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Related Concept Videos

Bernoulli's Principle01:01

Bernoulli's Principle

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Bernoulli's equation incorporates how fluid pressure changes across a static, incompressible fluid by equating the kinetic energy contribution to zero. It is also helpful in analyzing horizontal flows in which the gravitational energy density is constant throughout. The latter equation is so useful that it is called Bernoulli's principle. According to Bernoulli's principle, the fluid pressure drops if the speed increases and vice versa.
Bernoulli's principle has several...
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Bernoulli's Equation00:59

Bernoulli's Equation

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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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Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

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Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
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Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

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Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines.
999
Bernoulli's Principle: Applications01:17

Bernoulli's Principle: Applications

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There are many devices and situations in which fluid flows at a constant height and so can be analyzed using Bernoulli's principle. These devices include, but are not limited to, entrainment devices and fluid flow measuring devices.
Entrainment devices use a high fluid speed to create low pressures and, thus, entrain one fluid into another. Some examples of these devices are given below:
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Steady, Laminar Flow in Circular Tubes01:23

Steady, Laminar Flow in Circular Tubes

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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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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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The Bernoulli effect in horizontal granular flows.

Hui Cai1, Changcheng Sun2, Guoqing Miao3

  • 1School of Electrical Engineering, Yancheng Institute of Technology, Yancheng 224051, China. caihui@ycit.edu.cn.

Soft Matter
|November 22, 2021
PubMed
Summary
This summary is machine-generated.

The Bernoulli effect, seen in continuous fluids, also occurs in granular flows. Granular flow pressure remains constant despite velocity changes, influenced by vibration intensity and frequency.

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Area of Science:

  • Physics
  • Fluid Dynamics
  • Granular Materials Science

Background:

  • The Bernoulli effect describes the inverse relationship between fluid velocity and static pressure in continuous fluids.
  • Research on this effect in discrete media, such as granular flows, is limited.

Purpose of the Study:

  • To experimentally investigate the relationship between flow velocity and pressure in horizontal granular flows.
  • To determine if the Bernoulli effect manifests in granular systems under external excitation.

Main Methods:

  • Horizontal granular flows were generated and excited by vertical vibration.
  • The pressure dynamics within the granular flow were measured and analyzed.
  • The influence of vibration intensity and frequency on flow properties was examined.

Main Results:

  • Granular flow pressure was found to remain nearly constant over time and height, indicating a granular Bernoulli effect.
  • The random and directed motions of granules were observed to mutually restrict each other.
  • The pressure constant was dependent on vibration intensity and frequency, reflecting energy transfer dynamics.

Conclusions:

  • The Bernoulli effect is demonstrated in granular flows, though with distinct dynamics compared to continuous fluids.
  • Granular flow behavior exhibits unique properties influenced by particle interactions and external energy input.
  • The findings highlight the complex interplay between motion, pressure, and energy in discrete granular systems.