fluid mechanics lecture 1
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8/9/2019 Fluid Mechanics Lecture 1
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Engineering Fluid MechanicsCWR 3201 (Sec. 1)
Spring 2015
Dr. Kelly Kibler
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Course content WeekBasic concepts of FluidMechanics; Fluid properties
1
Fluid properties 2
Fluid statics 3
Fluid kinematics 4
Energy 6, 7
Momentum 8, 10
Dimensional analysis 12
Internal flow 13
Differential flow 14
Open channel flow 15
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Basic concepts of
fluid mechanicsEngineering Fluid Mechanics, Lecture 1
January 12, 2015Dr. Kelly Kibler
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INTRODUCTION- fluids
• Fluids are matter in liquid or gaseous phase.
• A fluid deforms continuously under the influence of shearstress , no matter how small.
• By contrast, solids can resist shear stress by deforming.
Engineering Fluid Mechanics- Basic concepts of fluid mechanics5
When a constant shear force is
applied, a solid eventually stops
deforming at some fixed strain angle
α, whereas a fluid never stops
deforming and approaches aconstant rate of strain.
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INTRODUCTION- fluids
• Fluids are matter in liquid or gaseous phase.
• A fluid deforms continuously under the influence of shearstress , no matter how small.
• By contrast, solids can resist shear stress by deforming.
Engineering Fluid Mechanics- Basic concepts of fluid mechanics6
When a constant shear force is
applied, a solid eventually stops
deforming at some fixed strain angle
α, whereas a fluid never stops
deforming and approaches aconstant rate of strain.
What would happen if the rubber were a fluid?
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INTRODUCTION- fluid mechanics
Fluid mechanics
behavior of fluids under the influence of forces fluid statics- fluids at rest fluid dynamics- fluids in motion
interaction of fluids at fluid-solid or fluid-fluid interfaces
Categories of fluid mechanicshydrodynamics- flow of incompressible fluidshydraulics- liquid flows in pipes of open channels gasdynamics- flow of fluids with significant density changesaerodynamics- flow of gases over bodies
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Fluid forces- components of stress
Stress – force per unit area
Normal stress (σ) – normalcomponent of force acting on asurface per unit area
Pressure – normal stress on a staticfluid
Shear stress (τ) – tangentialcomponent of force acting on asurface per unit area
Shear stress develops between layersof fluid moving at differentvelocities;
when fluids move shear stressdevelops.
When fluids are static, they are in astate of zero shear stress.
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The normal stress and shear stressat the surface of a fluid element.For fluids at rest, the shear stressis zero and pressure is the onlynormal stress.
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Phases of matterSolids
Intermolecular bonds are strong relative to liquids and gases.
Molecules are packed close together- because of the small distances, attractiveforces are large. Positions of individual molecules are fixed relative to one another.
Liquids Strength of intermolecular bonds is intermediate, weaker than solids but
strong relative to gases. Molecular spacing is similar to solids. Positions of individual molecules are not fixed relative to one another and
molecules may rotate and translate freely.Gases Intermolecular bonds are weak relative to liquids and solids. Molecules spaced far from one another- intermolecular forces are small. Molecular ordering is nonexistent; particles move at random. Molecules in the gas phase are at a higher energy state than those in liquid or
solid phase.
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Properties of liquids and gases
In a liquid, volume remains
relatively constant because of thestrong cohesive forces between themolecules.
As a result, a liquid takes the shapeof the container it is in, and it forms afree surface.
Gas molecules are widely spaced,and the cohesive forces betweenthem are very small.
Therefore, a gas expands until itencounters the walls of the container
and fills the entire available space. Unlike liquids, a gas in an open
container cannot form a free surface.
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Unlike a liquid, a gas does notform a free surface, and it expandsto fill the entire available space.
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Velocity profile at a solid-fluid interface
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Due to the no-slip condition, at a solid-fluid interface, the velocity of the fluidand the solid must be equal. If the solidis stationary, velocity of the fluid isequal to zero.
z
velocity
Boundary
layer
The no-slip condition Fluid in motion comes to a
complete stop (velocity = 0) at astationary solid-fluid interface.
