Experimenting with Fluid Mechanics - Assignment Example

COVER PAGE Purpose The conversion of pressure energy into kinetic energy and back to pressure energy is to be studies in a venture meter especially equipped for the purpose. The venture meter is calibrated, with its coefficient being determined, and the overall loss of mechanical energy across the venture being investigated. System and procedure The venture meter is located in a hydraulic bench and the system is represented schematically as can be seen in figure 1. When water is pumped from the reservoir serving as the holding tank it passes into the weigh tank which is the reservoir on the upper side after it has flown through the venture. The reservoir on the upper side is suspended such that it serves as one side of the balance. The other side of balance is able to hold a variety of mass sizes. If it happens that immediately at the moment the water in the reservoir located at the upper side is able just to put into balance the weight, then there is addition of a known mass on the same side. The mass of water that will flow to the reservoir on the upper side until a point is reached where there is restoration of balance at the point when the mass of water will be equal to the weight that has been added. By having the time elapsed timed for the two balance points there is then calculation of the average flow rate of the water. The venture is tube like having gradual contraction at the throat, and then we have a much more gradual expansion to the point where the initial tube size is achieved. In the set up we have a total of 11 piezometer tubes that are attached to the venture lengthwise. Figure 1 : Schematic representation Part 1 Theory The venture is used as a flow meter in industrial application. In the experiment we determine the coefficient for such use. In addition to the practical application, the venture comes in hand when it comes to the illustration of energy conversion in fluid mechanics. In this experiment we also trace the energy conversion as the fluid passes from one section to another. Bernoulli’s equation is used and is given as Where V=velocity in m/s g= acceleration due to gravity m/s2 P= Pressure in N/m2 =specific weight of the fluid = 9.789Kn/m3 for water at 200 C Z=height in m above the datum In terms of heads = velocity Head= kinetic energy per Newton of fluid flowing = Pressure Head = height to which will rise in the attached tube from the datum Z= Gravity Head = height above some datum = kinematic viscosity= 9.75x10-7m2/s for water at 20C With the venture standing at a level position, the gravity head will be constant along the length thus the term is neglected. Now using the a level venture the equation is reduced to This shows that the sum of energies of flow and pressure will be constant at any section. Procedure This was achieved by maintaining a constant flow rate and noting the height of water in the attached piezometer tubes. The is the height of water that is measured while is calculated using continuity equation Q=AV therefore V=Q/A Where Q = the flow rate in m3/s . This is obtained by dividing the 130N by the time it takes to accumulate enough water for raising it up, divided by weight density of water Results Calculating Q Table 1 Piezo tube Height of water(m) Diameter d(m) Area Velocity Velocity head A 0.139 0.0254 0.000508064 0.645588593 0.021243 B 0.135 0.023 0.000416588 0.787349596 0.031596 C 0.091 0.0183 0.000263726 1.243715657 0.078839 D 0.01 0.0159 0.000199088 1.647513692 0.138344 E 0.025 0.0166 0.000217004 1.511496358 0.116443 F 0.063 0.0179 0.000252323 1.299921777 0.086126 G 0.080 0.0193 0.000293336 1.118172129 0.063726 H 0.095 0.0207 0.000337436 0.972036539 0.048158 I 0.105 0.0220 0.00038115 0.860553588 0.037745 J 0.109 0.0234 0.000431204 0.760661729 0.029491 K 0.119 0.0254 0.000508064 0.645588593 0.021243 Figure 2 : Hydraulic head variation along the venturi Part 2 Theory This part involved the determination of a factor that accounts for the losses so as a venturi can be used as a flow meter. In this case only the initial piezometer tube A and the throat piezometer tube D are required Bernoulli’s equation may be arranged as From continuity equation =height of water in vertical tube at A(m) = height of water in vertical tube at D(m) Thus with the