Fluid Mechanics Lecture 1

8/9/2019 Fluid Mechanics Lecture 1

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Engineering Fluid MechanicsCWR 3201 (Sec. 1)

Spring 2015

Dr. Kelly Kibler



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



Basic concepts of

fluid mechanicsEngineering Fluid Mechanics, Lecture 1

January 12, 2015Dr. Kelly Kibler



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.



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.


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?



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




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.


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.



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.




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.


Unlike a liquid, a gas does notform a free surface, and it expandsto fill the entire available space.



Velocity profile at a solid-fluid interface


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.



Velocity profile at a solid-fluid interface


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.



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



Classification of fluid flows

viscous vs. inviscid flow


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.




regions of viscous vs. inviscid flow


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




internal vs. external flow


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




compressible vs. incompressible flow


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.




compressible vs. incompressible flow


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

l f f fl d fl




laminar vs. turbulent flow


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)

Cl f f fl d fl




natural (unforced) vs. forced flow


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.



Classification of fluid flowssteady vs. unsteady; uniform vs. nonuniform


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



Classification of fluid flowsdeveloping vs. fully developed flows


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.

l f f fl d fl



Classification of fluid flowsone, two, and three dimensional flows


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.

Cl f f fl d fl






Velocity varies both in r and z dimensions,thus flow is two-dimensional.

Cl ifi i f fl id fl






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.

P bl l i i fl id



Problem solving in fluidsdimensions and units


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.

P bl l i i fl id



Problem solving in fluidsconversion ratios


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

P bl l i i fl id



Problem solving in fluidsaccuracy, precision, and significant digits

28

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

Fluid Mechanics Lecture 1

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