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Boundary layer concept
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Laminar flow
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Laminar Boundary Layer Flow
The laminar boundary layer is a very smooth
flow, while the turbulent boundary layer contains
swirls or eddies.
The laminar flow creates less skin friction drag
than the turbulent flow, but is less stable.
Boundary layer flow over a wing surface begins
as a smooth laminar flow. As the flow continues
back from the leading edge, the laminar
boundary layer increases in thickness.
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Turbulent Boundary Layer Flow
At some distance back from the leading edge,the smooth laminar flow breaks down and
transitions to a turbulent flow.
From a drag standpoint, it is advisable to have
the transition from laminar to turbulent flow asfar aft on the wing as possible, or have a large
amount of the wing surface within the laminar
portion of the boundary layer.
The low energy laminar flow, however, tends to
break down more suddenly than the turbulent
layer.
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Flow through the pipes in
series
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Pipes in series is defined as the pipes of different lengthsand different diameters connected end to end to form a
pipe line.L1,L2,L3 = length of pipes 1,2 and 3
d1,d2,d3 = diameter of pipes 1,2,3
v1,v2,v3 = velocity of flow through pipes 1,2,3
f1,f2,f3 = coefficient of frictions for pipes 1,2,3
H = difference of water level in the two tanks
The discharge passing through the pipe is same.
Q=A1V1=A2V2=A3V3
The difference in liquid surface levels is equal to the sumof the total head loss in the pipes
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Parallel pipe system
Consider a main pipe which divide into two or more
branches as shown in figure
Again join together downstream to
form a single pipe then the branch pipes are said to be.
increased by connecting pipes in parallel
the rate of flow in the main pipe is equal to the sum of rate
of flow through branch pipes.
hence
Q =Q1+ Q2
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In this arrangement loss of head for each pipe is same
Loss of head for branch pipe1=loss of head for branch
pipe 2
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Moody diagram
Moody Diagram that can be used to estimate
friction coefficients
The Moody friction factor - (or f) - is used in the Darcy-
If the flow is transient - 2300 < Re < 4000- the flowvaries between laminar and turbulent flow and the
friction coefficient is not possible to determine.
The friction factor can usually be interpolated between
the laminar value at Re = 2300and the turbulent value at
Re = 4000
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Moody diagram
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Total energy gradient line
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Total energy gradient line is equal to sum ofpressure head ,velocity head and datum head
EL = H = p / W + v2 / 2 g + h = constant along astreamline
where
(EL ) Energy Line
For a fluid flow without any losses due to friction-
energy line would be at a constant level. In apractical world the energy line decreases alongthe flow due to losses.
A turbine in the flow reduces the energy line and apump or fan in the line increases the energy line
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Hydraulic Grade Line (HGL )
Hydraulic gradient line is the sum of
pressure head and datum headHGL = p / W + h
where
The hydraulic grade line lies one velocity headbelow the energy line.
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Hydro Power Plants
A Hydro Power Harvester.
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A Two-Way Welfare for the Globe
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Specific Speed
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,m
Specific Speed
Hea
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MORE ADAPTED TYPE OF TURBINE AS FUNCTION OF THE SPECIFIC SPEED.
Specific Speed in r.p.m. Turbine type Jump height in m
Until 18 Pelton of an injector 800From 18 to 25 Pelton of an injector 800 to 400
From 26 to 35 Pelton of an injector 400 to 100
From 26 to 35 Pelton of two injectors 800 to 400
From 36 to 50 Pelton of two injectors 400 to 100
From 51 to 72 Pelton of four injectors 400 to 100
From 55 to 70 Very slow Francis 400 to 200
From 70 to 120 Slow Francis 200 to 100
From 120 to 200 Normal Francis 100 to 50
From 200 to 300 Quick Francis 50 to 25
From 300 to 450 Extra-quick Francis 25 to 15
From 400 to 500 Extra-quick helix 15
From 270 to 500 Slow Kaplan 50 to 15
From 500 to 800 Quick Kaplan 15 to 5
From 800 to 1100 Extra-quick Kaplan Less than 5
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Varieties of Hydro Resources Available in Nature
Each Resource is naturally fit in the classification?