Fluid layer that “sticks” to thesurface slows the next fluid layer,
and so on, creating a characteristicparabolic velocity-depth profile.
Region of flow affected by thevelocity gradient is called theboundary layer
In turn, the fluid exerts drag forceon the solid in the direction offlow.
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Velocity profile at a solid-fluid interface
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Due to the no-slip condition, at a solid-fluid interface, the velocity of the fluidand the solid must be equal. If the solidis stationary, velocity of the fluid isequal to zero.
z
velocity
Laminarsublayer
Boundary
layer
The no-slip condition Region of flow affected by the
velocity gradient is called theboundary layer
Region of the boundary layerwhere the velocity gradient islinear is known as the laminarsublayer.
Because inertial forces aremore balanced by viscousforces in the laminar sublayer,flow properties are different inthis region.
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Influence of the solid-fluid interface to fluid velocities
In cross-sectional flow of the San Joaquin River, you can seethe influence of no-slip physics on fluid flow velocities
13River Ecohydraulics - Physical aquatic habitat of lotic ecosystems
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Classification of fluid flows
viscous vs. inviscid flow
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Viscosity is a measure of internalresistance to flow; the internal“stickiness” of the fluid.
When two layers of flow move relativeto one another, the slower layer tries toslow down the faster layer. A frictionforce develops between the layers; the
strength of the internal friction isdescribed by the viscosity. All fluids have viscosity, but we may
neglect viscous forces in some cases. In viscous flows frictional effects are
significant and may not be neglected.
In regions of inviscid flow, viscousforces are small relative to inertial orpressure forces and may be neglectedin analysis.
Neglecting viscous terms in inviscidflow regions greatly simplifies analysis
without much loss of accuracy.
In this picture, viscosity of the
fluids increases from left toright.
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Classification of fluid flows
regions of viscous vs. inviscid flow
Engineering Fluid Mechanics- Basic concepts of fluid mechanics15
At a solid-fluid interface, a
viscous flow regiondevelops very close to thesurface. This is thelaminar sublayer. Theremainder of the flow isthe inviscid flow region.
z
Laminar sublayer-viscous flow region
Inviscid flowregion
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Classification of fluid flows
internal vs. external flow
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Flow of an unbounded fluid overa surface is external flow.
Viscous effects are limited tosolid-fluid interfaces and inwake regions downstream ofobjects.
Flow completely bounded bysolid surfaces (e.g. in a pipe) isinternal flow.
Viscous effects influence theentire flow field.
Flows of liquid in a partially-filled duct with a free surface isopen channel flow.
External flow
Internal flow
Open channel flow
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Classification of fluid flows
compressible vs. incompressible flow
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Flows with nearly constant density are assumedincompressible.
If we assume a fluid is incompressible, we assume that thevolume of the fluid remains unchanged over the course ofmotion.
Application to liquids densities of liquids are nearlyconstant, therefore we may approximate liquids asincompressible.
Application to gases Gases are highly compressible.
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Classification of fluid flows
compressible vs. incompressible flow
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Gases are highly compressible. To determine if a gas flowmay be modeled as incompressible requires analysis ofMach number (Ma, dimensionless):
c = 346 ms-1 in air at STPMa < 1 Subsonic flow (some maybe modeled as incompressible)Ma = 1 Sonic flowMa > 1 Supersonic flowMa >> 1 Hypersonic flow
Gas flows can be modeled as incompressible if densityvariations are < 5% (usually when Ma < 0.3).
Good rule of thumb: compressibility may be neglected inproblems involving flows of air at STP at speeds under 100 ms-1
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Classification of fluid flows
laminar vs. turbulent flow
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Laminar flow- highlyordered fluid motioncharacterized by smoothlayers of fluid
Turbulent flow- Highly
disorganized fluid motioncharacterized by velocityfluctuations
Transitional flow- A flowthat alternates between
being laminar andturbulent.
