Reynold's Number


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ChE Laboratory Exp't, Reynold's Number -Final Report

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Reynold's Number

  1. 1. CEBU INSTITUTE OF TECHNOLOGY N. Bacalso Avenue, Cebu City Chemical Engineeing Department FINAL REPORT ChE Lab 1 Title of Experiment Juphil A. Lamanilao BSChE-5 Engr. Lyda P. Abellanosa Instructor
  2. 2. Abstract: The flow of real fluids can basically occur under two very different regimes namely laminar and turbulent flow. The laminar flow is characterized by fluid particles moving in the form of lamina sliding over each other, such that at any instant the velocity at all the points in particular lamina is the same. The lamina near the flow boundary moves at a slower rate as compared to those near the center of the flow passage. This type of flow occurs in viscous fluids, fluids moving at slow velocity and fluids flowing through narrow passages. The turbulent flow is characterized by constant agitation and intermixing of fluid particles such that their velocity changes from point to point and even at the same point from time to time. This type of flow occurs in low density. A fine filament of dye is introduced in to the flow of water through the glass tube where different types of flow are seen at its entrance. At low velocities the dye filament appeared as straight line through the length of the tube and parallel to its axis, characterizing laminar flow. As the velocity is increased the dye filament becomes wavy throughout indicating transition flow. On further increasing the velocity the filament breaks up and diffuses completely in the water in the glass tube indicating the turbulent flow.
  3. 3. Objectives: 1.) To experimentally determine the values of the upper and lower critical Reynold’s Number and compare these values with those found in literature. 2.) To tabulate observations on the behavior of the film of dye as a function of water velocity. Materials & Equipment: Reynold’s Apparatus, KMnO4 solution, stopwatch, beaker, funnel, stirring rod, thermometer. Sketch of the Set-up: Procedure: A. The equipment used was consisted of a horizontal glass tube immersed in a rectangular tank with water. A controlled flow of water was drawn through the tube by opening the valve. The entrance of the tube was flared and provision was made to introduce a fine filament of dye from as overhead flask into the water stream at the tube entrance. Initially, a thin film of dye is injected into the water stream at very slow water flow rate. Without turning off the flow of dye, the water flow rate was increased and with each incremental increase, quantity
  4. 4. of water was collected for flow rate measurements observation as to the behavior of the film of the dye was recorded as water flow varies from laminar to turbulent region. B. Procedure was repeated this time going from turbulent to laminar region. Tabulated Data & Result: LAMINAR FLOW TRIALS Volume, ml Time, s Discharge, Q(m3/s) Velocity,(m/s) NRE 1 175 33.94 5.156 x10-6 0.025645 491.05 2 150 33.98 4.41436x10-6 0.02196 421.09 3 141 34.72 4.0611x10-6 0.0202 387.307 4 150 34.64 4.33025x10-6 0.02154 412.976 5 150 34.18 4.3885x10-6 02183 418.534 6 150 33.44 4.4856 x10-6 0.02231 427.796 TURBULENT FLOW TRIALS Volume, ml Time, s Discharge, Q(m3/s) Velocity,(m/s) NRE 1 64.5 0.63 1.02381 x10-4 0.5092 9764.067 -4 2 48.5 0.44 1.10227 x10 0.5482 10512.37 3 52.5 0.53 8.9286 x10-5 0.49267 9447.024 4 62.5 0.70 8.9286 x10-5 0.44407 8515.175 5 45 0.57 7.8947x10-5 0.3927 7529.207 -4 6 59 0.59 1x10 0.49736 9537 Computations: (LAMINAR FLOW) Trial 1: NRE = (0.016)(0.02196)(2895.107) Given: Q = 175 ml/33.94 s 2.4157x10-3 T = 298.15 K = 5.156 x10-6 m3/s = 421.09 UH2O = 0.8937x10-3 