Experiment 1 Fluid Flow In A Smooth Pipe Abstract In this experiment, three variable flow meters are used to alter the flowrate. Changes in pressure drop due to the change in flowrate are then observed from the three pressure gauges that can measure pressure at different range and recorded. The shift from laminar flow to turbulent flow is seen from the results recorded, but it is observed more clearly from the water-soluble dye experiment that was carried out by the demonstrator.
Laminar flow turns to be turbulent when the Reynolds Number goes above a certain value, around 2000. Aims To look at how the pressure drop changes when the average velocity is altered in a circular pipe and to plot a graph of Friction Factor versus Reynolds Number. Another aim is to examine the shift from laminar flow to turbulent flow. Schematic Diagram Water Out Inverted Water-air Manometer Wet-wet Digital Differential Pressure (0-100kPa) Capsuhelic Differential Pressure (0-250kPa) 1600 L/hr 250 L/hr 70 L/hr 1. 5m Water In water-soluble dye
P P P Figure 1: Schematic Diagram of Apparatus Used and Direction of Flow in a Smooth Pipe Results A graph of log – log plot of f versus Re is plotted, and a straight line of best fit through the data points for laminar flow is drawn: Figure 2: Graph of log – log plot of f versus Re Discussions To calculate the slope of the best fit line from Figure 2, two points are selected: (600, 0. 02) and (200, 0. 07) slope=log(0. 02)-log? (0. 07)log600-log? (200) slope=-1. 14 Theoretically, in the laminar flow regime for pipe flow, f=16Re ogf=log? (16Re) logf=log16-log? (Re) logf=-logRe+1. 2 So, we expect the value of the slope to be -1. In Figure2, the slope found is -1. 14, which is close to -1. Both values agree with each other. At the maximum flowrate, Q = 1600L/hr = 4. 44 x 10-4 m3/s The parameters: d=0. 0126 m ? =999. 44 kg/m3 ? =0. 001222 kg/ms Sample calculation to calculate the velocity, V: V=QA V=Q? d24 V=4. 44? 10-4 m3/s? 0. 0126 m24 V=3. 56 m/s The pressure difference (pressure reading on the apparatus), ?
P is read from the pressure gauges, and at the maximum flowrate, ? P=19100 Pa For the Reynolds Number, Re: Re=? Vd? Re=999. 44 kg/m33. 56 m/s(0. 0126 m)0. 001222 kg/ms Re=36686. 48 The value of the calculated Re is slightly different from the one in Excel file, this is due to the difference in decimal places that are taken into account in the calculation. Fanning friction, f: f=? PLd2? V2 f=191001. 50. 01262999. 44(3. 56)2 f=0. 0063 Head loss, hf: ?P=? ghf 19100=999. 449. 81(hf) hf=1. 948 m Using the definition gz1+V122+P1? =gz2+V222+P2? the condition z1? z2 is true if the two pressure taps are not horizontal (at different height). While the condition V1? V2 is true if the cross sectional area of the pipe is not the same from the first pressure tap to the second pressure tap. Considering a viscous liquid that is being pumped through a smooth pipe with the parameters: ? =1460 kg/m3 ? =5. 2? 10-1Ns/m2 D=0. 1 m Q=5? 10-2 m3/s To determine the velocity, V=QA V=5? 10-2? 0. 124 m/s V=6. 37 m/s Then find the Reynolds Number, Re=? VD? Re=14606. 370. 15. 2? 10-1
Re=1788. 5 According to Figure 2, the Fanning friction factor is 0. 007. The Bernoulli equation: ?P? +g? z+? 12V2+2fLV2D+Ws=0 Horizontal pipe, so ? z=0 Constant pipe cross sectional area, so ? 12V2=0 Also, work done by pump, WP=-Ws So the Bernoulli equation is reduced to ?P? +2fLV2D-WP=0 WP=? P1460+20. 007L6. 3720. 1 F=WPL=6. 85? 10-4? PL+5. 68 N Conclusion A graph of Fanning Friction Factor is plotted. Laminar regime and turbulent regime is obviously separated. Laminar flow tends to change to turbulent when the flowrate is increased.
