Lecture 3
Flow Properties
Tools to describe flows
Velocity and velocity profile
• The velocity perpendicular to a surface is the
flow per unit of area
• In a generic reference, velocity is a vector with
3 components.
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Spatial variability: 1D, 2D, 3D flow
•
•
•
•
3D flow: velocity varies in all the directions of the space.
2D flow: velocity varies in two space directions.
1D flow: velocity varies in one direction of the space.
Uniform flow: the velocity is uniform, independent of
directions.
• Steady & Uniform (escoamento tampão): uniform and
steady.
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Velocity Profile
Uniform
Boundary layer type (tipo
camada limite)
Parabolic
Steady/permanent (estacionário/permanente) Flow: the velocity does not
change in time.
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Steady flow, imcompressible
flow and inviscid flow
• Steady flow (escoamento estacionário): flow
properties do not change over time (the partial
derivative of any property in order to time is null)
at any point in the system.
• Incompressible flow (incompressivel): density of
a fluid element does not change during its
motion (liquids and gas if the gas velocity is less
than 30% of the speed of sound of the gas).
• Inviscid flow (de fluido ideal): is the flow of an
ideal fluid that is assumed to have no viscosity.
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Streamlines
Streamlines are lines tangent to the
velocity vector.
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Pathline and streakline
• Pathline (trajetória) is the actual pathway of a
fluid particle.
• Streakline (linha de emissão) is the locus of
particles which have earlier passed through a
prescribed point (e.g. smoke from a chimney seen
from far away).
• Streamlines, pathlines and streaklines are
identical in steady flow
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Streamline, pathline and streakline
(Linha de corrente, trajectória e linha de emissão)
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• http://www.youtube.com/watch?v=rDhSdtMj
SpA&feature=relmfu
• http://www.youtube.com/watch?v=BsGbOgV
FoS0
• http://www.youtube.com/watch?v=nuQyKGu
XJOs&feature=related
• http://www.youtube.com/watch?v=DOUfyDH
xkYQ&feature=related
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Information given by the
streamlines
• How much is the flow passing across a streamline?
– Zero, because the velocity is parallel to streamlines!
• How does the flow rate vary between two streamlines from one cross
section to another?
– Remains constant.
• How does the velocity vary between two non-parallel streamlines?
– Increase when they approach and decrease when they move away (if ρ
constant).
• How the resultant of the forces varies between two streamlines?
– It is against the flow when streamlines move away and is in favor when they
approach. According to Newton's Law the resultant force is equal to mass times
acceleration. If the pressure is the most important force, we conclude that it
decrease when velocity increase.
• How the pressure varies from one side to the other of a streamline with
curvature?
– Increases to the outside. When we have curvature we gain velocity (and
momentum) perpendicular to the streamline, to the inside of the curve and so
we have to have an applied force.
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Basic principles of Fluid
mechanics
• Conservation of mass
•
=>
• Newton law:
•
=>
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Eulerian and lagrangian
description
E se o escoamento fosse não estacionário?
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Flow analysis techniques
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