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Related Concept Videos

Bernoulli's Equation: Problem Solving01:16

Bernoulli's Equation: Problem Solving

A Venturi meter is essential for measuring fluid flow rates in pipelines. It utilizes the relationship between fluid velocity and pressure described by Bernoulli's equation. When installed in a sewage system, the Venturi meter accurately determines the wastewater flow rate by measuring pressure differences.
The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity equation is...
Bernoulli's Equation00:59

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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 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:
Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

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.
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The Buckingham Pi Theorem01:09

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Dimensionless Groups in Fluid Mechanics01:15

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Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...

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Codimension-three bifurcations in a Bénard-Marangoni problem.

Sergio Hoyas1, Antonio Gil, Pablo Fajardo

  • 1CMT-Motores Térmicos, Universitat Politècnica de València, 46022 València, Spain. serhocal@mot.upv.es

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Summary

This study examines thermoconvective instabilities in an annular domain, identifying four instability patterns like hydrothermal waves and rolls. Understanding these patterns helps clarify experiments and control fluid behavior.

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Published on: October 5, 2018

Area of Science:

  • Fluid dynamics
  • Heat transfer
  • Nonlinear dynamics

Background:

  • Thermoconvection in annular domains is complex.
  • Understanding instability patterns is crucial for controlling fluid behavior.
  • Previous studies have not fully characterized instabilities at low Prandtl and Biot numbers.

Purpose of the Study:

  • To investigate the linear stability of thermoconvection in an annular domain.
  • To identify and map the different instability patterns.
  • To analyze the role of Prandtl and Biot numbers in bifurcations.

Main Methods:

  • Linear stability analysis.
  • Bifurcation theory.
  • Phase plane analysis of Biot-Prandtl numbers.

Main Results:

  • Identified four distinct instability patterns: first and second class hydrothermal waves, longitudinal rolls, and corotating rolls.
  • Mapped these instabilities to specific zones within a small region of the Biot-Prandtl plane.
  • Located codimension-two and codimension-three points defining zone boundaries and intersections.

Conclusions:

  • The findings clarify existing experimental results in thermoconvection.
  • New instability phenomena are predicted.
  • Provides insights into controlling instabilities by manipulating physical parameters.