FPL Friction in a Pipe filament of dye Laminar (viscous) 2-3-²33²3² Turbulent Transitional CIVE210: Hydraulics Lecturer: UNIVERSITY OF LIVERPOOL Notation Note: v= Symbol hf U P μ P L V g D f NR Meaning Head loss due to friction Coefficient of kinematic viscosity Dynamic viscosity Fluid density FPL Lab Script // CIVE210 Length of pipe Mean flow velocity Gravitational acceleration Pipe diameter Friction factor Reynolds Number Unit m m²/s Ns/m² kg/m³ m m/s m/s² m - UNIVERSITY OF LIVERPOOL 1 NR=Introduction hf² 1.1Theory fLV² 2 gD VD f: U Figure 1 - Pipe Friction Experiment Scheme The head loss due to friction is given by the following empirical relationship, known as Darcy's equation: 32 ULV h₁= gD² (2) It follows from Eq. (1) that for laminar flow: 64 R L 0.316 0.25 The dimensionless friction factor f is a function of NR (and of the pipe roughness if the pipe is rough). For a given pipe, f is normally plotted as a function of NR on log-log scales as Moody Chart. NR T If N₁ is less than about 2000, the flow is laminar and head loss is proportional to the velocity, as demonstrated by Poiseuille's equation for laminar flow: V FPL Lab Script // CIVE210 f= (3) If NR is above 4000, the flow is turbulent and the head loss is proportional to V", where n is in the range from 1.75 to 2.0. For turbulent flow, it was shown by Blasius that experimental results for smooth pipes conform to (4) for Reynolds number up to 105. (1) 2 UNIVERSITY OF LIVERPOOL Note that, if for given conditions (e.g. every high NŔ in a rough pipe), h is proportional to V² and fis constant. For NR in the region between 2000 and 4000, the flow undergoes a transition between laminar and turbulent, and the head loss, and therefore the friction factor, is subject to some variability. References: Webber, pp 76-86; Essery, pp 31-33. 1.2Aims and Objectives FPL Lab Script // CIVE210 1.2.1 Aims To demonstrate pipe friction phenomena, principles and their applications in both laminar and turbulent flows; to gain an insight into the nature of fluid flow in pipes and relationships for estimating energy losses; to highlight the use of experiments to bridge the gap between theoretical analyses and real flow situations. Also, to provide practice in report writing, personal-study skills, data analysis and interpretation. 1.2.2 Objectives To investigate the variation of hydraulic gradient with respect to the velocity and the friction L factor f (defined by Darcy's equation) with respect to the Reynolds number over the laminar, transition and turbulent flow regimes. 1.3Procedure Before the test, remove any air trapped in the pipe or manometer. Progressively increase the flow rate in 5 steps for both laminar and turbulent flows. At each step, read the head loss hf, measure the flow rate by measuring the volume over a period of time. Two pipes with diameter of 4.5mm and 7.7mm are used for laminar and turbulent flows respectively. Flows in both pipes are driven by a pump with a valve to adjust the flow rate and the head losses for the length of L=1m are measured by the water manometer (for laminar flow) and a digital pressure transducer (for turbulent flow). 1.4Results From your measurements at each flow steps, calculate the hydraulic gradient (- L mean velocity V (flow rate divided by cross-sectional area), non-dimensional friction factor f (equation 1) and Reynolds number NR with the constant dynamic viscosity of µ=8.9 × 104 Ns/m². h Plot hydraulic gradient against mean velocity in logarithmic scale to check the validity of the conclusions that x V, in laminar flow L h₂ × V n is in the range of 1.7 and 2.0, in turbulent flow L Plot friction factor against Reynolds number in logarithmic scale and compare the results from equation (3) and (4) in laminar and turbulent flow respectively. 3 UNIVERSITY OF LIVERPOOL A set of data listed in Table 1 is obtained from the same apparatus as in this experiment and it is provided for your reference to check your measured data. Table 1 - Distribution of Head Loss and Velocity in pipe Pipe diameter (mm) Head Loss (mH₂O) Velocity in Pipe (m/s) 0.0150 0.1117 0.0270 0.2123 0.0400 0.2694 0.0470 0.3371 0.1180 0.5390 D=4.5 D=7.7mm Flow 0.0408 0.1071 0.2447 0.6118 1.0605 P₁ FPL Lab Script // CIVE210 1.5Further discussion In our lab, pressure drops are measured by either digital device or a water manometer with two tubes open to the atmosphere as shown in Figure 1. Discuss how to obtain the pressure drop in the pipe if mercury U-shaped manometer is used as shown in Figure 2. P₂ I 0.4004 0.6931 1.1018 1.8958 2.5783 Mercury Figure 2 - Pipe Friction Experiment using mercury manometer 4