expt. 3 - efflux time (prelaboratory)

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Labutong, Fidel Ivan Pastores, Janet Stephanie Tagapan, John Paolo Yeung, Angelyn 4ChE-A

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This is a prelaboratory report about the experiment Efflux Time using the Efflux Time Apparatus. It shows the theory behind efflux time and the materials and method on how to do the experiment

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Labutong, Fidel IvanPastores, Janet StephanieTagapan, John PaoloYeung, Angelyn4ChE-A1. To determine the efflux time needed to drain a tank with a set of exit pipes with different lengths and diameters2. To derive mathematical correlation between the efflux time and the pipe size and the tank diameterPipe flows may be classified as laminar or turbulent. In case where any of the two situations are not strictly observed, flow is said to be transitional.Re 2,100Re 4,000Flow of fluid inside the pipe depends on the length and diameter of the pipe. The boundary layer is a dynamic phenomenon. Its thickness increases as the fluid moves downstream. Boundary layer from the walls grow to such an extent that they all merge on the centreline of the pipe.Once this takes place, inviscid core terminates and the flow is all viscous. The flow is now called a Fully Developed Flow.Le=0.06D () Laminar flowLe=4.4D()

16Turbulent flowEfflux time apparatusPailPipeViscosity and density of water was measured. Then 3.5liters of water was prepared in a pail and slowly poured intothe tank while covering the orifice. After emptying the pail,water was allowed to flow from the orifice and a second pailwas placed to catch the water falling. Time was recorded untilthe tank was empty.A pipe was thenattached to the orificeof the tank and wasfilled with water whilethe exit pipe is beingcovered.Upon draining, thetime it takes for aheight interval of 1-2cm from level viewport was recorded untilthe tank was empty.First pipe was then removed and replaced withanother pipe and the same procedure was used.Formation of vortex was also considered. Three trialswere done for each pipe.After using all 10 pipes, 50% glycerol-watermixture was used in place of water, following thesame process.Pipe No.Diameter(m)Length(m)Height Interval(cm)Velocity (m/s) Time(s)Reynolds No. Le(m)1 0.005 0.75 1.00 0.0017 98.95 313.760.094132 0.0075 0.77 1.00 0.0045 38.71 830.55 0.373 0.011 0.75 2.00 0.0092 14.19 1698.01 1.124 0.017 0.74 2.00 0.0228 8.23 4208.12 0.305 0.0185 0.74 2.00 0.0304 7.07 5610.83 0.346 0.013 0.58 2.00 0.0149 10.27 2750.05 2.157 0.0133 0.63 2.00 0.0154 9.78 2842.33 2.278 0.0134 0.88 2.00 0.0158 11.01 2916.16 2.349 0.0131 1.01 2.00 0.0148 13.49 2731.59 2.1510 0.01312 1.14 2.00 0.0168 10.07 3100.72 2.44Table 1. Experimental Data for Water Pipe No. D/d L/D Velocity (m/s) Time(s)Reynolds No.Le (m)1 33.74 4.47 0.0069 23.03 1282.24 0.382 22.49 4.54 0.0351 4.56 6480.71 2.923 15.34 4.46 0.1628 0.98 30041.36 0.274 9.92 4.40 1.4878 0.11 171627.02 0.565 9.12 4.38 2.0879 0.08 240848.68 0.646 12.98 3.46 0.3271 0.49 60372.99 0.367 12.68 3.74 0.3548 0.45 65492.45 0.378 12.59 5.23 0.3529 0.45 65136.30 0.379 12.88 5.98 0.3186 0.50 58811.06 0.3610 12.86 6.75 0.3176 0.50 58620.53 0.36Table 2. Theoretical Data for Water Pipe No.Diameter(mm)Length(m)Height Interval(cm)Velocity (m/s)Time(s)Reynolds No. Le(m)1 0.005 0.75 1.00 0.0013120.53 49.20 0.01472 0.0075 0.77 1.00 0.00 35.06 174.08 0.07833 0.011 0.75 2.00 0.01 15.15 488.17 0.32214 0.017 0.74 2.00 0.02 7.09 851.46 0.86845 0.0185 0.74 2.00 0.03 5.56 1067.16 1.18456 0.013 0.58 2.00 0.01 11.04 556.28 0.43397 0.0133 0.63 2.00 0.02 10.96 590.34 0.47108 0.0134 0.88 2.00 0.02 10.89 597.91 0.48079 0.0131 1.01 2.00 0.01 11.91 563.85 0.443110 0.01312 1.14 2.00 0.02 10.60 639.54 0.5034Table 3. Experimental Data for Glycerol SolutionPipe No. D/d L/D Velocity (m/s) Time(s) Reynolds No. Le1 33.74 4.47 0.00142443 112.33 53.90 0.022 22.49 4.54 0.007199378 22.22 272.44 0.123 15.34 4.46 0.033372758 4.79 1262.91 0.834 9.92 4.40 0.190659379 0.84 7215.03 7.365 9.12 4.38 0.267557279 0.60 10125.03 11.246 12.98 3.46 0.067067974 2.39 