knowledge of g, AD, AA and taking measurement of the amount of fluid flow is determined However, due to losses when the equation is in this form accurate result is not obtained and this makes it necessary to have a constant (c) to determine calibration Results With the use of relevant equations in excel the following result was obtained Table 1 TRIAL TIME(s) Weight(N) Height of water(cm) c A D 1 40.45 130 13.9 1 0.129 0.003431 0.000328 0.956778 2 40.87 130 13.6 2 0.116 0.003254 0.000325 0.998598 3 44.53 130 13.9 3 0.109 0.003154 0.000298 0.945493 4 47.10 130 13.9 4 0.099 0.003006 0.000282 0.937963 5 49.27 130 14.2 5 0.092 0.002898 0.00027 0.930139 6 50.98 130 14.2 6 0.082 0.002736 0.00026 0.952177 7 50.60 130 14.3 7 0.073 0.002581 0.000262 1.016746 8 58.75 130 14.5 8 0.065 0.002436 0.000226 0.928025 9 64.67 130 14.4 9 0.054 0.00222 0.000205 0.924964 10 68.98 130 14.6 10 0.046 0.002049 0.000193 0.939555 Figure 3 Figure 4 Discussion and conclusion The plot of pressure head, velocity and total head indicated that the pressure head was high at the start point of the venture this dropped gradually as the venture narrowed and it reached lowest at the throat. The trend then changed again such that the pressure increased to a maximum point at the point of attaining the maximum width. On the other hand the velocity head was initially low increasing gradually and was at the peak at the throat and then it then reduced gradually to the lowest value at the point where the venture reached its normal diameter. This observation shows that the venture was conforming to Bernoulli’s equation. A closer look at the graphs, however reveal the water heads does not go to their original values at the point where the venturi tube is at the maximum diameter. This is as a result of losses being incurred as a result of fluid viscosity. Just like in the case where friction is experienced in moving solids, experience of shear forces in fluids where there is some viscosity will have the ability to transform kinetic energy into heat energy resulting to the loss of energy in the flowing fluid. Most of the energy is changed to heat which makes the fluid to warm up with some being lost through radiation and conduction. In part 2 the equation that can be used to calculate the discharge through the pipeline when the fluid is made to pass through the venture is given. The theoretical equation assumes that there is no energy losses which are not true as it had seen in part 1. In this part the actual discharge that puts into consideration head losses is given. From the result it has been shown that the actual discharge will slightly be less than the theoretical discharge. In the case where this is not obeyed it could be linked to human errors such as poor timing. Systematic errors could also be a contributor to the deviations observed. Random errors could also have contributed to deviations observed. From the experiment it is shown that an increase in Reynolds number results to a coefficient of discharge of the venturi increasing as it can be seen in figure 3. However at very high velocity in the pipe the Reinhold’s number is expected to reach a turbulent level which is associated with high energy losses. At this point the coefficient of discharge will not be increasing but will seem to remain constant and at even higher turbulence level it will decrease. References R. B. Bird, O. Hassager, R. C. Armstrong, and C. F. Curtiss, (1977). Dynamics of polymeric liquids, vol 1, fluid-mechanics, vol 2, kinetic-theory, Current Contents/engineering Technology Applied Sci- ences no. 34, 18–18, PT: J; TC: 0; UT:WOS:A1988P600400001. P. E. Rouse, A theory of the linear viscoelastic properties of dilute solutions of coiling polymers, Journal of Chemical Physics 21 (1953), no. 7, 1272–1280 (English), PT: J; NR: 44; TC: 2602; J9: J CHEM PHYS; PG: 9; GA: UC113; UT:WOS:A1953UC11300031. J. F. Ryder and J. M. Yeomans, Shear thinning in dilute polymer solutions, Journal of Chemical Physics 125 (2006), no. 19, 194906, PT: J; UT: WOS:000242181800086. H. R. Warner, Kinetic-theory and rheology of di-lute suspensions of finitely extendible dumbbells, Industrial Engineering Chemistry Fundamentals11 (1972), no. 3, 379– (English), PT: J; NR: 25;TC: 254; J9: IND ENG CHEM FUND; PG: 0;GA: N0535; UT: WOS:A1972N053500017. Read More