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相关概念视频

Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

954
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:
954
Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

841
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.
841
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

171
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.
171
Uniform Depth Channel Flow01:27

Uniform Depth Channel Flow

67
Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant cross-section...
67
Navier–Stokes Equations01:28

Navier–Stokes Equations

469
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
469
Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

61
To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
61

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相关实验视频

Updated: Jun 21, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

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斯托克斯流通过一个二维的非均通道的变化方法.

Abhishek Banerjee1,2,3, Alexander Oron4, Yehuda Agnon5

  • 1Department of Mathematics, SRM Institute of Science and Technology Kattankulathur, Chennai, 603203, India. abhishek.rajnagr@gmail.com.

Scientific reports
|July 8, 2024
PubMed
概括

本研究引入了一种可变的方法来计算非均通道中的压力下降,使用通道形状函数提供准确的估计.

关键词:
欧勒 - 拉格朗日方程式有限体积方法的有限体积方法.斯托克斯的流量流动.变量微积分是一个变量微积分.

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Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure
07:15

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Published on: April 25, 2025

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Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

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相关实验视频

Last Updated: Jun 21, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

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Published on: July 19, 2016

11.6K
Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure
07:15

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Published on: April 25, 2025

236
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
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科学领域:

  • 流体动力学 流体动力学
  • 应用数学 应用数学 应用数学

背景情况:

  • 冲击流分析对于微流体学和生物力学至关重要.
  • 了解非均通道中的压力下降是复杂的.

研究的目的:

  • 开发一种对2D非均通道中的斯托克斯流的变化方法.
  • 根据通道几何学来得出平均压力下降的明确公式.

主要方法:

  • 使用拉格朗的静态性来导出欧勒-拉格朗方程.
  • 制定一组普通微分方程来估计压力下降.
  • 将结果与二级扩展滑理论进行比较.

主要成果:

  • 变化方法准确地估计了平均压力下降.
  • 结果显示与已建立的滑理论有很好的一致性.
  • 高级配方提高了压力下降计算的精度.

结论:

  • 拟议的变量方法为分析斯托克斯流提供了一个高效和准确的工具.
  • 衍生出的压力下降公式提供了与通道几何学的直接相关性.
  • 这项工作有助于精确建模复杂几何体内的流体行为.