EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of...

47
Fundamentals of Engineering Fundamentals of Engineering Fundamentals of Engineering Fundamentals of Engineering (FE) Exam (FE) Exam General Section General Section Fluid Mechanics Review Fluid Mechanics Review Steven Burian Steven Burian Steven Burian Steven Burian Civil & Environmental Engineering Civil & Environmental Engineering October 26, 2010 October 26, 2010 October 26, 2010 October 26, 2010

Transcript of EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of...

Page 1: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Fundamentals of EngineeringFundamentals of EngineeringFundamentals of Engineering Fundamentals of Engineering (FE) Exam(FE) Exam( )( )

General SectionGeneral SectionFluid Mechanics ReviewFluid Mechanics Review

Steven BurianSteven BurianSteven BurianSteven BurianCivil & Environmental EngineeringCivil & Environmental Engineering

October 26, 2010October 26, 2010October 26, 2010October 26, 2010

Page 2: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

XX Fluid MechanicsFluid MechanicsFluids and FEFluids and FE

X.X. Fluid MechanicsFluid MechanicsA. Flow measurementA. Flow measurementB. Fluid propertiesB. Fluid propertiesC. Fluid staticsC. Fluid statics

7% of FE Morning 7% of FE Morning SessionSession

C. Fluid staticsC. Fluid staticsD. Energy, impulse, and momentum equationsD. Energy, impulse, and momentum equationsE. Pipe and other internal flowE. Pipe and other internal flow

IV Fluid DynamicsIV Fluid DynamicsIV. Fluid DynamicsIV. Fluid DynamicsA. Bernoulli equation and mechanical energy balanceA. Bernoulli equation and mechanical energy balanceB. Hydrostatic pressureB. Hydrostatic pressureC. Dimensionless numbers (e.g., Reynolds Number)C. Dimensionless numbers (e.g., Reynolds Number)C. Dimensionless numbers (e.g., Reynolds Number)C. Dimensionless numbers (e.g., Reynolds Number)D. Laminar and turbulent flowD. Laminar and turbulent flowE. Velocity headE. Velocity headF. Friction losses (e.g., pipes, valves, fittings)F. Friction losses (e.g., pipes, valves, fittings)( g , p p , , g )( g , p p , , g )G. Pipe networksG. Pipe networksH. Compressible and incompressible flowH. Compressible and incompressible flowI. Flow measurement (e.g., orifices, Venturi meters)I. Flow measurement (e.g., orifices, Venturi meters)

10% of FE Afternoon 10% of FE Afternoon SessionSession

J. Pumps, turbines, and compressorsJ. Pumps, turbines, and compressorsK. NonK. Non--Newtonian flowNewtonian flowL. Flow through packed bedsL. Flow through packed beds

Page 3: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.
Page 4: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

FluidsFluidsFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

!! Fluids are substances in either the liquid Fluids are substances in either the liquid or gas phaseor gas phase

Fluid Fluid PropertiesProperties

!! Fluids cannot support shear, and they Fluids cannot support shear, and they deform continuously to minimize applieddeform continuously to minimize applied

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics deform continuously to minimize applied deform continuously to minimize applied

shear forcesshear forcesEnergy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 5: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

FE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 6: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

ViscosityViscositySh t (Sh t ( )) ff

FE Fluid FE Fluid Mechanics Mechanics

ReviewReview

!! Shear stress (Shear stress (!!):): force force required to slide one unit required to slide one unit area layer of a substance area layer of a substance over anotherover another

Fluid Fluid PropertiesProperties

over anotherover another!! Viscosity (Viscosity (""): ): measure of a measure of a

fluid’s resistance to flow fluid’s resistance to flow when acted upon by anwhen acted upon by an

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics when acted upon by an when acted upon by an

external force (i.e., ease with external force (i.e., ease with which a fluid pours)which a fluid pours)

!! As a fluid moves a shearAs a fluid moves a shear

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

!! As a fluid moves a shear As a fluid moves a shear stress is developed in it; stress is developed in it; magnitude is dependent on magnitude is dependent on viscosity of fluidviscosity of fluid

Momentum Momentum and Dragand Drag

viscosity of fluidviscosity of fluid

Page 7: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

F/AF/A is the fluid shear stress (is the fluid shear stress (!!)) and the constant and the constant of proportionality is the absolute viscosity (of proportionality is the absolute viscosity (""))::

FE Fluid FE Fluid Mechanics Mechanics

ReviewReview p p y y (p p y y (""))

du"! #Fluid Fluid

PropertiesProperties

dy"!

