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Boundary
Layers
By
neglecting the viscosity of the moving fluid an important
feature of the flow over a solid body has been lost. In the continuum approximation,
the fluid in contact with the surface of a solid body is at rest with
respect to the body. A long distance from the surface the flow will have its
undisturbed velocity. A velocity gradient therefore exists over some region,
the boundary layer, and viscous shear stresses will act on the fluid. These
stresses are larger for larger velocity gradients.
The development
of a boundary layer in a fluid passing over a stationary flat plate is illustrated
below. The thickness, d, of the
boundary increases with distance along the plate. Initially the flow is laminar
and the region of velocity change defines the thickness. In this region
the fluid particles have simple trajectories. As the fluid moves further down
the plate the flow undergoes a transition to turbulence. This behavior was
seen in the smoke tunnel pictures of flow over the top surface of a wing. The
fluid particles in the turbulent zone have complex trajectories and the mixing
of outer and close-to-the-wall fluid is increased by this motion. The velocity
gradient near the surface is larger than that for laminar flow and the
turbulent boundary layer extends further than the velocity gradient. The increased
near-surface velocity gradient in the turbulent region gives rise to
larger viscous shear stresses in the fluid. The wall friction in the turbulent
region is, therefore, higher than that in the laminar flow region. |
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