Any modification of the resource is required for better
harvesting of resource?
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The Size of A Power Plant
A Macro Power Plant : > 100 MW.
A Small Power Plant: 5 MW to 25 MW.
A Mini Power Plant: 500 kW to 2 MW.
A Micro Power Plant: 50 kW to 200 kW.
A Pico Power Plant: < 30 kW.
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East Flowing River : The Krishna
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East Flowing River : The Krishna
Catchment Area: 2,58,958 Sq. km
Annual Yield: 57,000 M.cum
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The West Flowing River: The Sharavathi
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MACRO -HYDRO-POWER POTENTIAL IN INDIA
BASINS/RIVERS POWER POTENIAL IN
MW
Basin/Rivers Probable Capacity (MW)
Indus Basin 33,832
India is blessed with immense amount of hydro-electric potential and
ranks 5th in terms of exploitable hydro-potential on global scenario.
,
Central Indian River
system
4,152
Western Flowing
Rivers of southern
India
9,430
Eastern Flowing
Rivers of southern
India
14,511
Brahmaputra Basin 66,065
Total 1,48,701
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LIST OF HYDRO ELECTRIC POWER STATIONS IN THE
COUNTRY WITH STATION CAPACITY ABOVE 25 MW
REGION/NO.OF
STATIONSNO.OF UNITS
CAPACITY
(MW)
NORTHERN 55 187 13678.25
WESTERN 28 101 7392.00
SOUTHERN 66 237 11294.45
EASTERN 15 55 3847.70
EASTERN 9 26 1116.00
ALL INDIA
(TOTAL)173 606 37328.40
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More Details of Macro Hydro Power Plants
STATION NO. OF UNITSX SIZE (MW)
CAPACITY (MW)
Bhakra l hydro electric
power station5*108 540.00
Bhakra r hydro electric
power station5*157 785.00
Ganguwa y ro e ectr c
power station1*29.25+2*24.2 77.65
Kotla hydro electric power
station1*29.25+2*24.2 77.65
Dehar hydro electric power
station6*165 990.00
Pong hydro electric power
station6*66 396.00
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MACRO HYDRO-POWER PROJECTS IN INDIA
S.N o. P roject R iver / State Insta lled
Capacity
1 Bhakra Sutlej & Beas/ H im achal P radesh 1225 M W
2 Dehar Sutlej / H im achal P radesh 990 M W
3 Kalinadi Stage-I Kalinadi 910 M W
4 Sharavathy Sharavathy / K arnataka 891 M W
5 Koyna Koyna / M aharashtra 880 M W
6 Nagarjuna-Sagar Krishna / Andhra P radesh 810 M W
7 Idduki stage-I Idukki, K alavu & Cheru than / K erala 780 M W
8 Srisailam Krishna / Andhra P radesh 770 M W
9 Salal Chenab / Jam m u & K ashm ir 690 M W
10 Ranjit Sagar Ravi / Punjab 600 M W
11 Cham era - I Ravi / H im achal Pradesh 540 M W
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Small Hydro Map of India
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Methodology of HEPP Development
Site Survey: Hydrological & geological Survey.
Estimation of Potential
Regulations & Environmental Concerns
Feasible Supply Tur ne Se ect on
Costing and Payback.
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Hydrological Survey: Flow Duration Curve
To measure the flow-rate vs time at a given site.
Direct Measurement of the flow rate.
The more robust option is to find out the flow-rate bywor ng ou e vo ume o wa er a was en er ng e
river.
This uses the rainfall data from met office.
