Abstract
In this
experiment we studied the effect of smoothness and roughness of a surface on
the boundary layer thickness and Reynolds number. And the relation of friction
with the streamlines (effect of viscosity). By the end of this experiment we
calculated Reynolds number, boundary layer thickness, and the momentum
thickness both experimentally and theoretically and for smooth and rough
surfaces.
Introduction
All
experimental observations indicate that a fluid in motion comes to a complete
stop at the surface and assumes a zero velocity relative to the surface. That
is, a fluid in direct contact with a solid “sticks” to the surface due to
viscous effects, and there is no slip. This is known as the no-slip condition.
Therefore, the
no-slip condition is responsible for the development of the velocity profile.
The flow region adjacent to the wall in which the viscous effects (and thus the
velocity gradients) are significant is called the boundary layer.
A fluid layer adjacent
to a moving surface has the same velocity as the surface.
A consequence
of the no-slip condition is that all velocity profiles must have zero values
with respect to the surface at the points of contact between a fluid and a
solid surface
The x-coordinate is measured along the plate surface from the leading edge of the plate in the
direction of the flow, and y is measured from the surface in the normal
direction. The fluid approaches the plate in the x-direction with a uniform velocity V,
which is practically identical to the free-stream velocity over the plate away
from the surface
Results
For the two cases the flow was
laminar (Re<Re.cr)
The smooth surface had much higher
velocity thus higher Reynolds number
For the smooth surface the boundary
layer thickness and the momentum thickness was less the for the rough surface
The values of the momentum thickness
experimentally was not very close to the ones calculated theoretically, also
for the boundary layer thickness there was a large error
Error in momentum thickness=67.7%,
72.7%
Conclusion
Friction force
per unit area is called shear stress, and is denoted by τ. Experimental studies
indicate that the shear stress for most fluids is proportional to the velocity
gradient
The values of
friction coefficient and the shear were as expected, higher values for the
rough surface.
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