Fluid Mechanics Experiments - Lab Report Example

Contents Contents 1 Abstract 2 CENTRE OF PRESSURE 2 Introduction 2 Aim 3 Results 4 Conclusion 11 References 12 REYNOLDS EXPERIMENT 13 Introduction 13 Results 14 Calculations 14 Conclusion 22 Abstract This paper gives an overview of the three fluid mechanics experiments that are the most common. These are designed within the concepts of the Reynolds Number and Centre of Pressure. The experiments were conducted separately. At first, an experiment was conducted with the aim of examining the main types of fluid flow, which include Laminar, Transitional and Turbulent flow. Further, the aforementioned experiment was aimed at establishing the relationship between the three types of fluid flow mentioned above and the Reynolds number. A number of parameters that are used in finding the Reynolds number were determined by altering a fluid’s flow velocity, thus the conditions for occurrence of laminar, transitional and turbulent flows were identified. In addition, the experiment’s center of pressure, for both partial and whole submerging of plane surfaces, was examined. In order to compare the theoretical and experimental centers of pressure, the submerged surfaces were placed at 0o and 30o. The experiment’s results fluctuated slightly as a result of the inaccuracy of measurements, which occasioned the difference between theoretical and experimental results. Despite the fact that there were some inaccurate measurements during the experiment, the right conclusions were drawn from the fitted curve in the graph. CENTRE OF PRESSURE Introduction Centre of Pressure is a term that is used to refer to the point on a given body where the total pressure sum acts on it. The action of the force on the Centre of Pressure results in an equivalent force and moment. The direction of the force is guided by the point of pressure (Centre of Pressure). The experiment utilised an apparatus comprising of a Perspex assembly with a semi-circular quadrant for containing water. On the opposing side of the aforementioned quadrant, the apparatus had an additional tank that had a weight hanger that gave the setup a trimming facility. The apparatus was set up in such a way that the axes of the Perspex quadrant’s cylindrical sides were aligned with the centre of rotation. This was meant to ensure that only the fluid pressure moment acts on the apparatus. Aim This experiment is aimed at measuring the centre of pressure in two scenarios: for a plane that is fully submerged i.e. 0o; and for a plane that is submerged partially i.e. trimmed at 30o. In addition, the experiment is aimed at making comparisons between the theoretical values that exist regarding the centre of pressure, and experimental values for the same. Results W (g) M =W x 9.81x R3 h (mm) h(m) h3 (m3) M+(yBR22*h/2) Yp (Experiment) Yp (Theoretical) 70 0.20601 170 0.17 0.004913 0.206635388 0 0.008235294 0.056666667 120 0.35316 150 0.15 0.003375 0.353711813 0 0.016 0.05 170 0.50031 135 0.135 0.00246038 0.500806631 0 0.025185185 0.045 220 0.64746 125 0.125 0.00195313 0.647919844 0 0.0352 0.041666667 270 0.79461 113 0.113 0.0014429 0.795025699 0 0.047787611 0.037666667 320 0.94176 105 0.105 0.00115763 0.942146269 0 0.060952381 0.035 370 1.08891 95 0.095 0.00085738 1.089259481 0 0.077894737 0.031666667 420 1.23606 90 0.09 0.000729 1.236391088 0 0.093333333 0.03 50 0.14715 140 0.14 0.002744 0.147665025 30 0.014285714 0.046666667 100 0.2943 125 0.125 0.00195313 0.294759844 30 0.032 0.041666667 150 0.44145 115 0.115 0.00152088 0.441873056 30 0.052173913 0.038333333 250 0.73575 100 0.1 0.001 0.736117875 30 0.1 0.033333333 300 0.8829 92 0.092 0.00077869 0.883238445 30 0.130434783 0.030666667 350 1.03005 84 0.084 0.0005927 1.030359015 30 0.166666667 0.028 400 1.1772 75 0.075 0.00042188 1.177475906 30 0.213333333 0.025 450 1.32435 70 0.07 0.000343 1.324607513 30 0.257142857 0.023333333 R1 is 100mm, R2 is 200mm, and R3 is 300 mm B is 75mm When M in Nm is plotted against h in m, the result is as follows: Graph for zero degrees (0o) Graph for thirty degrees (30o) Graph for fully submerged surface both at 0o and 30o When is plotted against h3, the following is the result: For a 0o angle For a 30o angle Graph for partially submerged surface both at 0o and 30o Yp (experimental) vs Yp (theoretical) yields the following graph: The graph shows considerable disparity between the theoretical and measured values. The result is because of measurement errors for both W and h, coupled with errors in calculating M. Conclusion The study successfully determined the centre of pressure for both partially submerged plane and wholly submerged plane. The study’s results indicated