Reynold's Experiment - Correlation between Increase of the Flow of Water and the Reynolds Number - Lab Report Example

Reynolds Experiment Course Tutor Date Introduction and Aims of the Experiment This experiment was aimed at investigating laminar, transition and fully turbulent flows in pipes in a bid to find out the conditions under which they occur. To begin with, laminar flow is defined as a flow in which fluid flow occurs in parallel layers without any signs of disturbance. Transition flow is a mixture of laminar and turbulent flow due to minimal disturbance that realizes Reynolds coefficients of 2,000 to 4,000. Turbulent flow is defined as flow that is characterised by chaotic properties such as eddies of all sizes thereby resulting to dissipation of heat energy as a large part of mechanical energy goes into the formation of this disturbance (Warhaft, 1997). Fluid flow in pipes has been found to be affected by such factors as the physical traits of the fluid (density and viscosity), velocity, changes in temperature, pipe parameters (inner diameter, internal pipe roughness and length), position of discharge and supply, number of fittings such as valves, entrance and exit conditions of the pipe and the pipe layout (Daxesoft Ltd, 2014). These factors were studied by Reynolds who postulated that the nature of flow depended on basic ratio of inertia to viscous force; a non-dimensional derivation which came that came to be referred to as Reynolds number. Further to this it was established that inertia forces are proportional to mass multiplied by velocity change divided by time. An expression of mass flow rate which is also equal to the density multiplied by the cross sectional area multiplied by velocity results to equation (1) below for viscous forces. Inertia forces (where d is internal pipe diameter). Viscous forces But is the kinematic viscosity force. Therefore the expression for Reynolds number becomes: (1) Reynolds made discoveries that the transition between laminar and turbulent flow occurs at approximately the same value of Re irrespective of the pipe size – thereby making the prediction of flow easier. The precise point at which these types of flow occur however remains a mystery due to complexity in boundary definition. Methodology Apparatus The experimental apparatus used to carry out this experiment basically resembled to that used by Reynolds in terms of the physical features. The bore of the glass tube was 12mm diameter supported by a large shroud of rust proof material. The shroud was open in the front part with a light colour on the inside surface to aid in coming up with visual observation. A constant head tank was positioned at the top of the shroud in order to allow for water to pass through the tube via a specially shaped bell-mouth entry. Water was supplied through the diffuser which was situated below the bell-mouth for purposes of flow uniformity. In order to achieve a smoother flow, the stilling bed was packed with glass beads just above the diffuser. The supply pipe was situated at the rear of the tank through a direct connection to the tap and the temperature control unit. An overflow pipe was fitted in order to enhance a constant head – this is the point where a flexible pipe was connected. A valve at the outlet was meant for tube controls – it was connected to a loose hose to allow for convenient draining. Flow was measured by checking the quantity of water against time or by using a flow meter connected to the drain pipe. Figure 1: Reynolds experimental setup. Procedure The methodology applied in carrying out this experiment followed the basic procedures to demonstrate the variance in pipe conditions with the flow velocity. A range of velocities was covered in order to come up with the Reynolds number for each of the pipe conditions depending on the viscosity of water due to varying temperatures. First of all, the apparatus was set up and the water supply turned on with a partial opening of the discharge valve situated at the base of the apparatus. The water level was adjusted until the level in the water tank achieved a constant head just above the over flow and was maintained at this level by a small flow down the overflow pipe. Since this is one of the objective conditions required for all the tests to be carried out, the supply rate was adjusted to maintain it at different flow rates through the tube. Another condition worth mentioning is that the overflow was sufficient in maintaining a constant head in the tank. The dye injector valve was opened and adjusted to obtain a fine filament of dye in the flow down the glass tube. It was noted that when the dye was dispersed, the tube reduced the water flow rate by closing the discharge valve and adjusting the supply