Fluid Mechanics Lab

EN 1029 Laboratory Laboratory FM Declaration In submitting this report, I hereby declare that, except where I have made undetermined and full reference to the contrive of others, this submission, and every last(predicate) the material (e. g. text, pictures, diagrams) contained in it, is my own work, has not previously been submitted for assessment, and I have not knowingly allowed it to be copied by some other student. In the case of group projects, the contribution of group members has been appropriately quantified. I understand that deceiving, or attempting to deceive, examiners by passing off the work of another as my own is plagiarism.I also understand that plagiarising anothers work, or knowingly allowing another student to plagiarise from my work, is against University Regulations and that doing so will result in loss of label and disciplinary proceedings. I understand and agree that the Universitys plagiarism software Turnitin may be utilize to check the originality of t he submitted coursework. Contents 1. Introduction 2. Theory 2. 1 touch on of a Water Jet 2. 2 feed in Through a Venturi Meter 3. Experimental agencys and results 3. 1 Experimental procedure Impact of a Water Jet 3. Experimental procedure Flow through a Venturi Meter 3. 3 Results Impact of a Water Jet 3. 4 Results Flow through a Venturi quantity 4. Discussion 4. 1 Impact of a body of water jet 4. 2 Venturi meter 5. Conclusion 6. References Appendices Abstract Rate of function was measured in 2 different experiments, Impact of a water jet and rise through a Venturi meter. The main accusive was to calculate the inter dislodge in urge and energy loss in endure which was put under pressure. The experiment showed that results obtained put up signifi keistertly defer from the theory if energy losings are not neglected. 1.Introduction Water is the most commonly used resource of renewable energy. In 21st century, hydropower is used in more than 150 countries roughly the world . It is also the most efficient method of producing energy with 90% efficiency output. Impact of a Water Jet is used to show how mechanical work can be created from water flow. When a fluid is put under pressure, the pressure gives it high velocity in a jet. Jet strikes the vanes of the turbine wheel. This wheel thus rotates under the impulse created by the water jet hitting the vanes. Venturi meter is used to measure discharge along a pipe.In this experiment, when pressure is dropped, there is an plus in velocity. Pressure magnitude is dependent on site of flow, so by measuring the pressure drop, discharge can be calculated. Main objective of both(prenominal) experiments is to calculate measure of flow under pressure. 2. Theory 2. 1 Impact of a Water Jet From impulse- nervous impulse reassign par it can be assumed that phalanx is generated payable to the change in momentum of the water. In other words, force equals the difference between the initial and final momentum flow . emplacement of jet impact apparatus used is given in inning 1 Figure 1Jet impinging on a vane is shown in Figure 2. Control volume V is used, bounded by a control excavate S. The entering velocity is u1 (m/s) and its in the x direction. The vane deflects water jet and the leaving velocity is u2 inclined at an angle ? 2 to the x direction. Pressure over the surface of the jet, apart from the part where it flows over the surface of the vane is atmospheric. The change in direction is due to force generated by pressure and shear stress at the vanes surface. The mass flow rate is . Mass flow rate is the mass of substance which passes through a given surface per unit time kg/s.Experiment was done for flat and hemispherical vane. Figure 2 Force on the het in the direction x is FJ (N), then momentum equation in the s- direction is FJ =(u2 cos ? 