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Flow In Circular PipesObjective To measure the pressure drop in
the straight section of smooth, rough, and packed pipes as a
function of flow rate.To correlate this in terms of the friction
factor and Reynolds number.To compare results with available
theories and correlations.To determine the influence of pipe
fittings on pressure dropTo show the relation between flow area,
pressure drop and loss as a function of flow rate for Venturi meter
and Orifice meter.
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APPARATUSPipe NetworkRotametersManometers
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Theoretical DiscussionFluid flow in pipes is of considerable
importance in process.Animals and Plants circulation systems.In our
homes.City water.Irrigation system.Sewer water system Fluid could
be a single phase: liquid or gasesMixtures of gases, liquids and
solids NonNewtonian fluids such as polymer melts, mayonnaise
Newtonian fluids like in your experiment (water)
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Theoretical DiscussionLaminar flowTo describe any of these
flows, conservation of mass and conservation of momentum equations
are the most general forms could be used to describe the dynamic
system. Where the key issue is the relation between flow rate and
pressure drop.If the flow fluid
is:NewtonianIsothermalIncompressible (dose not depend on the
pressure)Steady flow (independent on time).Laminar flow (the
velocity has only one single component)
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Laminar flowNavier-Stokes equations is govern the flow field (a
set of equations containing only velocity components and pressure)
and can be solved exactly to obtain the Hagen-Poiseuille relation
.Vz(r)InPzr+drrBody force due to gravityFlowIf the principle of
conservation of momentum is applied to a fixed volume element
through which fluid is flowing and on which forces are acting, then
the forces must be balanced (Newton second law) Pz+dzPz+dz
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Laminar flowContinue Forces balance
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Laminar flow ContinueMomentum isMass*velocity (m*v)Momentum per
unit volume is*vzRate of flow of momentum is*vz*dQdQ=vz2rdrbutvz =
constant at a fixed value of rLaminar flow
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Laminar flowContinueHagen-Poiseuille
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Turbulent flowWhen fluid flow at higher flowrates, the
streamlines are not steady and straight and the flow is not
laminar. Generally, the flow field will vary in both space and time
with fluctuations that comprise "turbulenceFor this case almost all
terms in the Navier-Stokes equations are important and there is no
simple solutionP = P (D, , , L, U,)
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Turbulent flowAll previous parameters involved three fundamental
dimensions,Mass, length, and time From these parameters, three
dimensionless groups can be build
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Friction Factor for Laminar Turbulent flowsFrom forces balance
and the definition of Friction FactorFor Laminar flow(Hagen -
Poiseuill eq)For Turbulent FlowAc: cross section area of the pipS:
Perimeter on which T acts (wetted perimeter)Rh hydraulic radius
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Turbulence: Flow InstabilityIn turbulent flow (high Reynolds
number) the force leading to stability (viscosity) is small
relative to the force leading to instability (inertia). Any
disturbance in the flow results in large scale motions superimposed
on the mean flow. Some of the kinetic energy of the flow is
transferred to these large scale motions (eddies).Large scale
instabilities gradually lose kinetic energy to smaller scale
motions.The kinetic energy of the smallest eddies is dissipated by
viscous resistance and turned into heat. (=head loss)
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Velocity DistributionsTurbulence causes transfer of momentum
from center of pipe to fluid closer to the pipe wall.Mixing of
fluid (transfer of momentum) causes the central region of the pipe
to have relatively constant velocity (compared to laminar
flow)Close to the pipe wall eddies are smaller (size proportional
to distance to the boundary)
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Surface RoughnessAdditional dimensionless group /D need to be
characterizeThus more than one curve on friction factor-Reynolds
number plot Fanning diagram or Moody diagramDepending on the
laminar region.If, at the lowest Reynolds numbers, the laminar
portion corresponds to f =16/Re Fanning Chart or f = 64/Re Moody
chart
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Friction Factor for Smooth, Transition, and Rough Turbulent
flow
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Fanning Diagramf =16/Re
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Pipe roughnesspipe materialpipe roughness (mm)glass, drawn
brass, copper0.0015commercial steel or wrought iron0.045asphalted
cast iron0.12galvanized iron0.15cast iron0.26concrete0.18-0.6rivet
steel0.9-9.0corrugated metal45PVC0.12
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Flow in a Packed pipeThe equations for empty pipe flow do not
work with out considerable modification Ergun EquationReynolds
number for a packed bed flow asDp is the particle diameter, is the
volume fraction that is not occupied by particlesThis equation
contains the interesting behavior that the pressure drop varies as
the first power of Uo for small Re and as Uo2 for higher Re.
