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Fluid Mechanics

Boundary layers are crucial in fluid mechanics, shaping how fluids interact with surfaces. They form thin regions where viscous effects dominate, causing velocity gradients near solid boundaries. Understanding boundary layers is key to analyzing drag, heat transfer, and flow separation.

Boundary layers can be laminar or turbulent, each with distinct characteristics. Laminar layers have smooth, orderly flow, while turbulent layers exhibit chaotic motion. Factors like pressure gradients and Reynolds numbers influence boundary layer behavior, affecting everything from aircraft wings to pipe flow.

Boundary Layer Fundamentals

Boundary layer formation concept

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  • Thin region near a solid surface where viscous effects dominate fluid behavior
    • Velocity gradients become large near the surface due to the no-slip condition (fluid particles have zero velocity relative to the surface)
    • Viscous forces are of the same order of magnitude as inertial forces in this region
  • Forms over immersed bodies as fluid particles adhere to the surface
    • Velocity increases from zero at the surface to the free-stream velocity at the outer edge of the boundary layer
    • Boundary layer thickness δ\delta grows along the surface in the direction of fluid flow (flat plate, airfoil)

Laminar vs turbulent boundary layers

  • Laminar boundary layer exhibits smooth and orderly fluid motion
    • Streamlines remain parallel to each other
    • Velocity profile is parabolic, with a gradual change in velocity from the surface to the free-stream
    • Characterized by lower skin friction compared to turbulent boundary layers
    • Occurs at lower Reynolds numbers (low velocity, small length scales, high viscosity)
  • Turbulent boundary layer exhibits chaotic and irregular fluid motion
    • Velocity and pressure fluctuations are present
    • Velocity profile is fuller, with a rapid change in velocity near the wall
    • Characterized by higher skin friction compared to laminar boundary layers
    • Occurs at higher Reynolds numbers (high velocity, large length scales, low viscosity)
    • Enhanced mixing and heat transfer due to turbulent fluctuations (heat exchangers, combustion chambers)

Boundary Layer Characteristics

Boundary layer thickness calculations

  • Boundary layer thickness δ\delta: distance from the surface where the velocity reaches 99% of the free-stream velocity
    • Mathematically expressed as δ=yu=0.99U\delta = y|_{u=0.99U_\infty}
  • Displacement thickness δ\delta^*: distance by which the external flow is displaced due to the presence of the boundary layer
    • Represents the loss of mass flow rate in the boundary layer compared to the free-stream flow
    • Calculated using the integral expression δ=0(1uU)dy\delta^* = \int_0^\infty (1 - \frac{u}{U_\infty}) dy
  • Momentum thickness θ\theta: measure of the momentum deficit in the boundary layer compared to the free-stream flow
    • Represents the loss of momentum flux in the boundary layer
    • Calculated using the integral expression θ=0uU(1uU)dy\theta = \int_0^\infty \frac{u}{U_\infty} (1 - \frac{u}{U_\infty}) dy

Pressure gradients in boundary layers

  • Favorable pressure gradient (accelerating flow) occurs when pressure decreases in the flow direction (dpdx<0\frac{dp}{dx} < 0)
    • Boundary layer thickness decreases
    • Transition from laminar to turbulent flow is delayed
    • Flow separation is less likely to occur (aircraft wings, diffusers)
  • Adverse pressure gradient (decelerating flow) occurs when pressure increases in the flow direction (dpdx>0\frac{dp}{dx} > 0)
    • Boundary layer thickness increases
    • Transition from laminar to turbulent flow occurs earlier
    • Flow separation is more likely to occur
      1. Separation point is characterized by a zero velocity gradient at the wall (uyy=0=0\frac{\partial u}{\partial y}|_{y=0} = 0)
      2. Reversed flow (negative velocity) is observed near the wall downstream of the separation point (airfoils at high angles of attack, sudden expansions in pipes)
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© 2025 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

© 2025 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.