Turbulence is characterized byReynolds number (Re, dimensionless)
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Classification of fluid flows
natural (unforced) vs. forced flow
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Forced flow- fluid is forcedto flow over a surface or ina pipe by external meanssuch as a pump or a fan.
Natural flow- fluid motionis due to natural means
such as buoyancy orgravity.
The fan is forcing air flow over the dog.
Water flows naturally over an elevation
gradient.
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Classification of fluid flowssteady vs. unsteady; uniform vs. nonuniform
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steady flow- properties offlow (velocity, temperature,volumetric flow ect.) at agiven point in space do notchange over time
unsteady flow- properties
of flow at a given point inspace change over time
transient flow- describesdeveloping flows
uniform flow- over a givenregion, properties of flowdo not change spatially
nonuniform flow-over agiven region, properties offlow vary through space
(a) An instantaneous snapshot of an
unsteady flow, and (b) a longexposure (time-averaged) picture ofthe same flow approximates thesteady flow condition.
Changeover time
Variationin space
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Classification of fluid flowsdeveloping vs. fully developed flows
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When a fluid flows over a surface (e.g. enters a pipe), the velocityprofile changes with z for some length until the flow stabilizes suchthat velocity is constant with respect to z.
Flow which has stabilized in this way is fully developed.
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Classification of fluid flowsone, two, and three dimensional flows
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Flow is said to be one-, two-, or three-dimensional if the velocityvaries in one, two or three dimensions, respectively.
Velocity of fully developed flow in a pipedepends only on r, thus it is one-dimensional.
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Classification of fluid flowsone, two, and three dimensional flows
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Flow is said to be one-, two-, or three-dimensional if the velocityvaries in one, two or three dimensions, respectively.
Velocity varies both in r and z dimensions,thus flow is two-dimensional.
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Classification of fluid flowsone, two, and three dimensional flows
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Flow is said to be one-, two-, or three-dimensional if the velocityvaries in one, two or three dimensions, respectively.
If the velocity variation in one or two dimension is small relative tothe other dimension(s), flow may be modeled as one- or two-dimensional.
Assuming one- or two-dimensional flow greatly simplifies problemsolving and computation time.
Since the antennae length is muchgreater than the diameter and the
flow of air over the length isuniform, air flow over the carantennae may be modeled as two-dimensional.
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Problem solving in fluidsdimensions and units
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Dimensions
Primary dimensions, for instance mass (m), length (L), time (t) Secondary dimensions are derived from primary dimensions, for
instance velocity (Ls-1), volumetric flow (L3s-1), force (mLs-2)
Units
Units express the magnitudes assigned to dimensions. Mass in kilograms (kg), length in meters (m), flow in cubic meters per second
(m3s-1)
Two systems used in this class: English and SI
Dimensional homogeneity
All equations must be dimensionally homogeneous (all terms musthave the same dimensions).
A formula that is dimensionally homogeneous is not necessarily right, buta formula that is not dimensionally homogeneous is definitely wrong.
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Problem solving in fluidsconversion ratios
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Unity conversion ratios are equal to 1 and unitless. May be inserted into any computation to properly convert units.
A formula that is dimensionally homogeneous is not necessarily right, buta formula that is not dimensionally homogeneous is definitely wrong.
Example 1-4: Using unity conversion ratios, show that 1.00
lbm weighs 1.00 lbf on earth.
To solve this problem, we will use the unity conversion: lbf
32.74lbm∙t
s
= 1
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Problem solving in fluidsaccuracy, precision, and significant digits
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Accuracy error (inaccuracy) is the value of a reading minus the true
value. Associated with repeatable, fixable errors. How close is the reading to the true value?
Precision error is the value of a given reading minus the mean of aset of readings. Associated with unrepeatable, random error. How good is your instrument at providing a consistent reading?
Significant digits indicate precision of a reading or calculation.
A solution to an engineering calculation may not be reported withmore precision than the information used to derive the solution.
The least significant numeral in a number implies the precision of ameasurement or calculation.
When performing calculations or manipulations of severalparameters, the final result is only as precise as the least preciseparameter in the problem.
Determine significant digits as a final step in a solution