valve necessarily in order to maintain a constant head. A laminar flow was also projected to be achieved under conditions whereby dye filament passes down the complete length of the tube without disturbance. The rate of flow was increased slowly by opening the discharge valve until the filament disturbances were observed. This discharge was recorded down as the inception point of transition to turbulent flow. Water supply was increased as required in order to maintain constant head conditions in the tank. The flow rate was further increased until the disturbances on the dye filament became rapidly diffused as shown in figure 2 below. Small eddies were noted just above the point where the dye filament was observed to completely break down. This point was recorded as the as the onset of full turbulent flow together with accompanying variables i.e. temperature and the flow rate. The flow rate was then decreased slowly until the dye returned to a steady filament representing laminar flow and the flow rate together with the temperature recorded. All the data drawn from this experiment was recorded in the table that is shown in the results section below. Figure 2: A graphical representation of laminar, transitional and turbulent flow. Results Table 1: Results. Volume Time Flow rate from flow meter Temperature Pipe diameter Velocity in the pipe Viscosity Re Type of flow (L) (S) (L/s) (°C) (mm) (m/s) (m2/s)x10-6 (Vd/v) 0.2 154.03 1.3x10-3 25 12 0.115 1000 1380 Laminar 0.2 26.22 7.6x10-3 26 12 0.675 1000 8100 Turbulent 0.2 8.60 2.3x10-2 28 12 2.05 1000 24,600 Turbulent 0.2 19.1 1.05x10-2 28 12 0.92 1000 11,040 Turbulent 0.2 41.2 4.85x10-3 12 0.429 1000 5148 Turbulent 0.2 86.1 2.32x10-3 12 0.205 1000 2460 Transition Calculations: Cross sectional area of the pipe = = = = 1380 = 8100 = 24,600 = 11,040 = 4,158 = 2,460 Figure 3: A graph of speed change against Reynolds coefficient change. Discussions From our definitions above, laminar flow is highly ordered with a smooth streamlines of fluid motion. Transition flow on the other side is characterised by a mixture of both laminar and turbulent flow (with a Reynolds coefficient ranging from 2,000 to 4,000. Lastly, turbulent flow is characterised by highly disorderly fluid motion with a high Reynolds coefficient and velocity fluctuations thereby leading to eddies. Reynolds experiment is very clear with all this kinds of flow with laminar exhibiting a thin filament of dye as a single straight line due to uniform flow. Uniform fluid flow shows no dispersion in fluid particles thus the molecules are maintained within a single line of flow. Turbulent flow was seen as dispersed or entangled threads of dye once the filament was injected into the system. These observations were referenced against the key graphic presentation shown in figure 2 above in order to carry out a comparative analysis of these types of flow. The experiment successfully portrayed the flows that were being investigated with a documentation of other observations and parameters including volume time and velocity. The major derivatives in this experiment were the Reynolds coefficient which was calculated as shown in the results section above in order to observe the limits within which these flows occur. The initial hypothesis that laminar flow occurs for Reynolds coefficient of up to 2000 was observed to be true. For other types of flows ranging from transition to turbulent flow, the derivatives obtained exhibited positive results for transition flow at Reynolds coefficient greater than 2000 but not exceeding 4,000. Beyond 4,000, the turbulent flow was seen due to high velocity of water. These results were then transformed into a graph of speed change against Reynolds coefficient change. The graph obtained showed a straight line which if extended would have gone back to the origin (0, 0). It was concluded from the graph that change in speed is directly proportion to change in Reynolds number. Conclusion Increasing the flow of water increases the Reynolds number as shown in the calculations carried out in the results section. Laminar flow is characterised by a thin line in the event of Reynolds experiment which exhibits low coefficients too. From the observations it can be said that most of the existing flows are turbulent owing to four results in turbulent flow against one each for the rest of the flows. Further, it is proven that Reynolds coefficient is dimensionless. References Daxesoft Ltd. (2014, May 8). Pipe Flow 3D - Fluid Flow Factors. Retrieved from Pipe Flow: http://www.pipeflow.co.uk/public/control.php?_path=/497/503/586 Warhaft, Z. (1997). Transition and Turbulence. Cambridge: Cambridge University Press. Retrieved from https://www.princeton.edu/~asmits/Bicycle_web/transition.html Read More