1 57:020 Mechanics of Fluids and Transfer Processes Exercise Notes for the Pipe Flow TM Measurement of Flow Rate, Velocity Profile and Friction Factor in Pipe Flows S. Ghosh, M. Muste, M. Wilson, S. Breczinski, and F. Stern 1. Purpose The purpose of this investigation is to provide students with hands-on experience using a pipe stand test facility and modern measurement systems including pressure transducers, pitot probes, and computerized data acquisition with Labview software, to measure flow rate, velocity profiles, and friction factors in smooth and rough pipes, determining measurement uncertainties, and comparing results with benchmark data. Additionally, this laboratory will provide an introduction to PIV analysis, using an ePIV system with a step-up model. 2. Experimental Design 2.1 Part 1: Pipe Flow The experiments are conducted in an instructional airflow pipe facility (Figure 1). The air is blown into a large reservoir located at the upstream end of the system. Pressure builds up in the reservoir, forcing the air to flow through any of the three horizontal pipes. Pressure taps are located on each pipe, at intervals of 1.524m, for static pressure measurements. Characteristics for each of the pipes are provided in Appendix A. At the downstream end of the system, the air 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 to be 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 the middle one is kept closed during the experiment. Velocity measurements in the top and bottom pipes are obtained using pitot probe (Figure 3). Figure1. Airflow pipe system Figure 2. Venturimeter Figure 3. Pitot-probe Pressures are acquired either manually, using simple and differential manometers for data acquisition, or automatically, with the manometers connected to an automated Data Acquisition (DA) system that converts pressure to voltages using pressure transducers. Data acquisition is controlled and interfaced by Labview software, described in Appendix B. The schematic of the two alternative measurement systems is provided in Figure 4. Figure4. Manual and automated measurement systems used in the experiment Data Acquisition Instrumentation Venturimeter Pitot tube Pressure tap Differential manometer Pressure transducer Labview Stagnation Static Simple manometer Pressure transducer Labview Labview Pressure transducer Simple manometer2 All pressure taps on the pipes, Venturi meters, and pitot probes have 0.635cm diameter quick coupler connections that can be hooked up to the pressure transducers. 2.1.1 Data reduction (DR) equations In fully developed, axisymmetric pipe flow, the axial velocity u = u(r), at a radial distance r from the pipe centerline, is independent of the direction in which r is measured (Figure 5). However, the shape of the velocity profile is different for laminar and turbulent flows. Laminar and turbulent flow regimes are distinguished by the flow Reynolds number, defined as DQVD 4Re  (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 the fluid. For fully developed laminar flow (Re < 2000), an analytical solution for the differential equations of the fluid flow (Navier-Stokes and continuity) can be obtained. For turbulent pipe flows (Re > 2000), there is no exact solution, hence semi-empirical laws for velocity distribution are used instead. The pipe head loss due to friction is obtained from the Darcy-Weisbach equation: Figure 5. Velocity distributions for fully developed pipe flow: a) laminar flow; b) turbulent flow 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 viscous effects, and g is the gravitational acceleration. The Moody diagram provides the friction factor for pipe flows with smooth and rough walls in laminar and turbulent regimes. The friction factor depends on the Reynolds number and the relative 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 data reduction equation (DRE) for the measurement of the velocity profiles is obtained by applying Bernoulli’s equation for the Pitot tube:   2/12)(StatStagSMSMawzrzgru (3) where u(r) is the velocity at the radial position r, g is the gravitational acceleration, )(rzStagSM is the stagnation pressure head determined by the Pitot probe located at radial position r, and StatSMzis the static pressure head in the pipe, equal to that of the ambient pressure inside the glass-walled box. These pressure head readings are given in height of a liquid column (ft of water). The DRE for the friction factor is one of the Darcy Weisbach equation forms (Roberson & Crowe, 1997), given as follows:  jSMiSMawzzLQDgf 2528 (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, and jSMiSMzz  is the difference in pressure between pressure taps i and j. The flow rate Q is directly measured using the calibration equations for the Venturi meters (Rouse, 1978): awDMtdzgACQ 2 (5) where Cd is the discharge coefficient, tA is the contraction area, and DMz 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 A lists Venturi meter characteristics. Alternatively, the flow rate can be determined by integrating the measured velocity distribution over the pipe cross-section, as follows:3 rirdrruQ0)(2 (6) 2.2 Part 2: ePIV EFD Lab 1 investigated the use of ePIV as a method for visualizing streamlines around