Figure 4. Valve manifoldLaboratory Experiment #2Measurement of Velocity Profile and Friction Factor in Pipe Flows1. Purpose3.4 Uncertainty AssessmentTable 1. Pipe characteristicsBottom1. Using the Venturi meterAPPENDIX BFigure B.3. Schematic of ADASInitial SetupFigure B.7. Set pipe air temperatureDischarge MeasurementsFigure B.8. Click on the DPD tap to measure Differential Pressure for Discharge estimationFigure B.9. Click on Acquire PressureFigure B.10. Click on Write ResultsFigure B.11. Write results to a fileFigure B.13. Enter position of pitot-tubeFigure B.14. Click OK when ready for static pressure measurementFigure B.15. Click on Write ResultsFigure B.18. Click on Write Results57:020 Mechanics of Fluids and Transfer ProcessesLaboratory Experiment #2 Measurement of Velocity Profile and Friction Factor in Pipe Flows M. Muste, F. Stern, M. Wilson, and S. Ghosh1. PurposeTo measure velocity profiles and friction factors in smooth and rough pipe flows, determine the measurement uncertainties,and to compare the measurements with benchmark data.2. Experiment DesignIn a fully developed, axisymmetric pipe flow (see Figure 1), the axial velocity (the only velocity component) at somedistance r from the pipe centerline, u = u (r) is the same whatever the direction in which r is considered. However, theshape of the velocity profile is different for laminar or turbulent.Laminar and turbulent flow regimes are distinguishedby the flow Reynolds number defined as DQVD 4Re  (1)where V is the pipe average velocity, D is the pipediameter, Q is the pipe flow rate, and ν is thekinematic viscosity of the fluid. For fully developedlaminar flow (Re < 2000), analytical solution for thedifferential equations of the fluid flow (Navier-Stokesand continuity) can be obtained. For turbulent pipeflows (Re > 2000), there is no exact solution of theNavier-Stokes equations. Semi-empirical laws forvelocity distribution are used instead for turbulentflows. ( a )( b ) 2 Rrd hd AAP a r a b o l i cc u r v eu ( r )u ( r )r2 Ruum a xm a xVVww2 RFigure 1. Velocity distributions for fully developedflow in a pipe flow: a) laminar flow; b) turbulent flowVelocity distribution in pipe flows is directly linked to the distribution of the shear stress within the pipe cross section(http://css.engineering.uiowa.edu/fluidslab/referenc/concepts.html - select Pressure-Driven Pipe Flows). The pipe-headloss due friction is obtained from the Darcy-Weisbach equation:gVDLfhf22 (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 to viscouseffects, and g is the gravitational acceleration. Moody chart provides the friction factor for pipe flows with smooth andrough walls in laminar and turbulent regimes. The friction factor depends on Re and relative roughness k/D of the pipe (forlarge enough Re, the friction factor is solely dependent on the relative roughness).The experiments are conducted in an instructional airflow pipe facility sketched in Figure 2. The air is blown into a largereservoir located at the upstream end of the system. Pressure built up in the reservoir forces air to flow through any of thethree straight experimental pipes. Pressure taps are located along each of the pipes to allow pressure head measurements.The pipe characteristics for each of the pipes included in the facility are provided in Appendix A. At the downstream end ofthe system, the air is directed downward and back through any of three pipes of varying diameters fitted with Venturimeters. Six gate valves are used for directing the flow. The top three valves control flow through the experimental pipes,while the bottom three valves control which venturi meter is used. Velocity distributions in the pipes are measured with Pitot tubes housed in glass-walled boxes, as sketched in Figure 3. Thedata reduction equation (DRE) for the measurement of the velocity profiles is obtained by applying Bernoulli’s equation forthe Pitot tube  2/12)(StatStagSMSMawzrzgru(3)1where u(r) is the velocity at the radial position r, g is the gravitational acceleration, )(rzStagSM is the stagnation pressurehead sensed by the Pitot probe located at radial position r, StatSMzis the reading for the static pressure head in the pipe,equal to that of the ambient pressure in the glass-walled box. The readings of the pressure heads in Equation (3) are inheight of a liquid column (ft of water), hence the density of water, ρw, and air, ρa are also involved in the equation to accountfor pressure conversion. P r e s s u r eT a p sA D A S2A D A S1M o t o rC o n t r o l l e rF l o o r6 ’ - 6 ”R e s e r v o i r2 . 0 ” s m o o t h0 . 5 ” s m o o t h2 . 0 ” r o u g hR e l i e fV a l v e sB l o w e rD = 2 . 0 ”D = 1 . 0 ”D = 0 . 5 ”ttt3 6 ’ - 0 ”V e n t u r i M e t e rG a t e V a l v e sT h e r m o m e t e r1234V a l v eM a n i f o l dS i m p l eM a n o m e t e rP i t o t T u b eH o u s i n g sV a l v e sD i f f e r e n t i a lM a n o m e t e rV e n t u r iM e t e r sFigure 2. Airflow pipe systemA number of equally spaced pressure taps are located along each of the pipes to allow for head measurements andsubsequent calculation of pipe friction factor. The location of the pressure taps is provided in Appendix A. DRE for thefriction factor is one of the Darcy Weisbach equation forms (Roberson & Crowe, 1997) jSMiSMawzzLQDgf 2528(4)where D is the pipe diameter, L is the length of pipe between the taps i and j, jSMiSMzz  is the difference in pressure(height of water column) between the taps i and j, and Q is the pipe flow rate. The flow rate (discharge) can be directlymeasured using the calibration equations for the Venturi meters (Rouse, 1978) awDMtdzgACQ 2(5)where Cd is the discharge coefficient, tA is the contraction area, DMz is the head drop across the Venturi measured inheight of liquid column (ft of water) by the differential manometer or ADAS. Appendix A lists Venturi meter characteristicsand provides details on the derivation of Equation (5). Alternatively, the flow rate can be determined by integrating themeasured velocity distribution over the pipe cross-section rirdrruQ0)(2(6)Pressure measurements can be