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Hydrological Cycle
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Catchment Area
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Catchment Area: 2,58,958 Sq. km
Annual Yield: 57,000 M.cum
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Rain Fall Data : Hydrograph
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Flow Duration Curve
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Average Flow duration Curve
Average Flow duration Curve
Mean of 10 30 years
u
mecs
% of time
D
ischarge,
Qm
Q100%
Q95%
Q50%
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Definition of A Turbo MachineDefinition of A Turbo Machine
Turbines are energy developing machines. Turbines convert fluid energy intoTurbines are energy developing machines. Turbines convert fluid energy into
mechanical energy. The mechanical energy developed by the turbines is usedmechanical energy. The mechanical energy developed by the turbines is used
in running an electric generator, which is directly connected, to the shaft of thein running an electric generator, which is directly connected, to the shaft of the
electrical generator.electrical generator.
Earlier days methodEarlier days method wooden wheelwooden wheel
Overshot WheelOvershot Wheel
Had very good efficiency
Could not handle large quantity of water
Undershot Wheel
Low Efficiency
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General layout of HydroGeneral layout of Hydro--Power PlantPower Plant
a) Reservoir
Reservoirs ensure supply of water through out the year, by storing water
during rainy season and supplying the same during dry season.
b)b) DamDame unct on o t e am s to ncrease t e reservo r capac ty an to ncrease t ee unct on o t e am s to ncrease t e reservo r capac ty an to ncrease t e
working head of the turbine.working head of the turbine.
c) Penstockc) Penstock
A pipe between dam and turbine is known as penstock. It will carry the waterA pipe between dam and turbine is known as penstock. It will carry the water
from dam to turbine. Penstock is commonly made of steel pipes covered withfrom dam to turbine. Penstock is commonly made of steel pipes covered withRCC.RCC.
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d)d) Surge tank/Surge tank/ForebayForebay
When the rate of water flow through the penstock is suddenly decreased, theWhen the rate of water flow through the penstock is suddenly decreased, the
pressure inside the penstock will increase suddenly due to water hammerpressure inside the penstock will increase suddenly due to water hammerand thereby damage the penstock.and thereby damage the penstock.
Surge tank/Surge tank/ForebayForebay is constructed between the dam and turbine. It will actis constructed between the dam and turbine. It will act
as a pressure regulator during variable loads.as a pressure regulator during variable loads.
e)e) TurbineTurbine
Turbines convert the kinetic and potential energy of water into mechanicalTurbines convert the kinetic and potential energy of water into mechanical
energy to produce electric power.energy to produce electric power.
f) Generator and Transformerf) Generator and Transformer
Electric generator converts mechanical energy into electrical energy. A stepElectric generator converts mechanical energy into electrical energy. A step
up transformer will increase the voltage for loss free transmission.up transformer will increase the voltage for loss free transmission.
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General layout of HydroGeneral layout of Hydro--Power PlantPower Plant
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Advantages of hydraulic power plants
Operating cost is very low
Less Maintenance cost and less manpower required
Pollution free
Quick to start and easy to synchronize
Advantages and Disadvantages of HPPAdvantages and Disadvantages of HPP
an e use or rr ga on an oo con ro
Long plant life.
Disadvantages of Hydraulic Power Plants
Initial cost of total plant is comparatively high
Power generation depends on availability of water Cost of transmission is high since most of the plants are in remote areas
Project duration is long.
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1) Gross Head
Difference Between the Head race level and Tail race level
Static (No water flow) / Total Head H1
2) Net or Effective Head
Head of Hydraulic TurbinesHead of Hydraulic Turbines
Head available at the entrance of the turbine: H = H1 - hf
a) Net Head for a Reaction Turbine
H = {(P1/w) + (V12/2g) + Z1} {Z2 + V2
2/2g)}
b) Net Head for Impulse Turbine
H = {(P1/w) + (V12/2g) + Z1} Z2
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1) Hydraulic Efficiency due to hydraulic losses
Power developed by the runner
Net power supplied at the turbine entrance
SI Unit: kW
Efficiencies of Hydraulic TurbinesEfficiencies of Hydraulic Turbines
Metric Unit : Horse Power/Water Horse Power (W.H.P)
2) Mechanical Efficiency Due to mechanical losses ( bearing friction)
Power available at the turbine shaft (P)Power developed by the runner
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3) Volumetric Efficiency due to amt of water slips directly to the tail race
Amount of water striking the runner
Amount of water supplied to the turbine
ContCont
4) Overall Efficiency
Power available at the turbine shaft (P)
Net power supplied at the turbine entrance
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Classification of TurbinesClassification of Turbines
Turbines are classified according to several considerations as indicated below.Turbines are classified according to several considerations as indicated below.