2538.02 1.987 12.68 3.74 0.072755152 2.20 2753.24 2.208 12.59 5.23 0.072359501 2.21 2738.26 2.209 12.88 5.98 0.06533283 2.45 2472.36 1.9410 12.86 6.75 0.065121179 2.46 2464.35 1.94Table 4. Theoretical Data for Glycerol SolutionRe = (Dtankv)/ Le = 0.06D(Re) for laminar Le = 4.4D(Re)1/6for turbulent Efflux Time = 8LR2ln( 1+ H/L) * for laminar Efflux Time = 5LR2ln( 1+ H/L) * for turbulent Using pipe 1:Re = (laminar)Le = 0.06(0.005)( 313.76) = 0.09413mEfflux Time8(0.0009155)(0.754)(0.084352)ln(1+* Efflux Time = 23.03sD/d = (0.08435)(2)/0.005 = 33.74L/D = 0.75/(0.08435)(2) = 4.47Using Pipe 4:Re = (turbulent)Le = 4.4(0.017)( 4208.12)1/6 = 0.30mEfflux Time =5(0.0009155)(0.74)(0.084352)ln(1+* Efflux Time = 0.11sPlot of Height Interval (cm) vs Time (s) for water0.002.004.006.008.0010.0012.0014.0016.000.00 20.00 40.00 60.00 80.00 100.00Pipe 1Pipe 2Pipe 3Pipe 4Pipe 5Pipe 6Pipe 7Pipe 8Pipe 9Pipe 10Height Interval (cm) vs Time (s)0.002.004.006.008.0010.0012.0014.0016.000.00 20.00 40.00 60.00 80.00 100.00 120.00Pipe 1Pipe 2Pipe 3Pipe 4Pipe 5Pipe 6Pipe 7Pipe 8Pipe 9Pipe 10Height Interval (cm) vs Time (s)Plot of Height Interval (cm) vs Time (s) for glycerol solution00.20.40.60.811.20.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00Le (m) vs D/d00.20.40.60.811.20.00 10.00 20.00 30.00 40.00Le vsD/dPlot of entry length vs Ratio of Diameters for Water and Glycerol Solution2.102.152.202.252.302.352.402.452.500.00 2.00 4.00 6.00 8.00Le vs L/D0.430.440.450.460.470.480.490.50.513.00 4.00 5.00 6.00 7.00Le vs L/DPlot of Entry Length vs Ratio of Length of Exit Pipe with Tank Diameter for Water and Glycerol Solutiony = 0.1287x2- 1.778x + 12.586R = 0.99830.0020.0040.0060.0080.00100.00120.000.00 10.00 20.00 30.00 40.00ExperimentalTheoreticalEfflux Time(s) vs D/dy = 0.199x2- 4.0194x + 28.716R = 0.99660.0020.0040.0060.0080.00100.00120.00140.000.00 10.00 20.00 30.00 40.00experimentaltheoreticalEfflux Time (s) vs D/dPlot of Efflux Time vs Ratio of Diameters for Water and Glycerol Solution y = -2.756x + 35.24R = 0.0090.0020.0040.0060.0080.00100.00120.000.00 2.00 4.00 6.00 8.00Efflux Time(s) vs L/DTheoreticalExperimentaly = -3.6064x + 40.976R = 0.01060.0020.0040.0060.0080.00100.00120.00140.000.00 2.00 4.00 6.00 8.00 10.00 12.00experimentaltheoreticalEfflux Time (s)vs L/DPlot of Efflux Time vs Ratio of Length of Exit Pipe with Tank Diameter for Water and Glycerol Solution 1. Give practical applications of the principle of efflux time. What areas of chemical engineering can we apply this concept.The principle of efflux time can be applied for the pipe connections that we cansee everywhere. For the industry, it can beused to measure the time it takes for a fluidto flow out of the pipe or vessels. It isimportant to know the time it takes to emptya tank because it is the time to process a reactor volume. For reactors, efflux time is a factor used to determine down time. Fluid mechanics is an area of chemical engineering where we can apply the concept of efflux time. 2. In cases where there is a desired efflux time, what design consideration must be applied?If you are given a desired efflux time, the design of the container should be in a way that diameter and length of the container will be taken into account.For water at pipe 1: % Difference = at pipe 5: % Difference = For glycerol at pipe 1: % Difference = at pipe 5: % Difference = The efflux time has been determined for a tank with a set of exit pipes with varying lengths and diameters. Efflux time was found to be higher for longer pipes and lower for pipes with larger diameter. However, experimental results were not matched with the theoretical values. This may have resulted from the presence of vortex when draining the tanks, surface roughness, dirt and inaccurate gathering of data for recording the time. From the calculated least and highest % difference, it was observed that it both occurred at pipe 1 and 5 for the two liquids used respectively. 1.Pour the fluid slowly so that the tank will not overflow.2. Be alert when recording time.3. Be observant, look for signs of vorticity. 4. Clean the area after the experiment.5. DONT PLAY IN YOUR WORKPLACE.