substantial differences between the theoretical values for centre of pressure and the experimental values for the same. The discrepancies were explained by the fact that errors could have occurred in the apparatus and/or experimental procedures. Specifically, the discrepancies could have emanated from the fact that the weights of the pan and that of the balance were neglected in the experimental procedure. References Holton, J. R., & Hakim, G. J. (2012). An introduction to dynamic meteorology. Academic press. Mohitpour, M., Golshan, H., Murray, M. A., &Mohitpour, M. (2000). Pipeline design & Holton, J. R., & Hakim, G. J. (2012). An introduction to dynamic meteorology. Academic press. Renardy, M. (2012). Well-posedness of the hydrostatic MHD equations. Journal of Mathematical Fluid Mechanics, 14(2), 355-361. Sardain, P., &Bessonnet, G. (2004). Forces acting on a biped robot. Center of pressure-zero moment point. Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 34(5), 630-637. REYNOLDS EXPERIMENT Introduction Turbulent, Laminar, and Transitional flows can be quantified and characterized as follows using the Reynolds number. NR > 4000 – Turbulent flow NR < 2000 – Laminar flow For 2000 < NR < 4000 – Transition region In Laminar flow, the fluid slowly moves in layers through a pipe, and thus no mixing occurs. On the other hand, turbulent flow is characterized by a high velocity flow of fluid in which in-pipe mixing occurs. It is important to note at this point that the flow type can be influenced by the fluid’s viscosity. A fluid that is more viscous tends to flow smoothly resulting in Laminar flow as a result of the low Reynolds number that comes with viscous fluids. Fluids that move in pipes at low velocities tend to occasionally form eddies. After they are formed, these eddies are expeditiously flattened out by the viscous forces of the fluid, causing the fluid to move in the pipe with a Laminar Flow. When the velocity of the fluid moving in the pipe is increased, more eddies are formed, which results in complex mixing of the entire fluid. After the complex mixing of the fluid starts, then the fluid is said to be moving with turbulent flow. There is however a Transitional region, which is the point between turbulent flow and laminar flow. That is, the point where the flow is neither turbulent nor laminar, whereby turbulence is not full-blown and laminar flow has not completely ended. When the velocity at which a dyed fluid moved in a transparent pipe is varied, then one can study turbulent, laminar and transition flows. This will enable the Reynolds number to be derived because the flow rate of the fluid can be determined for each flow type; i.e. turbulent, laminar and transitional. Results Volume Time Flow rate Temperature Pipe Diameter Velocity in Pipe Viscosity Re Type of Flow (L) (s) (L/s) (C) (mm) (m/s) 0.295 5 0.059 27 12 0.5217 0.8334 7515.60 Turbulent 0.295 5 0.059 27 12 0.5217 0.8334 7515.60 Turbulent 0.300 5 0.060 27 12 0.5306 0.8334 7642.99 Turbulent 0.155 60 0.00258 27 12 0.0228 0.8334 328.45 Laminar 0.145 60 0.00241 27 12 0.02138 0.8334 307.84 Laminar 0.150 60 0.00250 27 12 0.02210 0.8334 318.21 Laminar 0.265 80 0.003125 27 12 0.02122 0.8334 305.69 Laminar 0.250 80 0.00227 27 12 0.02007 0.8334 289.12 Laminar 0.230 80 0.00209 27 12 0.02564 0.8334 369.36 Laminar Calculations Flow rate calculations: Pipe velocity calculations: Reynolds Number Calculations A graph of Reynolds number vs Velocity Conclusion From the values of the Reynolds number calculated, the flow is clearly categorized into laminar flow, which has a Reynolds number above 2000, and turbulent flow, which has a Reynolds number above 4000. Despite the fact that one of the objectives of the experiment is to have a transitional flow between turbulent and laminar, with a Reynolds number between the range 2000 > NR < 4000, the experimental results could only be categorized as either turbulent or laminar. Measurement and errors occurred during the experiment. They are the main reason why the experiment could not establish transitional flow because it was difficult to have a clear-cut occurrence of transitional flow. The main difficulty was that it was tasking to maintain a steady speed of fluid flow for a time long enough to allow taking of accurate measurements, because the equipment in the laboratory were not in their best conditions. Despite the errors in the experiment and the resultant failure to establish the transitional flow, the experiment’s results are remarkably reliable. It was proved that the Reynolds number is dimensionless. That is, no unit was left after the calculation of the Reynolds number and thus it does not have a unit. Read More