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.

APPARATUSPipe NetworkRotametersManometers

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)

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)

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

Laminar flowContinue Forces balance

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

Laminar flowContinueHagen-Poiseuille

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,)

Turbulent flowAll previous parameters involved three fundamental dimensions,Mass, length, and time From these parameters, three dimensionless groups can be build

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

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)

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)

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

Friction Factor for Smooth, Transition, and Rough Turbulent flow

Fanning Diagramf =16/Re

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

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

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

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

Energy Loss due to Gradual Expansion angle ()A2A1

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

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

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.

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

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).

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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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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