ii)) Based on working principleBased on working principle
a)a) Impulse turbineImpulse turbine
bb Reaction turbineReaction turbine
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Impulse Turbine:The pressure of liquid does not change while flowing through the rotor of the
machine. In Impulse Turbines pressure change occur only in the nozzles of
the machine.
One such example of impulse turbine is Pelton Wheel.
ContCont
Reaction Turbine:
The pressure of liquid changes while it flows through the rotor of the
machine. The change in fluid velocity and reduction in its pressure causes
a reaction on the turbine blades; this is where from the name Reaction
Turbine may have been derived.
Francis and Kaplan Turbines fall in the category of Reaction Turbines.
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ContCont
ii)ii) Based on working mediaBased on working media
a)a) Hydraulic turbineHydraulic turbine
b)b) Steam turbineSteam turbine
c)c) Gas turbineGas turbine
d)d) Wind TurbineWind Turbine
Head is the elevation difference of reservoir water level and D/S water level.Head is the elevation difference of reservoir water level and D/S water level.
a)a) High head turbineHigh head turbine (Above 250 m)(Above 250 m) Pelton TurbinePelton Turbine
b)b) Medium head turbineMedium head turbine (60(60 250 m)250 m) Francis TurbineFrancis Turbine
c)c) Low head turbineLow head turbine (Below 60 m)(Below 60 m) Kaplan TurbineKaplan Turbine
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iv)iv) Based on specific speedBased on specific speed
Turbines can be classified based on Specific Speed. Specific speed is definedTurbines can be classified based on Specific Speed. Specific speed is defined
as the speed in rpm of a geometrically similar turbine, which is identical inas the speed in rpm of a geometrically similar turbine, which is identical in
shape, dimensions, blade angles and gate openings with the actual turbineshape, dimensions, blade angles and gate openings with the actual turbine
working under unit head and developing unit power. Specific speed is used toworking under unit head and developing unit power. Specific speed is used to
ContCont
..
Specific speedSpecific speed Ns = N P / H5/4
a)a) Low specific speedLow specific speed (8.5(8.5 30)30) -- PeltonPelton TurbineTurbine
b)b) Medium specific speed (50Medium specific speed (50 340)340) -- Francis TurbineFrancis Turbinec)c) High specific speedHigh specific speed (255(255 860)860) -- Kaplan TurbineKaplan Turbine
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v)v) Based on disposition of turbine main shaftBased on disposition of turbine main shaft
a)a) Horizontal shaftHorizontal shaft
b)b) Vertical shaftVertical shaft
vi)vi) Based on flow through the runnerBased on flow through the runner
a)a) Radial flowRadial flow
ContCont
..
2.2. OutwardOutward
b)b) Axial flowAxial flow -- Kaplan TurbineKaplan Turbine
c)c) Mixed flowMixed flow -- Francis TurbineFrancis Turbine
d)d) Tangential flowTangential flow -- PeltonPelton TurbineTurbine
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PeltonPelton Wheel TurbineWheel Turbine
Design of Pelton Wheel Turbine
It has a circular disk with cup shaped blades/buckets,
Water jet emerging from a nozzle is tangential to the circumference of the
wheel.
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Working Principle of Pelton Turbine
Water jets emerging strike the buckets at splitter.
Stream flow along the inner curve of the bucket and leave it in the direction
opposite to that of incoming jet.
The high pressure water can be obtained from any water body situated at
some height or streams of water flowing down the hills.
The change in momentum (direction as well as speed) of water stream
produces an impulse on the blades of the wheel of Pelton Turbine. This
impulse generates the torque and rotation in the shaft of Pelton Turbine.