2 u1) (1) From Newtons Action- Reaction law, force F on the vane is equal and opposite to Fj F =(u1 u2 cos ? 2 ) (2) For flat plate ? 2 = 90 so cos ? 2 = 0. Therefore F =u1 (3) For the hemispherical cup, its assumed that ? 2 = 180 so cos ? 2 = -1,so F =( u1 + u2 )(4) The effect of change of elevation on jet speed and the loss of speed due to friction over the surface of the vane is neglected.Therefore u1 = u2. So, F=2u1(5) If resistance forces are neglected, this is the maximum possible cheer of force on the hemispherical cup. Rate at which momentum enters the control volume, or rate of flow of momentum in the jet, is detonated by symbol J. J =u1(6) For the flat plate rate of flow of momentum in the jet is equal to the force on the vane. This is shown in equation (3). F=J(7) For the hemispherical cup, maximum possible value of the force is from equation (5) F=2J (8) If the velocity of the jet is uniform over its cross section it can be concluded that =? 1A (9) 2. 2 Flow Through a Venturi Meter Piezometer tubes were bored into a wall and links were made from a each of these to vertical manometer tubes, which were plac ed in front of a millimetre scale. Venturi meter is shown in Figure 3 Figure 3 Its assumed that the fluid used is frictionless and incompressible, fluid flow is steady, and energy equation was derived along a stream line. Bernoullis theorem states that u122g+ h1 = u222g+ h2 = un22g+ hn (10) From continuity equation Q=U1A1=U2A2=UnAn(11) here Q is discharge rate( m3/s), and A is cross-sectional area of the pipe(m2) substituting for u1 gives u222ga2a12+ h1 = u222g+h2 (12) Solving equation (3) for u2 gives u2 =2g(h1-h2)1-a2a12 (13) From equation (4) Q=a22g(h1-h2)1-a2a12 (14) In previous equation it was assumed there was no energy loss in the flow and the velocity was constant. In reality, there is some energy loss and velocity is not uniform. Equation (5) is therefore corrected to Q=Ca22g(h1-h2)1-a2a12(15) Where C is the coefficient of the meter.Its value normally lies in within range 0. 92 to 0. 99. Ideal pressure distribution is given in equation (7) hn-h1u222g=a2a12-a2an2 (16) 3. Exp erimental procedures and results 3. 1 Experimental procedure Impact of a Water Jet The apparatus shown in Figure 1 was levelled and lever was balanced, with roll in the hay weight at zero setting. Weight of the jockey was measured. diameter of the nozzle, top of the inning of the vane above the nozzle and the distance from the pivot of the lever to the centre of the vane were recorder. Water was then released through the supply valve and flow rate increased to maximum.The force on the vane displaces the lever, which is then restored to its balanced position by sliding the jockey weight along the lever. The mass flow rate can be established by gathering of water over a timed interval. Additional readings are then taken at build of reducing flow rates. The most efficient way of reducing flow is to place jockey weight precisely at desired position, and then ordinate the flow control valve to bring the lever to the balanced position. Range of settings of the jockey position may be separated efficiently into uniform steps. 3. Experimental procedure Flow through a Venturi Meter The objective of this experiment is to establish the coefficient of the meter C. Bench vale and control vale should be open so water can flow to clear air pockets from the supply system. The control valve is then progressively closed, so the meter is exposed to a steadily increase pressure. This will cause water to pass up the tubes. When water levels have risen to a suitable height, the bench valve is slowly closed, so that, as both valves are lastly shut of, the meter is left holding static water under adequate pressure.Amounts were then recorded for values of (h1 h2) and discharge value Q is recorded. The rate of flow is measured by gathering of water in weighing tank, whilst values of h1 and h2 were read from the scale. Similar readings may be taken at a sequence of reducing values of h1 h2. About 6 readings, proportionately spread in the range of 250 mm to zero. By reading off from all the tubes at any of the settings used, the pressure distribution along the length of the Venturi meter may be logged. 