Impact of a Jet

Impact Of a Jet Introduction: Over the years, engineers have found many ways to utilize the force that can be imparted by a jet of fluid on a surface diverting the flow. For example, the pelt on wheel has been used to make flour. Further more, the impulse turbine is still used in the first and sometimes in the second stages of steam turbine. Firemen make use of the kinetic energy stored in a jet to deliver water above the level in the nozzle to extinguish fires in high-rise buildings. Fluid jets are also used in industry for cutting metals and debarring.Many other applications of fluid jets can be cited which reveals their technological importance. This experiment aims at assessing the different forces exerted by the same water jet on a variety of geometrical different plates. The results obtained experimentally are to be compared with the ones inferred from theory through utilizing the applicable versions of the Bernoulli and momentum equations. Objectives: i. To measure the force p roduced by a jet on flat and curved surfaces. ii. To compare the experimental results with the theoretically calculated valuesProcedure: 1. Stand the apparatus on the hydraulic bench, with the drainpipe immediately above the hole leading to the weighing tank, see figure 4. Connect the bench supply hose to the inlet pipe on the apparatus, using a hose-clip to secure the connection. 2. Fit the flat plate to the apparatus. If the cup is fitted, remove it by undoing the retaining screw and lifting it out, complete with the loose cover plate. Take care not to drop the cup in the plastic cylinder. 3. Fit the cover plate over the stem of the flat plate and hold it in position below the beam.Screw in the retaining screw and tighten it. 4. Set the weigh-beam to its datum position. First set the jockey weight on the beam so that the datum groove is at zero on the scale, figure 5. Turn the adjusting nut, above the spring, until the grooves on the tally are in line with the top plate as shown i n figure 6. This indicates the datum position to which the beam must be returned, during the experiment, to measure the force produced by the jet. 5. Switch on the bench pump and open the bench supply valve to admit water to the apparatus.Check that the drainpipe is over the hole leading to the weighing tank. 6. Fully open the supply valve and slide the jockey weight along the beam until the tally returns to record the reading on the scale corresponding to the groove on the jockey weight. Measure the flow rate by limiting the collection of 8Kg of water in the bench-weighing bank. 7. Move the jockey weight inwards by 10 to 15cm and reduce the flow rate until the beam is approximately level. Set the beam to exactly the correct position (as indicated by the tally) by moving the jockey weight, and record the scale reading.Measure the flow rate. 8. Repeat step 6 until you have about 6 sets of readings over the range flow. For the last set, the jockey should be set at about 10cm from the zero position. At the lower flow rates you can reduce the mass of water collected in the weighing tank to 8Kg. 9. Switch off the bench pump and fit the hemispherical cup to the apparatus using the method in steps 2 and 3. Repeat step 4 to check the datum setting. 10. Repeat steps 5 to 9, but this time move the jockey in steps of about 25cm and take the last set of readings at about 20cm. 11.Switch of the bench pump and record the mass m of the jockey weight, the diameter d of the nozzle, and the distance s of the vanes from the outlet of the nozzle. Data and Results: Table 1: Results for Flat Plate Water Mass, Mw (KgTime, t (S)Distance, ?y (m)Mass Flow, m (Kg/s)Velocity, u (m/s) Initial Velocity, uo (m/s) Momentum, muo (N)Force on vane, F (N) 240. 560. 6642. 86546. 47545. 782342125. 89 240. 560. 6742. 86546. 47545. 782342126. 29 240. 560. 6442. 86546. 47545. 782342125. 89 240. 550. 6243. 64556. 41555. 7232425124. 32 241. 040. 5423. 08294. 27293. 581281121. 19 41. 380. 2317. 39221. 7 2221. 0496459. 025 Table 2: Results for Hemispherical Cup Water Mass, Mw (KgTime, t (S)Distance, ?y (m)Mass Flow, m (Kg/s)Velocity, u (m/s) Initial Velocity, uo (m/s) Momentum, muo (N)Force on vane, F (N) 240. 551. 3243. 63556. 28555. 5913334. 1652. 19 240. 561. 3242. 85546. 33545. 6413095. 3651. 79 240. 581. 3141. 38527. 59526. 9112645. 8451. 40 240. 591. 2840. 67518. 54517. 8512428. 4050. 23 241. 031. 1323. 30297. 08296. 397113. 3644. 34 241. 200. 7320. 00225224. 315383. 5128. 64 Calculations: 1. Mass flow rate, mf = mw / T In table 1: [ m= 24 / 0. 6= 42. 86 Kg/s] In table 2: [m=24 / 0. 55= 43. 63 Kg/s] 2. Velocity at nozzle exit, u= m / ? A , m = ? uA u= m / (1000 x78. 85Ãâ€"10^-6) u= 12. 75 x m In table 1: u= [12. 75 / 42. 86 = 546. 47m/s] In table 2: u= [12. 75 / 43. 63 = 556. 28m/s] 3. Velocity at impact with vane, uo: From Bernoulli’s equation: uo ^2 = u^2-2gs uo^2 = u^2 – (2 x 9. 81x 0. 035) In table 1: uo = [(v546. 78^2) – 0. 687] =545. 79 m/s In tabl e 2: uo = [(v556. 8^2) – 0. 687] =555. 59 m/s 4. Momentum flow in the jet at impact,J Moment,J = m x uo In table 1: [J= 42. 86 x 545. 