Horizontal shaft - Not more than 2 jets are used andVertical shaft - Larger no. of jets (upto 6) are used.
Iron/Steel casing to prevent splashing of water and to lead water to the tail
race.
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Chapter 8: Flow in Pipes
Eric G. PatersonDepartment of Mechanical and Nuclear Engineering
The Pennsylvania State University
Spring 2005
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Note to Instructors
These slides were developed1, during the spring semester 2005, as a teaching aid
for the undergraduate Fluid Mechanics course (ME33: Fluid Flow) in the Department of
Mechanical and Nuclear Engineering at Penn State University. This course had two
sections, one taught by myself and one taught by Prof. John Cimbala. While we gave
common homework and exams, we independently developed lecture notes. This was
also the first semester that Fluid Mechanics: Fundamentals and Applicationswas
used at PSU. My section had 93 students and was held in a classroom with a computer,
projector, and blackboard. While slides have been developed for each chapter ofFluid
Chapter 8: Flow in PipesME33 : Fluid Flow 2
,
electronic presentation. In the student evaluations of my course, there were both positive
and negative comments on the use of electronic presentation. Therefore, these slides
should only be integrated into your lectures with careful consideration of your teaching
style and course objectives.
Eric PatersonPenn State, University Park
August 2005
1 These slides were originally prepared using the LaTeX typesetting system (http://www.tug.org/)and the beamer class (http://latex-beamer.sourceforge.net/), but were translated to PowerPoint forwider dissemination by McGraw-Hill.
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Objectives
1. Have a deeper understanding of laminar andturbulent flow in pipes and the analysis of fully
developed flow
2. Calculate the major and minor losses
Chapter 8: Flow in PipesME33 : Fluid Flow 3
and determine the pumping power
requirements
3. Understand the different velocity and flow rate
measurement techniques and learn their
advantages and disadvantages
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Introduction
Average velocity in a pipeRecall - because of the no-slip
condition, the velocity at the walls of
a pipe or duct flow is zero
We are often interested only in Vavg,
which we usually call just V(drop the
Chapter 8: Flow in PipesME33 : Fluid Flow 4
su scr p or conven ence
Keep in mind that the no-slip
condition causes shear stress and
friction along the pipe walls
Friction force of wall on fluid
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Introduction
For pipes of constantdiameter and
incompressible flow
Vavgstays the same
down the pipe, even if
Chapter 8: Flow in PipesME33 : Fluid Flow 5
the velocity profile
changes
Why? Conservation of
Mass
same
Vavg Vavg
samesame
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Introduction
For pipes with variable diameter, mis still thesame due to conservation of mass, but V1 V2
D1
Chapter 8: Flow in PipesME33 : Fluid Flow 6
D2
V2
2
1
V1 m m
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Laminar and Turbulent Flows
Chapter 8: Flow in PipesME33 : Fluid Flow 7
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Laminar and Turbulent Flows
Critical Reynolds number(Recr) for flow in a round pipe
Re < 2300 laminar
2300 Re 4000 transitional
Re > 4000 turbulent
Definition of Reynolds number
Chapter 8: Flow in PipesME33 : Fluid Flow 8
approximate.
For a given application, Recrdepends upon
Pipe roughness
VibrationsUpstream fluctuations,disturbances (valves, elbows, etc.that may disturb the flow)
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Laminar and Turbulent Flows
For non-round pipes, define thehydraulic diameterDh= 4Ac/PAc= cross-section area
P= wetted perimeter
Chapter 8: Flow in PipesME33 : Fluid Flow 9
Example: open channel
Ac= 0.15 * 0.4 = 0.06m2
P= 0.15 + 0.15 + 0.5 = 0.8m
Dont count free surface, since it does notcontribute to friction along pipe walls!
Dh= 4Ac/P= 4*0.06/0.8 = 0.3m
What does it mean? This channel flow isequivalent to a round pipe of diameter0.3m (approximately).
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The Entrance Region
Consider a round pipe of diameter D. The flowcan be laminar or turbulent. In either case, the
profile develops downstream over several
diameters called the entry length Lh. Lh/Dis a
function of Re.
