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323 ME Lab Report Experiment #3 Venturi Meter September 28, 2007 Submitted by: John Luff Submitted to: Dr. Perwez Kalim Division of Engineering and Physics Wilkes University, Wilkes-Barre, Pa. Abstract In this experiment a team of five students used the combination of a venturi meter and manometer in order to measure the flow rate or discharge of a pipe. Through the course of the experiment both actual and theoretical discharge were calculated using the obtained time and manometer readings. Though the beginning of the in-lab experiment got off to a rough start, for the most the lab went smoothly, and although our C values seem to be a little off, we produced very good graphical Log and values. 2 Experimental Data & Procedure Table 1 No . Manometer Readings h hl ht m mm mm Qtheo = k * h m3/s Actual Discharge Time sec t1 = 41.36 t2 = 42.49 t3 = 42.61 1 175 20 0.155 0.3787 t4 = 43.48 t5 = 43.05 tavg. = 42.2 t1 = 35.75 t2 = 35.59 t3 = 35.32 2 238 28 0.210 0.4408 t4 = 36.20 t5 = 36.30 tavg. = 35.85 t1 = 37.16 t2 = 37.81 t3 = 37.55 3 205 10 0.195 0.4248 t4 = 38.22 t5 = 38.6 tavg. = 37.86 t1 = 35.73 t2 = 35.19 t3 = 35.08 4 270 60 0.210 0.4408 t4 = 36.30 t5 = 36.20 tavg. = 35.64 t1 = 52.86 t2 = 53.68 t3 = 54.57 5 250 45 0.105 0.3117 t4 = 55.20 t5 = 55.70 tavg. = 54.29 Cavg= 0.9249 18kg 0.3370 0.9249 -0.4724 -0.9788 8.1173 18kg 0.4766 0.9249 -0.3219 -0.6778 8.1173 18kg 0.4592 0.9249 -0.3380 -0.7100 8.1173 18kg 0.4766 0.9249 -0.3219 -0.6778 8.1173 18kg 0.4094 0.9249 -0.3878 -0.8097 8.1173 Mass Kg Qact m3/s C= Qact/Qtheo log10Qa log10h % Error In Q 3 Table 2 Area Inlet m 0.5309 Area Throat m 0.2011 gravity (g) m/s2 9.81 Venturimeter Constant (k) 0.9619 Density of Water (N/m2) 9810 In order to obtain the results in table 1 the team conducted the following procedure: 1. The first step the team took was selecting a weight to use. The weight the team chose to was a 6kg weight, which brought the total to 18kg (This weight was used for all flow rates). 2. The next step was choosing a flow rate, which was done by controlling the bench supply valve and the flow control valve. The team made sure that the height difference between h1 and ht was always greater than 100mm. The difference in heights was then recorded in the experimental data table. 3. The third step was turning the hydraulic bench on and letting the water flow until the bar with the weight connected to it hit the stopper. During this step a team member would time how long it took for the bar to hit the stopper. 4. This time was recorded, and then recorded in the experimental data table. 5. After repeating step numbers three and four, five times the team would calculate the overall average time. 6. Steps one through five were repeated for a total of five different flow rates. Introduction The determination of flow rate is one of the most common problems dealt in with fluid mechanics. Often times to calculate flow rate a device known as a venturi meter is used. Venturi meters have been around for a long time and they are based off the principle of Bernoulli's theorem. The way they work is that they have two cones, one diverging and the other converging. When a liquid is run through the converging cone into a pipe with a much smaller cross-sectional area the water's flow velocity is increased and subsequently so is the waters velocity head, which causes a change in pressure head. To measure this change in pressure head, a manometer can be used. The change in pressure head can then be used to calculate flow rate of the liquid. 4 Results, Discussion, and Analysis Figure 1 log10(Qa) vs. log10(h) -0.2500 -0.6000 -1.0000 -0.9500 -0.9000 -0.8500 -0.8000 -0.7500 -0.7000 -0.6500 -0.3000 y = 0.5x + 0.017 -0.3500 log10(Qa) -0.4000 -0.4500 -0.5000 log10(h) Figure 2 Calibration Curve 310 305 Actual Discharge 300 295 290 285 280 0 0.05 0.1 Height 0.15 0.2 0.25 5 Figure 3 C vs. Re at throat 1.0000 0.9000 0.8000 0.7000 0.6000 C 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 0 200000 400000 600000 800000 Re 1000000 1200000 1400000 1600000 When the experiment was first started, the team ran into a lot of trouble trying to find flow rates that would produce a difference in height between h1 and ht that was equal to or greater than 100mm. The reason for this I believe was because of air bubbles trapped inside the pipe, so in order to fix the problem, with Dr. Kalims help, air was let out of the manometer manifold. After that little set back the rest of the in-lab experiment went very smoothly, the team had no other set backs. However, during the calculations part of the lab I did find it strange that all my calculated C values were identical (Table 1 and Figure 3). After re-doing and looking at the equations needed to find C (Eq. 1, Eq. 2 and Eq. 3) several times, the only reason for this that I could come up with was that the numbers were just very close and with rounding they all came out to be the same. Comparing the theoretical values of Log.( .25, from Eq. 8)) and (.5, given) we did fairly well, because our graphical Log = 0.017 and our graphical = .5. 6 Equations Used: * All equations come from reference 1. (1) Qtheo = k * h Qact. = At * 2 g (h1 ht ) At 1 ( )^2 Al (2) C= Qtheo. Qact. Al * At * 2 g . Al ^ 2 At ^ 2 (3) k= (4) Re = VD (5) Vt = 2 g (h1 ht ) At 1 ( )^2 Al (6) Log Qact. = Logh + Log y = mx + c m = and c = Log = .98*k & Log = Log (.98*k) (7) (8) 7 References: 1. Kalim, Perwez. Fluid Mechanics Laboratory Manual. Fourth. Wilkes University: Division of Engineering and Physics, 2006. 2. Crowe, Clayton T., Donald F. Elger, and John A. Roberson. Engineering Fluid Mechanics. Eighth. Hoboken: John Wiley & Sons, 2005. 8 ... View Full Document