in nature, from biological membranes to cosmological scales.
  • Inertial forces from space curvature affect particle motion in these systems.

Purpose of the Study:

  • To reveal a fundamental process in curved-space fluid dynamics.
  • To investigate energy loss in fluids due to intrinsic space curvature.

Main Methods:

  • Theoretical analysis of fluid dynamics in intrinsically curved geometries.
  • Investigating the role of inertial forces and viscous stresses.

Main Results:

  • Free fluid motion in curved spaces exhibits energy loss solely from intrinsic curvature.
  • Local curvature sources generate viscous stresses due to inertial forces.
  • Curvature-induced viscous forces cause significant, previously unnoticed energy dissipation.

Conclusions:

  • Intrinsic space curvature is a source of energy dissipation in fluid dynamics.
  • This phenomenon may be significant in diverse physical systems involving curved geometries.