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Accelerating Fluids

Accelerating Fluids

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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Steady, Laminar Flow in Circular Tubes

Steady, Laminar Flow in Circular Tubes

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...

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...

Steady, Laminar Flow Between Parallel Plates

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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.

Eulerian and Lagrangian Flow Descriptions

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Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...

Newtonian Fluid: Problem Solving

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Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
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Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

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Layer-Based Simulation for Three-Dimensional Fluid Flow in Spherical Coordinates.

Ruihong Cen, Bo Ren

IEEE Transactions on Visualization and Computer Graphics

|February 8, 2024

Summary

This summary is machine-generated.

This study introduces a 3D spherical coordinate fluid flow simulator. It handles arbitrary terrain and offers artistic control for graphics applications.

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Area of Science:

Computer Graphics
Computational Physics
Fluid Dynamics

Background:

Fluid flows in spherical coordinates are gaining interest in computer graphics.
Existing research primarily addresses 2D manifold flows, leaving 3D simulations with challenges.
Unresolved issues include boundary conditions for arbitrary obstacles and artistic control in 3D spherical simulations.

Purpose of the Study:

To propose a practical simulator for 3D fluid flow motions in spherical domains.
To address limitations in existing 3D spherical coordinate fluid simulations.
To provide flexible artistic controls for art design.

Main Methods:

A layer-by-layer structure for simulation.
A boundary-aware pressure solving scheme.
Building upon conventions of 2D-manifold spherical-coordinate simulations.

Main Results:

Successful recovery of horizontal and vertical flow motions.
Simulation within a spherical shell of finite thickness.
Capability to handle arbitrary terrain shapes.

Conclusions:

The proposed method enables practical 3D fluid flow simulations in spherical coordinates.
It effectively handles complex terrains and offers artistic control.
It extends previous 2D methods to a 3D domain.