Related Experiment Video
Updated: Jun 21, 2025
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
11.6K
Variational approach for Stokes flow through a two-dimensional non-uniform channel
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
Summary
This study introduces a variational method to calculate pressure drop in non-uniform channels, offering accurate estimates using channel shape functions.
Area of Science:
- Fluid dynamics
- Applied mathematics
Background:
- Stokes flow analysis is crucial for microfluidics and biomechanics.
- Understanding pressure drop in non-uniform channels is complex.
Purpose of the Study:
- To develop a variational approach for Stokes flow in 2D non-uniform channels.
- To derive an explicit formula for average pressure drop based on channel geometry.
Main Methods:
- Utilizing the stationarity of the Lagrangian to derive Euler-Lagrange equations.
- Formulating a set of ordinary differential equations for pressure drop estimation.
- Comparing results with second-order extended lubrication theory.
Main Results:
- The variational approach accurately estimates average pressure drop.
- Results show excellent agreement with established lubrication theory.
- Higher-order formulations enhance the precision of pressure drop calculations.
Conclusions:
- The proposed variational method provides an efficient and accurate tool for analyzing Stokes flow.
- The derived pressure drop formula offers direct correlation with channel geometry.
- This work contributes to the precise modeling of fluid behavior in complex geometries.
Related Concept Videos
01:30Bernoulli'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
01:16Bernoulli'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.
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
01:17Steady, 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
01:27Uniform 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
01:28Navier–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
01:18Uniform 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