FlowDpA
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Energy Loss in ValvesFunction of valve type and valve
positionThe complex flow path through valves can result in high
head loss (of course, one of the purposes of a valve is to create
head loss when it is not fully open)Ev are the loss in terms of
velocity heads
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Friction Loss Factors for valves
ValveKLeq/DGate valve, wide open0.157Gate valve, 3/4
open0.8540Gate valve, 1/2 open4.4200Gate valve, 1/4 open20900Globe
valve, wide open7.5350
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Energy Loss due to Gradual Expansion angle ()A2A1
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Sudden Contraction (Orifice Flowmeter)Orifice flowmeters are
used to determine a liquid or gas flowrate by measuring the
differential pressure P1-P2 across the orifice plateReynolds number
based on orifice diameter RedFlow103104
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Venturi Flowmeter The classical Venturi tube (also known as the
Herschel Venturi tube) is used to determine flowrate through a
pipe. Differential pressure is the pressure difference between the
pressure measured at D and at d
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Boundary layer buildup in a pipePipe EntrancevBecause of the
share force near the pipe wall, a boundary layer forms on the
inside surface and occupies a large portion of the flow area as the
distance downstream from the pipe entrance increase. At some value
of this distance the boundary layer fills the flow area. The
velocity profile becomes independent of the axis in the direction
of flow, and the flow is said to be fully developed.
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Pipe Flow Head Loss(constant density fluid flows)Pipe flow head
loss is proportional to the length of the pipeproportional to the
square of the velocity (high Reynolds number)Proportional inversely
with the diameter of the pipeincreasing with surface
roughnessindependent of pressureTotal losses in the pipe system is
obtained by summing individual head losses of roughness, fittings,
valves ..itc
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Pipe Flow SummaryThe statement of conservation of mass, momentum
and energy becomes the Bernoulli equation for steady state constant
density of flows. Dimensional analysis gives the relation between
flow rate and pressure drop.Laminar flow losses and velocity
distributions can be derived based on momentum and mass
conservation to obtain exact solution named of Hagen -
PoisuilleTurbulent flow losses and velocity distributions require
experimental results. Experiments give the relationship between the
fraction factor and the Reynolds number. Head loss becomes minor
when fluid flows at high flow rate (fraction factor is constant at
high Reynolds numbers).
