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Fluid Pressure over Curved Plate of Constant Width

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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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Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
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When a solid is dipped inside a liquid, the liquid surface becomes curved near the contact. For some solid–liquid interfaces, the liquid is pulled up along the solid, while for others, the liquid surface is convex or depressed near the solid surface. This phenomenon can be explained using the concept of cohesive and adhesive forces.
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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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Steady, Laminar Flow Between Parallel Plates01:17

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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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Fluid Pressure over Flat Plate of Constant Width01:05

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When a body is submerged in water, it experiences fluid pressure acting normal on its surface and distributed over its area. For better design structures, it is crucial to determine the magnitude and location of the resultant force acting on the surface. In the case of a rectangular plate of constant width submerged in water, the pressure increases with depth, resulting in a linearly varying trapezoidal pressure distribution from the upper to the lower edge of the plate.
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Related Experiment Video

Updated: Apr 12, 2026

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces
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Cusps and cuspidal edges at fluid interfaces: Existence and application.

R Krechetnikov1

  • 1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada AB T6G 2G1.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2015
PubMed
Summary
This summary is machine-generated.

This study links fluid dynamics singularities to geometric ones at fluid interfaces. A key finding is that surface tension variation is necessary for geometric singularities, which are crucial for energy conversion.

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Area of Science:

  • Fluid Dynamics
  • Geometric Singularity Theory
  • Interfacial Phenomena

Background:

  • Investigating the relationship between dynamic and geometric singularities in fluid dynamics.
  • Understanding unbounded velocity fields and diverging curvature at fluid interfaces.

Purpose of the Study:

  • To establish a connection between real fluid interfaces and geometric singularity theory.
  • To identify conditions for the existence of interfacial singularities.
  • To explore the interplay between dynamic and geometric singularities.

Main Methods:

  • Focusing on generic interfacial singularities: genuine cusps and cuspidal edges.
  • Analyzing singularities in both two and three dimensions.
  • Developing explicit asymptotic solutions for flow fields and interface shapes near steady-state singularities.

Main Results:

  • Established a necessary condition for geometric singularities: variation of surface tension.
  • Demonstrated that dynamic and geometric singularities entail each other only in 3D cusps.
  • Provided explicit asymptotic solutions for flow and interface behavior near singularities.

Conclusions:

  • Geometric singularities are linked to fluid dynamics, with surface tension variation being a key factor.
  • The interplay between dynamic and geometric singularities is specific to 3D cusps.
  • Interfacial singularities are fundamental to chemical-to-mechanical energy conversion.