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Related Concept Videos

Boundary Layer Characteristics01:18

Boundary Layer Characteristics

When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

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.
Dry Friction01:30

Dry Friction

Dry friction occurs between two solid surfaces in contact as they attempt to move relative to one another. In daily life, dry friction is encountered in various forms, such as when walking on the ground, sliding an object across a table, or rubbing hands together. Despite its ubiquity, the underlying mechanisms behind dry friction are not readily visible.
To illustrate this concept, imagine a wooden crate resting on a rough, non-uniform horizontal surface. When an external force is applied to...
Frictional Force01:07

Frictional Force

When a body is in motion, it encounters resistance because the body interacts with its surroundings. This resistance is known as friction, a common yet complex force whose behavior is still not completely understood. Friction opposes relative motion between systems in contact, but also allows us to move. Friction arises in part due to the roughness of surfaces in contact. For one object to move along a surface, it must rise to where the peaks of the surface can skip along the bottom of the...
Characteristics of Dry Friction01:21

Characteristics of Dry Friction

Dry friction occurs when two solid surfaces slide against each other without any lubrication or fluid present. It causes resistance when pushing objects along a surface, like a gardener pushing a wheelbarrow. The force applied to move the cart causes dry friction between the wheel and the ground.
Before the wheelbarrow starts moving, the static frictional force acts tangentially to the contact surface, opposing the force that is about to induce the motion. This frictional force prevents the...
Concept of Pressure at a Point01:15

Concept of Pressure at a Point

The concept of pressure at a point in a fluid establishes that pressure within a fluid is uniform in all directions at a specific location. This uniformity occurs because fluid molecules exert force evenly across any point due to their random motion and continuous collisions within the fluid. Pressure at a point is determined by the surrounding fluid molecules and is influenced by factors like depth and density, rather than by shape or orientation.
In a fluid at rest, pressure acts equally in...

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Related Experiment Video

Updated: Jun 5, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

Skin friction in zero-pressure-gradient boundary layers.

Victor Yakhot1

  • 1Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA. vy@bu.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary

This study presents a new solution for fluid dynamics boundary layers. It reveals how boundary layer thickness and skin friction change with increasing Reynolds number (Re) in high-flow conditions.

Area of Science:

  • Fluid Dynamics
  • Aerodynamics
  • Computational Fluid Dynamics

Background:

  • The Navier-Stokes-Prandtl equations govern fluid flow, but exact solutions for boundary layers are complex.
  • Understanding boundary layer behavior is crucial for predicting drag and heat transfer in various applications.

Purpose of the Study:

  • To develop a self-consistent, global approach for solving the Navier-Stokes-Prandtl equations.
  • To analyze the asymptotic behavior of boundary layer thickness and skin friction at high Reynolds numbers.

Main Methods:

  • Formulation of a theoretical framework based on an expansion in a small dimensionless parameter.
  • Derivation of scaling laws for boundary layer thickness (δ) and skin friction coefficient (λ).
  • Analysis of the limit as the Reynolds number based on boundary layer thickness approaches infinity (Re(δ)→ ∞).

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Knowledge Based Cloud FE Simulation of Sheet Metal Forming Processes

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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Main Results:

  • Established a relationship for boundary layer thickness: δ(x) ∝ x/ln(Rex).
  • Determined the scaling for skin friction: λ ∝ 1/ln(δ(x)).
  • Showed that the derivative of boundary layer thickness approaches zero at large distances (dδ(x)/dx → 0).

Conclusions:

  • The presented global approach provides a consistent solution for zero-pressure-gradient boundary layers.
  • The derived asymptotic scaling laws offer new insights into fluid flow behavior at high Reynolds numbers.
  • This theoretical framework has implications for aerodynamic design and performance prediction.