78 = 23421 N] In table 2: [J=43. 63 x 555. 59 = 13334. 1N] 5. Force on vane F, F = (W x y) / 0. 15 In table 1: [F= (5. 89 x 0. 66) / 0. 15 =25. 89 N] In table 2: [F= (5. 89 x 1. 33) / 0. 15 =52. 19 N] 6. Slope of the graph, From flat plate graph, m m= (17500-10200) / (25-15) m= 730 From Hemispherical Cup graph, m m= (8500-6000) / (48-35) m=192. 30 Discussion . Turning the adjusting nut above the spring until the grooves on the tally are in the line with the top plate as shown in figure 6. 2. Recording the reading on the scale corresponding to the groove on the jockey weight. 3. Starting timer and adding weights when beam moves to horizontal. Stopping timer when beam moves to horizontal again. 4. The values of F theoretical (calculated from 4g? x) are close to those found experimentally. So we connect these points with a straight line. 5. Also f rom this graph we see that the calculated F (4g? ) is equal to the double of mu ? 2mu 6. It is clear from Fig that the force produced on each of the vanes is proportional to the momentum flow in the jet as it strikes the vane. From the data collected during the experiment, it is found that for different plate of vane used, the force exerted on the plate by the water will be different and it varies from flat and hemispherical plate. This is supported by the data of the column, distance of jockey from zero position which is the mean of knowing the force needed to balance the force exerted by the water. . We were to plot graphs of Force versus delivery of momentum for each plate on the same graph and we found the graphs posses different slope where the values are 2 and 1. 1 for hemispherical and flat plate respectively. We were able to plot the two plates on the same graph and although the relative slope is correct where hemispherical has the greater slope followed by flat plate, but t he calculation of the slope will not be correct because the value of x-axis is the same for all two graphs.So in order to obtain the correct value of slopes, the individual plotting of the graph has been plotted and the slope has been calculated. 8. When the water from the nozzle strikes the plate, it has the same initial velocity for the two plates but the velocity changes due to the obstruction by the plate and it will be different for each plate due to the geometrical effect. The geometry of the hemispherical plate minimizes the obstruction of the plate so the water will flow more freely relative to that of the flat plate.So, for the same flow rate, the hemispherical has a relatively higher final velocity than flat plate. Percentage of error of experiment: Accuracy = (muo-4g? X /4g? X) *100% For flat plate: (31. 20-1. 96/1. 96)=10. 2% (2. 10-1. 96/1. 96)=7. 14% (1. 73-1. 57/1. 57)=10. 2% (1. 35-1. 18/1. 18)=14. 4% (0. 9-0. 78/0. 78)=15. 4% Factor: Parallax error, during adjusting the level gauge to point, Water valve was not completely close and Press stopwatch start button late. For hemispherical cup: (4. 74-4. 1/4. 71)=0. 64% (4. 08-3. 92/3. 92)=4. 08% (3. 6-3. 14/3. 14)=14. 6% (2. 7-2. 35/2. 35)=14. 9% (1. 90-1. 57/1. 57)=21. 0% (0. 94-0. 78/0. 78)=20. 5% Factor: Parallax error, during adjusting the level gauge to point, Water valve was not completely close and Press stopwatch start button late. Question: Suggest two ways to improve accuracy of results? 1. It is by repeating the experiment a few times which make the results more reliable. 2. Measuring use highly precise digital measurement. 3.If the line didn’t pass through the origin that means that there is an error, because if the force is zero ( the jet doesn’t touch the vane) the should be placed at the origin which means ? y=0 so F=0 4. F = m (uo = u) u ? uo because we neglect reduction of speed so that u=uo fo = 2muo but the force on the hemispherical cup less than twice that on the flat plate. 5. The effect on the calculated force on the flat plate if the jet was assumed to leave the plate at 1? upward will be a moment in the x-direction which will decrease the moment in the y-direction F=m (1. 9uo) and it won’t effect the results too much. Conclusion As a conclusion, the experiment that have been carried out were successful, even though the data collected are a little bit difference compared to the theoretical value. The difference between the theoretical value and the actual value may mainly due to human and servicing factors such as parallax error. This error occur during observer captured the value of the water level. Besides that, error may occur during adjusting the level gauge to point at the white line on the side of the weight pan.Other than that, it also maybe because of the water valve. This error may occur because the water valve was not completely close during collecting the water. This may affect the time taken for the water to be collecte d. There are a lot of possibilities forth experiment will having an error. Therefore, the recommendation to overcome the error is ensure that the position of the observer’s eye must be 90 ° perpendicular to the reading or the position. Then, ensure that the apparatus functioning perfectly in order to get an accurate result.