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BackgroundSeveral scientists have contributed to the science of fluid mechanics
• Archimedes ( 250 B.C) : Principles of hydrostatic and flotation
• Newton: Momentum equation.
• Reynold: Laminar & Turbulence.
• Prandtl: Boundary layer.
• Euler & Bernoulli: Fluid motion.
• Mach: Supersonic flow.
• Riemann: Shock waves.
Introduction to Fluid Mechanics
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Definitionsa. Fluid Mechanics (there is more than one definition)
b. Fluid (Liquid, Gas & Plastic solids)
• Fluid is defined as a substance that continually deforms (flows)under an applied shear stress regardless of how small the applied stress.
• Anything that flows, either liquid or gas. Some solids can also exhibit fluid behavior over time.
• The science that deals with the action of forces on fluid.
• The branch of mechanics that deal with gases and liquids, either at rest or in motion.
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Dimensions
A Dimension is a category that represents a physical quantity such as mass, length, time , momentum, force , acceleration, and energy.
Primary Dimensions
L m
M kg
T sθ Ki AC cd
MoleAmount of Matter
Amount of light
Electric Current
Temperature
Time
Mass
Length
Units (SI)SymbolDimension
N
Other dimensions not mentioned in the table are called
Secondary Dimensions
Examples of Secondary dimensions
(Force, acceleration, momentum)
[ ] [ ] DimensionsCalledamF :×=
[ ] [ ] 22
dimPr
TML
TLMamF
forceofensionimary
=×=×=
=
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Dimensionless Groups
A Dimensionless Group is any arrangement of variables in which the primary dimensions cancel out. Examples: Mach number: (M), Reynolds number; (Re)
A Dimensional Homogeneity is when the primary dimensions on each term are the same.
Dimensional Homogeneity
Primary dimensions on a derivative
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Primary dimensions of an integral
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Dimensional Homogeneity
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Dimensional Homogeneity
Prove the equation below for dimension homogeneity
)()( ybayyV −=
[ ] [ ]
[ ] [ ]
[ ] [ ]
[ ] [ ]LbhaveweEqninEqnSubstitute
LTaei
TLaLAnd
Tab
TLabL
aLabLTL
ayabyybayyV
=
=
=
=
=
−=
−=−=
),1.()2.(
)2.(..........1..,
)1....(....................1,
)()(
2
2
2
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Applications and Connections of Fluid Mechanics
1. Hydraulics
1. Hydrology
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Flow Classification3. Aerodynamics
4. Bio-fluid Mechanics
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5. Acoustics
Flow Classification
6. Micro-channel flow
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7. Computational Fluid Dynamics
Flow Classification
8. Petroleum Engineering
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9. Atmospheric Science
Flow Classification
10. Electrical Engineering
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11. Environmental Engineering
Flow Classification
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END
of Chapter One