3. 3 Results Impact of a Water Jet dickens sets of readings were taken, one for the flat plate other for the hemispherical plate. send back 1 contains readings for the flat plate and Table 2 results for the hemispherical plate. These tables can be found in Appendix 2. Mass flow is calculated by dividing the Quantity (kg) by Time (s) taken to collect water. Quantity should be converted to m3 where 1 kg water will be 1/1000 m3. e. g. If quantity is 30 kg, time taken is 52. 69 s, mass flow is 0. 569 103 x Q. Using the equation (9), u1 can be calculated. From uo2 = u12 2gs , uo can be deduced. For flat plate J can be calculated using equation (6). F is calculated from F X 150 = W x yData from Table 1 and 2 are plotted on a graph to give a compare between forces and rate of momentum flow of the impact. Graph is presented in Figure 4. Additional information are giv en in Apendex 2 Figure 4 (serial publication 1-flat plate, Series 2- hemispherical plate) 3. 4 Results Flow through a Venturi meter Two sets of data were compared. Values shown in Table 4 are measurements of h1 and h2 at different discharges. In this part of the experiment C is assumed to be constant over a range of measurement. Closer inspection of Table 4 shows C is not constant as Q varies.Piezometer measurements are recorded in Table 5 and compared with ideal pressure distribution given In Table 3. Figure 5 Graph shown in Figure 5 gives variation of (h1 -h2)1/2 With Q. Equation of the graph line is y= 0. 581 x h1-h2=0. 581 x Qx 103 Q =5. 81 x 10-4h1-h2 (16) Substitute (16) in equation (15) to get a value of C. C= 0. 604 Figure 6 shows both ideal and set of results obtained in the experiment. Series 1 shows ideal pressure distribution, and series2 shows obtained results. Figure 6 4. Discussion 4. 1 Impact of a water jet Theory compares well with the experiment considering that th e two lines have different gradients.In theory, gradients of lines are significantly steeper, and this might be because an error in the experiment occurred. Likely errors that might have occurred are measurements of mass of jockey weight distance L from centre of vane to pivot of lever or diameter of water jet emerging from nozzle. If Mass of jockey was incorrectly logged by 0. 001kg, Force on the vane would have 2% error. The graph that was obtained shows force on the hemisphere us less than twice the flat plate. This can be concluded from the line gradient. This implication is supported by the theory.In theory, no friction losings or any other kind of energy losses were included in equations. In the actual experiment, there were some energy losses like friction over the surface of the vane and effect of change of elevation on jet speed. It was assumed that velocity of the jet was uniform over its cross section, which would imply ideal flow. Its likely that this was not the case, a nd momentum gained by the change in velocity. 4. 2 Venturi meter Value of C determined in table A is higher than it theoretically should be. This is probably due errors that occurred in the experiment, like parallax rror. Air in pipes could have also caused an error in the experiment. Value of C obtained from Figure 5 gives a more true-to-life(prenominal) value of 0. 604. The difference between the ideal pressure results and values recorded in the experiment is acceptable considering the coefficient of the meter C that is not included in ideal pressure distribution. Flow of 1x 10-3 m3/s is expected to lie on a negative hn-h1u222g value. 