Newtonian fluids:Newtonian fluids: strains are proportional to thestrains are proportional to the

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Newtonian fluids:Newtonian fluids: strains are proportional to the strains are proportional to the applied shear stressapplied shear stress

NonNon--Newtonian fluids:Newtonian fluids: fluid shear stress can befluid shear stress can be

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

NonNon--Newtonian fluids:Newtonian fluids: fluid shear stress can be fluid shear stress can be computed using the power lawcomputed using the power lawMomentum Momentum

and Dragand Drag

"The kinematic viscosity is the ratio of The kinematic viscosity is the ratio of the absolute viscosity to mass density:the absolute viscosity to mass density: $

"% #

Page 8: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

FE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 9: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Surface TensionSurface TensionFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

!! The “skin” that seems to form on the free surface The “skin” that seems to form on the free surface of a fluid is caused by intermolecular cohesive of a fluid is caused by intermolecular cohesive forces and is known as surface tension, forces and is known as surface tension, &&

Fluid Fluid PropertiesProperties

!! Surface tension can be interpreted as the tensile Surface tension can be interpreted as the tensile force between two points a unit distance apart on force between two points a unit distance apart on the surfacethe surface

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics the surfacethe surface

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 10: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

CapillarityCapillarityFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

!! Capillary action Capillary action is caused by surface tension is caused by surface tension between the liquid and a vertical solid surfacebetween the liquid and a vertical solid surface

!! In water, adhesive forces between liquid In water, adhesive forces between liquid

Fluid Fluid PropertiesProperties

, q, qmolecules and surface are greater than cohesive molecules and surface are greater than cohesive forces between water molecules; adhesive forces forces between water molecules; adhesive forces cause water to attach itself to and climb solid cause water to attach itself to and climb solid vertical surfacevertical surface

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

vertical surfacevertical surfaceEnergy, Energy,

Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 11: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

PressurePressureFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

!! Hydrostatic pressure is the pressure a Hydrostatic pressure is the pressure a fluid exerts on an immersed object or fluid exerts on an immersed object or

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow jj

on container wallson container walls!! Pressure is equal to the force per unit Pressure is equal to the force per unit

Momentum Momentum and Dragand Drag

area of the surface:area of the surface:

FAFP #

Page 12: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

PressurePressureFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

!! Gage pressure:Gage pressure: measured relative to a reference measured relative to a reference pressure pressure -- typically local atmospheric pressuretypically local atmospheric pressure

!! Absolute pressure:Absolute pressure: measured relative to ameasured relative to a

Fluid Fluid PropertiesProperties

!! Absolute pressure:Absolute pressure: measured relative to a measured relative to a perfect vacuumperfect vacuum

!! Absolute, gage, and atmospheric pressure are Absolute, gage, and atmospheric pressure are

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

related as follows:related as follows:

PPabsabs = = PPgagegage + + PPatmatm

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 13: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

PressurePressureFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

PP1 gage1 gageFluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

PPPP2 gage2 gage

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

PP1 abs1 abs

PP2 abs2 absMomentum Momentum and Dragand Drag

Munson et al. (2002)

Page 14: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Hydrostatic PressureHydrostatic PressureFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

''P = change in pressureP = change in pressure(( = specific weight of fluid= specific weight of fluid

''P = P = ('('hh(( p gp g''h = change in depth in fluidh = change in depth in fluid

***Incompressible fluid at rest***Incompressible fluid at rest

Page 15: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

ManometryManometryM tM t

FE Fluid FE Fluid Mechanics Mechanics

ReviewReview

!! Manometers measure pressure or Manometers measure pressure or pressure differencespressure differences

!! Differential manometers:Differential manometers: both endsboth ends

Fluid Fluid PropertiesProperties

Differential manometers:Differential manometers: both ends both ends connected to pressure sourcesconnected to pressure sources

!! Open manometers:Open manometers: one end open one end open h hh h

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

to the atmosphereto the atmosphereEnergy, Energy,

Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 16: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Solving Manometer ProblemsSolving Manometer ProblemsFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

1.1. Select a convenient starting point (usually at Select a convenient starting point (usually at one of the endpoints)one of the endpoints)

Fluid Fluid PropertiesProperties

2. Using 2. Using ''P = P = ((h, write expressions for changes in h, write expressions for changes in pressure from starting point to point at pressure from starting point to point at

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics p g p pp g p p

opposite end of manometer system. Watch opposite end of manometer system. Watch algebraic signs!algebraic signs!Energy, Energy,

Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

3. Equate expression from step 2 to pressure at 3. Equate expression from step 2 to pressure at final pointfinal point

Momentum Momentum and Dragand Drag

4. Substitute known values and solve for desired 4. Substitute known values and solve for desired quantityquantityq yq y

Page 17: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

BarometersBarometersFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 18: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

BuoyancyBuoyancyFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

!! The buoyant force exerted by a fluid is equal to The buoyant force exerted by a fluid is equal to the weight of the fluid displaced and is directedthe weight of the fluid displaced and is directed

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

the weight of the fluid displaced and is directed the weight of the fluid displaced and is directed vertically upward (Archimedes’ Principle):vertically upward (Archimedes’ Principle):

FF VV

Momentum Momentum and Dragand Drag

FFbb = = ((VVdd

wherewhere FFbb = the buoyant force= the buoyant forcebb yy(( = specific weight of the fluid= specific weight of the fluidVVdd = displaced volume of the fluid= displaced volume of the fluid

Page 19: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Displaced VolumeDisplaced VolumeFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Displaced volume

Page 20: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Solving Buoyancy ProblemsSolving Buoyancy ProblemsFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

!! If the object is at rest in the fluid, use the If the object is at rest in the fluid, use the equation of static equilibrium in the equation of static equilibrium in the

Fluid Fluid PropertiesProperties

vertical direction,vertical direction, ))FFyy = 0= 0Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

!! The buoyant force passes vertically The buoyant force passes vertically through the through the centroidcentroid of the displaced of the displaced

l f fl id Thi i t i ll d thl f fl id Thi i t i ll d th

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

volume of fluid. This point is called thevolume of fluid. This point is called thecenter of buoyancy.center of buoyancy.Momentum Momentum

and Dragand Drag

Page 21: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Fluid Forces on SurfacesFluid Forces on SurfacesFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

!! Pressure on a horizontal plane surface is uniform Pressure on a horizontal plane surface is uniform over the surfaceover the surfaceR lt t f f di t ib ti tR lt t f f di t ib ti t

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

!! Resultant force of pressure distribution acts Resultant force of pressure distribution acts through center of pressure of surface and is:through center of pressure of surface and is:

PAR

Momentum Momentum and Dragand Drag

PAR #R = resultant vertical forceR = resultant vertical forceP = pressure on the horizontal surfaceP = pressure on the horizontal surfaceA = area of submerged horizontal surfaceA = area of submerged horizontal surface

Page 22: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Fluid Forces on SurfacesFluid Forces on SurfacesFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 23: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Free SurfaceFluid Forces on SurfacesFluid Forces on SurfacesFE Fluid FE Fluid

Mechanics Mechanics ReviewReview

*

OFree Surface

Fluid Fluid PropertiesProperties

hhC x

y

yc

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

dF

R

yR

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

A

dA

Momentum Momentum and Dragand Drag

I Iy

"Centroid, c

"Center of Pressure, CP

AhAPR cavg (## cc

xcR y

AyIy +# c

c

xycR x

AyI

x +#

Page 24: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Laminar and Turbulent FlowLaminar and Turbulent FlowFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Laminar Flow:Laminar Flow:!! Relatively low velocitiesRelatively low velocities

Fluid Fluid PropertiesProperties

!! No mixing or a very small degree No mixing or a very small degree of mixingof mixingFl id t fl iFl id t fl i

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

!! Fluid appears to flow in Fluid appears to flow in continuous layers with no continuous layers with no interaction between the layersinteraction between the layers

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Turbulent Flow:Turbulent Flow:Momentum Momentum and Dragand Drag

!! Relatively high velocitiesRelatively high velocities!! High degree of mixingHigh degree of mixing!! Fluid motion appears chaoticFluid motion appears chaotic

Page 25: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Flow DistributionFlow DistributionFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 26: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Reynolds NumberReynolds NumberFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 27: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Reynolds NumberReynolds NumberFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Re < 2000 laminar flowRe < 2000 laminar flowCircular Pipe FlowCircular Pipe FlowFluid Fluid

PropertiesProperties

2000 < Re < 4000 transition region2000 < Re < 4000 transition regionRe > 4000 turbulent flowRe > 4000 turbulent flow

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Open ChannelOpen ChannelEnergy, Energy,

Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Re < 500 laminar flowRe < 500 laminar flow500 < Re < 2000 transition region500 < Re < 2000 transition regionRe > 2000 turbulent flowRe > 2000 turbulent flow