Chapter 8: Flow in PipesME33 : Fluid Flow 10
Lh
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Fully Developed Pipe Flow
Comparison of laminar and turbulent flowThere are some major differences between laminar and
turbulent fully developed pipe flows
Laminar
Can solve exactly (Chapter 9)
Chapter 8: Flow in PipesME33 : Fluid Flow 11
Flow is steady
Velocity profile is parabolic
Pipe roughness not important
It turns out that Vavg = 1/2Umax and u(r)= 2Vavg( 1 - r 2/R2)
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Fully Developed Pipe Flow
TurbulentCannot solve exactly (too complex)
Flow is unsteady (3D swirling eddies), but it is steady in the mean
Mean velocity profile is fuller (shape more like a top-hat profile,with very sharp slope at the wall)
Pipe roughness is very important
Chapter 8: Flow in PipesME33 : Fluid Flow 12
Vavg 85% of Umax (depends on Re a bit)
No analytical solution, but there are some good semi-empiricalexpressions that approximate the velocity profile shape. See text
Logarithmic law (Eq. 8-46)
Power law (Eq. 8-49)
ns an aneous
profiles
Fully Developed Pipe Flow
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Fully Developed Pipe Flow
Wall-shear stress
Recall, for simple shear flows u=u(y), we had=du/dy
In fully developed pipe flow, it turns out that
=du/dr
Chapter 8: Flow in PipesME33 : Fluid Flow 13
w w
w,turb > w,lamw = shear stress at the wall,
acting on the fluid
Fully Developed Pipe Flow
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Fully Developed Pipe Flow
Pressure drop
There is a direct connection between the pressure drop in a pipe andthe shear stress at the wall
Consider a horizontal pipe, fully developed, and incompressible flow
w
Chapter 8: Flow in PipesME33 : Fluid Flow 14
Lets apply conservation of mass, momentum, and energy to this CV(good review problem!)
1 2L
P1 P2V
Fully Developed Pipe Flow
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Fully Developed Pipe Flow
Pressure drop
Conservation of Mass
Chapter 8: Flow in PipesME33 : Fluid Flow 15
Conservation of x-momentum
Terms cancel since 1 = 2and V1 = V2
Fully Developed Pipe Flow
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Fully Developed Pipe Flow
Pressure drop
Thus, x-momentum reduces to
Energy equation (in head form)
or
Chapter 8: Flow in PipesME33 : Fluid Flow 16
cancel (horizontal pipe)
Velocity terms cancel again because V1 = V2, and 1 = 2 (shape not changing)
hL = irreversible head
loss & it is felt as a pressure
drop in the pipe
Fully Developed Pipe Flow
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Fully Developed Pipe Flow
Friction Factor
From momentum CV analysis
From energy CV analysis
Chapter 8: Flow in PipesME33 : Fluid Flow 17
qua ng e wo g ves
To predict head loss, we need to be able to calculate w. How?
Laminar flow: solve exactly
Turbulent flow: rely on empirical data (experiments)
In either case, we can benefit from dimensional analysis!
Fully Developed Pipe Flow
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Fully Developed Pipe Flow
Friction Factor
w = func( V, , D, ) = average roughness of theinside wall of the pipe
-analysis gives
Chapter 8: Flow in PipesME33 : Fluid Flow 18
Fully Developed Pipe Flow
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Fully Developed Pipe Flow
Friction Factor
Now go back to equation forhL and substitute fforw
Chapter 8: Flow in PipesME33 : Fluid Flow 19
Our problem is now reduced to solving for Darcy friction factorf
Recall
Therefore
Laminar flow: f = 64/Re (exact)
Turbulent flow: Use charts or empirical equations (Moody Chart, a famousplot offvs. Re and /D, See Fig. A-12, p. 898 in text)
But for laminar flow, roughness
does not affect the flow unless itis huge
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Chapter 8: Flow in PipesME33 : Fluid Flow 20
Fully Developed Pipe Flow
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Fully Developed Pipe Flow
Friction Factor
Moody chart was developed for circular pipes, but canbe used for non-circular pipes using hydraulic diameter
Colebrook equation is a curve-fit of the data which isconvenient for computations (e.g., using EES)
Chapter 8: Flow in PipesME33 : Fluid Flow 21
Both Moody chart and Colebrook equation are accurateto 15% due to roughness size, experimental error,curve fitting of data, etc.
