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Related Concept Videos

Pressure of Fluids01:14

Pressure of Fluids

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There are many examples of pressure in fluids in everyday life, such as in relation to blood (high or low blood pressure) and in relation to weather (high- and low-pressure weather systems). A given force can have a significantly different effect, depending on the area over which the force is exerted. For instance, a force applied to an area of 1 mm2 has a pressure that is 100 times greater than the same force applied to an area of 1 cm2. That's why a sharp needle is able to poke through...
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Hydrostatic pressure on curved surfaces is a fundamental concept in fluid mechanics with broad applications in the civil engineering field. When fluid is in contact with a curved surface, as in a reservoir, dam, or storage tank, it exerts pressure that varies in magnitude and direction along the curved surface. To assess the total hydrostatic force exerted by the fluid on a curved structure, engineers typically isolate the fluid volume adjacent to the surface and analyze the forces acting on...
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Fluid Pressure over Flat Plate of Variable Width01:02

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When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.
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Pressure Variation in a Fluid at Rest01:11

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In a fluid at rest, the pressure at any point beneath the fluid surface depends solely on the depth, not on the container's shape or size. This principle, known as hydrostatic pressure, arises because, in stationary fluids, there is no acceleration, meaning the forces within the fluid balance out. Only vertical forces, caused by the weight of the fluid above, contribute to pressure changes with depth.
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When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
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Fluid Pressure over Curved Plate of Constant Width01:12

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When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the...
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Hydrodynamic fluctuation-induced forces in confined fluids.

Christopher Monahan1, Ali Naji2, Ronald Horgan3

  • 1Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA. chris.monahan@rutgers.edu.

Soft Matter
|October 20, 2015
PubMed
Summary

We investigated hydrodynamic forces between walls in a fluid. We found correlations decay with distance, showing counter-phase interactions, a secondary Casimir effect.

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Area of Science:

  • Fluid dynamics
  • Statistical mechanics
  • Soft matter physics

Background:

  • Hydrodynamic interactions are crucial in confined fluids.
  • Fluctuation-induced forces, like the Casimir effect, are significant at small scales.
  • Understanding these forces is key to predicting fluid behavior in confined geometries.

Purpose of the Study:

  • To investigate thermal, fluctuation-induced hydrodynamic interaction forces between parallel walls in a viscous fluid.
  • To analyze the characteristics of force correlations, including variance and cross-correlations.
  • To explore the nature of these correlations as a secondary Casimir effect.

Main Methods:

  • Utilizing the linearized, stochastic Navier-Stokes formalism of Landau and Lifshitz.
  • Calculating hydrodynamic fluctuations in a classical, compressible, viscous fluid.
  • Analyzing two-point, time-dependent force correlations between rigid, planar walls with no-slip boundary conditions.

Main Results:

  • The mean fluctuation-induced force vanishes; focus is on force correlations.
  • Force variance on a single wall is finite and independent of plate separation at large distances.
  • Cross-plate force correlations decay with inverse inter-plate distance, are negative, and exhibit damped oscillations.

Conclusions:

  • The study reveals long-range hydrodynamic correlations between bounding plates.
  • These correlations exhibit counter-phase behavior, indicating an attractive or repulsive interaction.
  • The findings describe a secondary Casimir effect in the absence of a primary one.