Momentum Momentum and Dragand Drag

Re > 2000 turbulent flowRe > 2000 turbulent flow

Page 28: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

OneOne--Dimensional FlowsDimensional FlowsFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 29: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Compressible FlowsCompressible FlowsFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Continuity:Continuity:mm !! #

Fluid Fluid PropertiesProperties

AA

21 mm #Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

222111 vAvA $$ #Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

RTP $Ideal Gas Law:Ideal Gas Law:Momentum Momentum

and Dragand Drag

RTP $#[P is pressure][P is pressure][ p ][ p ][R is the gas constant][R is the gas constant][T is temperature][T is temperature]

Page 30: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Incompressible FluidsIncompressible FluidsFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Continuity Equation:Continuity Equation:Fluid Fluid PropertiesProperties

2211 vAvA #Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 31: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Bernoulli EquationBernoulli EquationFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 32: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Mechanical Energy EquationMechanical Energy EquationFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 33: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Friction LossFriction LossFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Valid for laminar and turbulent flowValid for laminar and turbulent flowMomentum Momentum and Dragand Drag

Page 34: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Moody ChartMoody ChartFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 35: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Friction LossFriction LossFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

HazenHazen--Williams Equation:Williams Equation:

54.063.08490 SCR#vFluid Fluid

PropertiesProperties

849.0 SCR#vv = velocity [m/s]v = velocity [m/s]

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics y [ ]y [ ]

C = roughness coefficient [varies from 140 to 100]C = roughness coefficient [varies from 140 to 100]R = hydraulic radius = A/WP [m]R = hydraulic radius = A/WP [m]

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

V lid f t b l t fl f tV lid f t b l t fl f t

S = slope of HGL = hS = slope of HGL = hLL/L [dimensionless]/L [dimensionless]Momentum Momentum and Dragand Drag

Valid for turbulent flow of waterValid for turbulent flow of water

Page 36: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Minor LossMinor LossFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

fitting,ffL hhh +#Fluid Fluid PropertiesProperties

g2vCh2

fitting,f #Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics g2

[C = loss coefficient (or resistance coefficient)][C = loss coefficient (or resistance coefficient)]Energy, Energy,

Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 37: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

HGL and EGLHGL and EGLFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 38: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

HGL and EGLHGL and EGLFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Total Head or Energy

Grade Line Velocity Head

Fluid Fluid PropertiesProperties

(EGL)(v2/2g)

H d li

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Pressure Head

Hydraulic Grade Line

HGLEnergy, Energy,

Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

(P/()Momentum Momentum and Dragand Drag

Elevation

Z = 0Head (z)

Page 39: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

PumpPump--TurbinesTurbinesFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Net head added to system Net head added to system by mechanical deviceby mechanical device

Fluid Fluid PropertiesProperties

PP 22

by mechanical deviceby mechanical deviceFluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

g2vzPhh

g2vzP 2

22

2Ls

21

11 ++#,+++

((Energy, Energy,

Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 40: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Open Channel & Pipe FlowOpen Channel & Pipe FlowFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 41: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

ImpulseImpulse--MomentumMomentumFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 42: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

ImpulseImpulse--MomentumMomentumFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

x111x222x vQvQF $$) ,#Fluid Fluid PropertiesProperties

111222 vQvQF $$) ,#Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

y111y222y vQvQF $$)Energy, Energy,

Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

z111z222z vQvQF $$) ,#Momentum Momentum and Dragand Drag

Sum of theSum of theNet rate of Net rate of

t t it t iSum of the Sum of the external forcesexternal forces

momentum entering momentum entering control volumecontrol volume

Page 43: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Drag ForceDrag ForceFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 44: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Drag CoefficientDrag CoefficientFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 45: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Pipe NetworksPipe NetworksFE Fluid FE Fluid Mechanics Mechanics

ReviewReview

Fluid Fluid PropertiesProperties

Fluid StaticsFluid Statics

Fluid Fluid DynamicsDynamics

Energy, Energy, Friction Loss, Friction Loss, and Pipe Flowand Pipe Flow

Momentum Momentum and Dragand Drag

Page 46: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.
Page 47: EngineeringFundamentals of Engineering (()FE ) · PDF fileEngineeringFundamentals of Engineering (()FE ) Exam Section Revie w BurianSteven Burian Engineering 2010October 26, 2010.

Good Luck!!!Good Luck!!!

Steve BurianSteve BurianDepartment of Civil & Environmental EngineeringDepartment of Civil & Environmental Engineering

@@[email protected]@eng.utah.edu