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Images - Laminar/Turbulent Flows Laser - induced florescence
image of an incompressible turbulent boundary layer Simulation of
turbulent flow coming out of a tailpipe Laminar flow (Blood
Flow)Laminar flowTurbulent
flowhttp://www.engineering.uiowa.edu/~cfd/gallery/lim-turb.html
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Pipes are Everywhere!Owner: City of Hammond, IN Project: Water
Main Relocation Pipe Size: 54"
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Pipes are Everywhere! Drainage Pipes
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Pipes are Everywhere! Water Mains
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Sheet1
areaFlowrateFlowrateFlowratevelosityPresure dropPresure
dropPresure dropDP/LFriction FactorFriction FactorFDPDPDP/Lmass
velosityFlowrateReDPDP/L
D (in)D (mm)D
(m)(m)^2(cc/min)(cc/sec)m^3/sec(m/sec)Rein(water)mPa(N/M2)f exp
(P1)f equ
1/8"0.2696.83260.00683260.000036680630050.0000050.13631177149.31E+020.802.00E-02196.00001.05E+020.019800.01430
1/8"0.2696.83260.00683260.0000366806600100.000010.27262354281.86E+031.904.75E-02465.50002.50E+020.011760.01203
1/8"0.2696.83260.00683260.000036680687014.50.00001450.39530413712.70E+034.501.13E-011102.50005.93E+020.013240.01096
1/8"0.2696.83260.00683260.0000366806105017.50.00001750.47709119993.26E+036.221.56E-011523.90008.19E+020.012570.01046
1/8"0.2696.83260.00683260.00003668061200200.000020.54524708563.73E+038.302.08E-012033.50001.09E+030.012840.01011
1/8"0.2696.83260.00683260.0000366806140023.33333333330.00002333330.63612159994.35E+0310.002.50E-012450.00001.32E+030.011370.00973
1/8"0.2696.83260.00683260.00003668061500250.0000250.6815588574.66E+0311.002.75E-012695.00001.45E+030.010890.00956
1/8"0.2696.83260.00683260.0000366806250041.66666666670.00004166671.13593142847.76E+0334.008.50E-018330.00004.48E+030.012120.00842
1/8"0.2696.83260.00683260.0000366806400066.66666666670.00006666671.81749028551.24E+0472.301.81E+0017713.50009.52E+030.010070.00748
1/8"0.2696.83260.00683260.000036680660001000.00012.72623542821.86E+04143.003.58E+0035035.00001.88E+040.008850.00676
P2
areaFlowrateFlowrateFlowratevelosityPresure dropPresure
dropPresure dropDP/LFriction FactorFriction Factor
D (in)D (mm)D
(m)(m)^2(cc/min)(cc/sec)m^3/sec(m/sec)Rein(water)mPa(N/M2)f exp
(P2)f equ
1/2"0.62215.79880.01579880.0001961159400066.66666666670.00006666670.33993500525.37E+031.102.75E-02269.50001.45E+020.010360.00923
1/2"0.62215.79880.01579880.000196115960001000.00010.50990250788.06E+032.305.75E-02563.50003.03E+020.009630.00834
1/2"0.62215.79880.01579880.00019611599100151.66666666670.00015166670.77335213681.22E+045.701.43E-011396.50007.51E+020.010370.00751
1/2"0.62215.79880.01579880.0001961159120002000.00021.01980501561.61E+049.602.40E-012352.00001.26E+030.010050.00701
1/2"0.62215.79880.01579880.000196115916000266.66666666670.00026666671.35974002072.15E+0415.203.80E-013724.00002.00E+030.008950.00653
1/2"0.62215.79880.01579880.0001961159180003000.00031.52970752332.42E+0419.004.75E-014655.00002.50E+030.008840.00634
1/2"0.62215.79880.01579880.000196115920000333.33333333330.00033333331.69967502592.69E+0421.005.25E-015145.00002.77E+030.007910.00617
P3
areaFlowrateFlowrateFlowratevelosityPresure dropPresure
dropPresure dropDP/LFriction FactorFriction Factor
D (in)D (mm)D
(m)(m)^2(cc/min)(cc/sec)m^3/sec(m/sec)Rein(water)mPa(N/M2)f exp
(P3)f equ
3/4"0.82420.92960.02092960.000344180710000166.66666666670.00016666670.48424176461.01E+041.203.00E-02294.00001.58E+020.007210.00787
1/2"0.82420.92960.02092960.0003441807120002000.00020.58109011751.22E+041.503.75E-02367.50001.98E+020.006260.00752
1/2"0.82420.92960.02092960.0003441807180003000.00030.87163517631.82E+043.408.50E-02833.00004.48E+020.006300.00680
1/2"0.82420.92960.02092960.000344180714000233.33333333330.00023333330.67793847041.42E+042.205.50E-02539.00002.90E+020.006740.00724
1/2"0.82420.92960.02092960.000344180720000333.33333333330.00033333330.96848352922.03E+044.701.18E-011151.50006.19E+020.007060.00662
0.94488
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