5. Conclusion From both experiments it can be concluded that the flow was not ideal and there were significant energy losses that differ obtained results from theoretical results.In the impact of a water jet experiment it was proven that force on a flat plate is less than the force on the hemispherical plate. Therefore change in momentum flow was sm aller. In the Venturi meter experiment it was shown that ideal pressure distribution differs from obtained results because energy losses effect the results. The errors in both experiments can affect the results significantly an lead to wrong assumptions. References silver-tongued Mechanics, Third Edition? JF Douglas, JM Gasiorek, JA Swafield? Longman Mechanics of Fluids? BS Massey, Van Nostrant Reinhold? Chapman & HallAppendix 1-Nomenclature Symbol Quantity SI units F Force N J Rate of flow of momentum N u velocity m/s Mass flow rate Kg/s D diameter m h height m A Cross-section area m2 ? Angle of elevation degrees ? density Kg/m3 Appendix 2-Raw data Impact of a water jet Diameter of nozzleD= 10. 0 mm Cross sectional area of nozzle A =? D24=7. 85 x 10-5 m2 Height of vane above nozzle tips= 35 mm = 0. 035 m Distance from centre of vane to pivot of leverL= 150 mm Mass of jockey weightM= 0. 600 kg Weight of jockey weightW =Mg = 0. 600 x9. 81 =5. 89 NQuantity (kg) T(s) y(mm) 103 x Q(m3 /s) U1(m/s) U0(m/s) J(N) F(N) 30 52. 69 65 0. 569 7. 25 7. 20 4. 13 2. 55 30 57. 81 55 0. 519 6. 61 6. 56 3. 43 2. 16 30 61. 28 45 0. 490 6. 24 6. 18 3. 06 1. 77 15 22. 76 35 0. 659 8. 40 8. 36 5. 54 1. 37 15 28. 12 25 0. 533 6. 80 6. 75 3. 62 0. 98 15 37. 09 15 0. 404 5. 15 5. 08 2. 08 0. 59 15 75. 09 5 0. 200 2. 54 2. 40 0. 51 0. 196 Table 1 Quantity(kg) T(s) y(mm) 103 x Q(m3/s) U1(m/s) U0(m/s) J(N) F(N) 30 52. 87 120 0. 567 7. 23 7. 18 8. 24 4. 71 30 56. 8 105 0. 527 6. 72 6. 67 7. 08 4. 12 30 60. 78 90 0. 494 6. 29 6. 24 6. 21 3. 53 15 21. 75 75 0. 690 8. 79 875 6. 07 2. 94 15 24. 60 60 0. 610 7. 77 7. 73 9. 48 2. 35 15 28. 32 45 0. 530 6. 75 6. 70 7. 16 1. 77 15 37. 32 30 0. 402 5. 12 5. 05 4. 12 1. 18 Table 2 Venturi Meter Piezometer Tube No. N Diameter of cross-section(mm) Areaa(m2) A(1)BCD(2)EFGHJKL 26. 0023. 2018. 4016. 0016. 8018. 4720. 1621. 8423. 5325. 2426. 00 0. 0005310. 0004230. 0002660. 0002010. 0002220. 0002680. 0003190. 0003750. 0004350. 00050. 000531 0. 150. 69 00. 8701. 0000. 9520. 8660. 7940. 7330. 6800. 6340. 615 0. 1430. 2260. 5721. 0000. 8230. 5630. 3970. 2880. 2140. 1610. 143 0. 000-0. 083-0. 428-0. 857-0. 679-0. 420-0. 253-0. 145-0. 070-0. 0180. 000 Table 3 Quantity (kg) T(s) h1(mm) h2(mm) 103 x Q(m3/s) (h1- h2)(mm) (h1 -h2)1/2(mm)1/2 C 12 17. 67 346 20 0. 679 0. 326 0. 571 1. 236 12 17. 53 346 20 0. 685 0. 326 0. 571 1. 248 12 17. 60 346 20 0. 682 0. 326 0. 571 1. 242 12 20. 69 330 84 0. 580 0. 246 0. 496 1. 216 12 18. 40 330 84 0. 652 0. 246 0. 496 1. 367 12 19. 5 330 85 0. 616 0. 246 0. 496 1. 212 12 21. 36 324 114 0. 562 0. 210 0. 458 1. 275 12 20. 90 324 114 0. 574 0. 210 0. 458 1. 303 12 21. 13 324 114 0. 568 0. 210 0. 458 1. 289 12 20. 00 336 58 0. 600 0. 278 0. 527 1. 183 12 18. 31 336 58 0. 655 0. 278 0. 527 1. 292 12 19. 16 336 58 0. 628 0. 278 0. 527 1. 239 6 12. 23 310 176 0. 491 0. 134 0. 366 1. 395 6 12. 32 310 176 0. 487 0. 134 0. 366 1. 342 6 12. 28 310 176 0. 489 0. 134 0. 366 1. 389 6 17. 11 298 224 0. 351 0. 074 0 . 272 1. 342 6 18. 5 298 224 0. 317 0. 074 0. 272 1. 212 6 18. 03 298 224 0. 334 0. 074 0. 272 1. 277 6 0 296 296 0 0 0 0 6 0 296 296 0 0 0 0 6 0 296 296 0 0 0 0 Table 4 Piezometer Tube No. Q=0. 682 x 10-3u222g 0. 587 m hn(mm) hn h1(m) hn-h1u222g A(1) 346 0. 000 0 B 328 -0. 018 -0. 0307 C 202 -0. 144 -0. 245 D(2) 20 -0. 326 -0. 555 E 52 -0. 294 -0. 501 F 142 -0. 204 -0. 348 G 190 -0. 156 -0. 266 H 224 -0. 122 -0. 208 J 246 -0. 100 -0. 170 K 264 -0. 082 -0. 140 L 268 -0. 078 -0. 133 Table 5 Appendix C