Implicit equation for f which can be solved
using the root-finding algorithm in EES
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Types of Fluid Flow Problems
In design and analysis of piping systems, 3problem types are encountered
1. Determine p (or hL) given L, D, V (or flow rate)Can be solved directly using Moody chart and Colebrookequation
Chapter 8: Flow in PipesME33 : Fluid Flow 22
3. Determine D, given L, p, V (or flow rate)
Types 2 and 3 are common engineeringdesign problems, i.e., selection of pipe
diameters to minimize construction andpumping costs
However, iterative approach required sinceboth Vand Dare in the Reynolds number.
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Types of Fluid Flow Problems
Explicit relations have been developed whicheliminate iteration. They are useful for quick,
direct calculation, but introduce an additional 2%
error
Chapter 8: Flow in PipesME33 : Fluid Flow 23
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Minor Losses
Piping systems include fittings, valves, bends, elbows,tees, inlets, exits, enlargements, and contractions.
These components interrupt the smooth flow of fluid and
cause additional losses because of flow separation and
mixing
Chapter 8: Flow in PipesME33 : Fluid Flow 24
e n ro uce a re a on or e m nor osses assoc a e
with these components
KL is the loss coefficient.
Is different for each component. Is assumed to be independent of Re.
Typically provided by manufacturer or
generic table (e.g., Table 8-4 in text).
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Minor Losses
Total head loss in a system is comprised ofmajor losses (in the pipe sections) and the minor
losses (in the components)
Chapter 8: Flow in PipesME33 : Fluid Flow 25
If the piping system has constant diameter
i pipe sections j components
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Chapter 8: Flow in PipesME33 : Fluid Flow 26
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Chapter 8: Flow in PipesME33 : Fluid Flow 27
Pi i N k d P S l i
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Piping Networks and Pump Selection
Two general types ofnetworks
Pipes in seriesVolume flow rate is
constant
Chapter 8: Flow in PipesME33 : Fluid Flow 28
Head loss is thesummation of parts
Pipes in parallelVolume flow rate is thesum of the components
Pressure loss across allbranches is the same
Pi i N t k d P S l ti
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Piping Networks and Pump Selection
For parallel pipes, perform CV analysis betweenpoints A and B
Chapter 8: Flow in PipesME33 : Fluid Flow 29
Since p is the same for all branches, head lossin all branches is the same
Pi i N t k d P S l ti
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Piping Networks and Pump Selection
Head loss relationship between branches allows the following ratiosto be developed
Chapter 8: Flow in PipesME33 : Fluid Flow 30
Real pipe systems result in a system of non-linear equations. Veryeasy to solve with EES!
Note: the analogy with electrical circuits should be obvious
Flow flow rate (VA) : current (I)Pressure gradient (p) : electrical potential (V)
Head loss (hL): resistance (R), however hL is very nonlinear
Pi i N t k d P S l ti
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Piping Networks and Pump Selection
When a piping system involves pumps and/orturbines, pump and turbine head must be included inthe energy equation
Chapter 8: Flow in PipesME33 : Fluid Flow 31
The useful head of the pump (hpump,u) or the headextracted by the turbine (hturbine,e), are functions ofvolume flow rate, i.e., they are not constants.
Operating point of system is where the system is inbalance, e.g., where pump head is equal to the headlosses.
P d t
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Pump and systems curves
Supply curve for hpump,u:determine experimentally by
manufacturer. When using EES,
it is easy to build in functional
relationship for hpump,u.
System curve determined from
equations
Operating point is the
intersection of supply and
demand curves
If peak efficiency is far fromoperating point, pump is wrong
for that application.