Measurement of Flow Rate, Velocity Profile and Friction Factor in Pipe Flows1. Purpose3.1.4 Uncertainty AnalysisTable A1. Pipe characteristicsBottomAPPENDIX BStep 1: Initial SetupFigure B.3. Set pipe air temperatureStep 2: Discharge MeasurementsFigure B.4. Open DPD menuFigure B.5. Click on Acquire PressureFigure B.7. Enter position of pitot-tubeFigure B.8. Click OK when ready for static pressure measurementFigure B.11. Click on Write Results57:020 Mechanics of Fluids and Transfer ProcessesExercise Notes for the Pipe Flow TMMeasurement of Flow Rate, Velocity Profile and Friction Factor in Pipe Flows S. Ghosh, M. Muste, M. Wilson, S. Breczinski, and F. Stern1. PurposeThe purpose of this investigation is to provide students with hands-on experience using a pipe stand test facilityand modern measurement systems including pressure transducers, pitot probes, and computerized data acquisition withLabview software, to measure flow rate, velocity profiles, and friction factors in smooth and rough pipes, determiningmeasurement uncertainties, and comparing results with benchmark data. Additionally, this laboratory will provide anintroduction to PIV analysis, using an ePIV system with a step-up model.2. Experimental Design2.1 Part 1: Pipe FlowThe experiments are conducted in an instructional airflow pipe facility (Figure 1). The air is blown into a largereservoir located at the upstream end of the system. Pressure builds up in the reservoir, forcing the air to flow through anyof the three horizontal pipes. Pressure taps are located on each pipe, at intervals of 1.524m, for static pressuremeasurements. Characteristics for each of the pipes are provided in Appendix A. At the downstream end of the system, theair is directed downward and back, through any of three pipes of varying diameters fitted with Venturi meters (Figure 2).The top three valves control flow through the experimental pipes, while the bottom three valves control the Venturi meter tobe used. The Venturi meter with 5.08cm diameter is used to measure the total flow rate, while the other two are kept closed.Six gate valves are used for directing the flow. The top and bottom 5.08cm pipes are used for measurements, while themiddle one is kept closed during the experiment. Velocity measurements in the top and bottom pipes are obtained usingpitot probe (Figure 3). Figure1. Airflow pipe system Figure 2. Venturimeter Figure 3. Pitot-probePressures are acquired either manually, using simple and differential manometers for data acquisition, orautomatically, with the manometers connected to an automated Data Acquisition (DA) system that converts pressure tovoltages using pressure transducers. Data acquisition is controlled and interfaced by Labview software, described inAppendix B. The schematic of the two alternative measurement systems is provided in Figure 4. Figure4. Manual and automated measurement systems used in the experiment1All pressure taps on the pipes, Venturi meters, and pitot probes have 0.635cm diameter quick coupler connections that canbe hooked up to the pressure transducers.2.1.1 Data reduction (DR) equationsIn fully developed, axisymmetric pipe flow, the axial velocity u = u(r), at a radial distance r from the pipecenterline, is independent of the direction in which r is measured (Figure 5). However, the shape of the velocity profile isdifferent for laminar and turbulent flows.Laminar and turbulent flow regimes aredistinguished by the flow Reynolds number, defined as Re=VDν=4 QπDν (1)Where, V is the average pipe velocity, D is the pipe diameter,Q is the pipe flow rate, and ν is the kinematic viscosity of thefluid. For fully developed laminar flow (Re < 2000), ananalytical solution for the differential equations of the fluidflow (Navier-Stokes and continuity) can be obtained. Forturbulent pipe flows (Re > 2000), there is no exact solution,hence semi-empirical laws for velocity distribution are usedinstead. The pipe head loss due to friction is obtained fromthe Darcy-Weisbach equation:Figure 5. Velocity distributions for fully developedpipe flow: a) laminar flow; b) turbulent flowhf=fLDV22 g (2)where, f is the (Darcy) friction factor, L is the length of the pipe over which the loss occurs, hf is the head loss due toviscous effects, and g is the gravitational acceleration. The Moody diagram provides the friction factor for pipe flows withsmooth and rough walls in laminar and turbulent regimes. The friction factor depends on the Reynolds number and therelative roughness k/D of the pipe (for large enough Re, the friction factor is solely dependent on the relative roughness).Velocity distributions in the pipes are measured with Pitot tubes housed in glass-walled boxes (Figure 3). The datareduction equation (DRE) for the measurement of the velocity profiles is obtained by applying Bernoulli’s equation for thePitot tube:u(r )=[2⋅gρwρa⋅[zSMStag(r)−zSMStat]]1/ 2(3)where u(r) is the velocity at the radial position r, g is the gravitational acceleration, zSMStag(r ) is the stagnation pressurehead determined by the Pitot probe located at radial position r, and zSMStatis the static pressure head in the pipe, equal tothat of the ambient pressure inside the glass-walled box. These pressure head readings are given in height of a liquidcolumn (ft of water). The DRE for the friction factor is one of the Darcy Weisbach equation forms (Roberson & Crowe,1997), given as follows:f =gπ2D58 LQ2ρwρa(zSMi−zSMj)(4)where ρw, is the density of water, ρa is the density of air, L is the pipe length between pressure taps i and j, andzSMi−zSMj is the difference in pressure between pressure taps i and j. The flow rate Q is directly measured using thecalibration equations for the Venturi meters (Rouse, 1978): Q=CdAt√2 gΔzDM⋅ρwρa(5)where Cd is the discharge coefficient, At is the contraction area, and ΔzDM is the head drop across the Venturi,measured in height of a liquid column (ft of water) by the differential manometer or the pressure transducer. Appendix A2lists Venturi meter characteristics. Alternatively, the flow rate can be determined by integrating the measured velocitydistribution over the pipe cross-section, as follows: Qi= 2 π∫0ru (r)rdr(6)2.2 Part 2: ePIVEFD Lab 1