Pa-s pH2O= 997.08 kg/m3 V= Q/A Trial 3: From Perry’s ChE Handbook: = (5.156 x10-3 m3/s) Q = 141 ml/34.72 s Sp. grav(KMnO4) = 2.703 2.01062x10-4 m2 = 4.0611x10-6 m3/s pKMnO4= (2.703)(997.08 kg/m3) = 0.025645 m/s = 2895.107 kg/m3 V= Q/A by interpolation: NRE = (0.016)(0.02565)(2895.107) = (4.0611x10-6 m3/s) U KMnO4 = 2.4157x10-3 Pa-s 2.4157x10-3 2.01062x10-4 m2 Di =0.016 m = 491.05 = 0.0202 m/s A = [3.1416(0.016m)2]/4 NRE = (0.016)(0.0202)(2895.107) = 2.01062x10-4 m2 Trial 2: 2.4157x10-3 NRE = (DVp)/u Q = 150 ml/33.98 s = 387.307 = 4.41436x10-6 m3/s V= Q/A = (4.41436x10-6 m3/s) 2.01062x10-4 m2 = 0.02196 m/s
  5. 5. Trial 4: = (4.4856x10-6 m3/s) Q = 150 ml/34.64 s 2.01062x10-4 m2 NRE = (0.016)(0.5482)(2895.107) = 4.33025x10-6 m3/s = 0.02231 m/s 2.4157x10-3 = 10512.37 V= Q/A NRE = (0.016)(0.02231)(2895.107) = (4.33025x10-6 m3/s) 2.4157x10-3 Trial 3: 2.01062x10-4 m2 = 427.796 Q = 52.5ml/0.53 s = 0.02154 m/s = 9.90567 x10-5 m3/s (TURBULENT FLOW) NRE = (0.016)( 0.02154)(2895.107) V= Q/A 2.4157x10-3 Trial 1: = (9.90567 x10-5 m3/s) = 412.976 Q = 64.5 ml/0.63 s 2.01062x10-4 m2 = 1.02381 x10-4 m3/s = 0.49267 m/s Trial 5: Q = 150 ml/34.18 s V= Q/A NRE = (0.016)(0.49267)(2895.107) -6 = 4.3885x10 m /s 3 = (1.02381x10-4 m3/s) 2.4157x10-3 2.01062x10-4 m2 = 9447.024 V= Q/A = 0.5092 m/s = (4.3885x10-6 m3/s) 2.01062x10-4 m2 NRE = (0.016)(0.509*2)(2895.107) Trial 4: = 0.02183 m/s 2.4157x10-3 Q = 62.5ml/0.70 s = 9764.067 = 8.9286 x10-5 m3/s NRE = (0.016)(0.02183)(2895.107) 2.4157x10-3 Trial 2: V= Q/A = 418.534 Q = 48.5ml/0.44 s = (8.9286 x10-5 m3/s) = 1.10227 x10-4 m3/s 2.01062x10-4 m2 Trial 6: = 0.44407 m/s Q = 150 ml/33.44 s V= Q/A -6 = 4.4856 x10 m /s 3 = (1.10227x10-4 m3/s) NRE = (0.016)(0.44407)(2895.107) 2.01062x10-4 m2 2.4157x10-3 V= Q/A = 0.5482 m/s = 8515.175 Trial 5: Q = 45ml/0.57 s = 7.8947x10-5 m3/s V= Q/A = (7.8947x10-5 m3/s) 2.01062x10-4 m2 = 0.3927 m/s NRE = (0.016)(0.3927)(2895.107) 2.4157x10-3 = 7529.207
  6. 6. Data Analysis : When discharge and Re having a small dye line was seen almost straight. This was clearly seen from stretches, until Re = 2000 i.e. from trial 1-6 (refer to the first table). This indicates laminar flow. When the discharge was further increased, the dye line moved towards pipe walls and still remains in a single line. This was seen in between the lower Re & upper Re when Re = 4000. Such flow indicates transition state and when the discharge is further increased, the straight streak line of the dye was seen for a small distance less than one third length of the pipe and then dye is thoroughly mixed in the flow this was turbulent flow. Re is more than 4000. Recommendation: In this experiment, the tank is of sufficient capacity to store water. So as to recommend, there should be a cock provided at the end of the glass tube to control the flow. The use of potassium permanganate is to give a brightly visible reddish streak such that it will be easy to determine what type of flow. Also, there should be proper materials when collecting the actual discharged water into the graduated cylinder where flow rate is further increased and since flow features are becoming different. Application to ChE: Aside from the application to fluid mechanics as to characterize different flow regimes, it is also an important quantity used in aerodynamics and hydraulics. Turbulent flow models of low Reynold’s number may be used to predict the electronic component heat transfer. This could ultimately help reduce the current dependency on experimental prototyping. With the new MEMS-based optical shear stress sensor, it is now possible to extend wall shear stress measurements to high Reynold’s number flows which can be obtained in the same manner using other techniques such as the oil film interferometry technique.