Fluid Mechanics Lab

EN 1029 Laboratory Laboratory FM Declaration In submitting this report, I hereby decl atomic number 18 that, except where I have do clear and full reference to the work of others, this submission, and all the material (e. g. text, pictures, diagrams) contained in it, is my own work, has non previously been submitted for assessment, and I have not knowingly allowed it to be copied by another student. In the case of group projects, the division of group members has been appropriately quantified. I figure that deceiving, or attempting to deceive, examiners by sack off the work of another as my own is plagiarism.I also insure that plagiarising anothers work, or knowingly allowing another student to plagiarise from my work, is against University Regulations and that doing so bequeath result in loss of marks and disciplinary proceedings. I down the stairsstand and agree that the Universitys plagiarism softw ar Turnitin whitethorn be apply to check the originality of the submitted coursework. Contents 1. Introduction 2. possible action 2. 1 refer of a piddle Jet 2. 2 blend Through a Venturi fourth dimension 3. Experimental procedures and results 3. 1 Experimental procedure Impact of a urine Jet 3. Experimental procedure mix by dint of a Venturi amount 3. 3 Results Impact of a Water Jet 3. 4 Results Flow through a Venturi beatnik 4. Discussion 4. 1 Impact of a water system cat valium 4. 2 Venturi meter 5. Conclusion 6. References Appendices Abstract ordinate of liquify was measured in two contrary proves, Impact of a water putting green and feed through a Venturi meter. The main accusive was to calculate the change in impulse and cypher loss in pay heed which was put under rack. The experiment showed that results obtained rat significantly skirt from the theory if muscle losses are not neglected. 1.Introduction Water is the intimately commonly use resource of renewable free energy. In 21st century, hydropower is utilize in more than one hundred fifty countries around the world. It is also the to the highest degree businesslike method of producing energy with 90% efficiency output. Impact of a Water Jet is apply to show how mechanical work can be created from water flow. When a fluid is put under pressure, the pressure gives it spicy pep pill in a jet. Jet strikes the brands of the turbine wheel. This wheel and then rotates under the impulse created by the water jet hitting the wind steels. Venturi meter is used to measure discharge along a pipe.In this experiment, when pressure is dropped, there is an sum up in fastness. push magnitude is dependent on rate of flow, so by measuring the pressure drop, discharge can be calculated. primary(prenominal) objective of both experiments is to calculate rate of flow under pressure. 2. Theory 2. 1 Impact of a Water Jet From impulse-momentum change compare it can be imitation that big businessman is generated due to the change in momentum of the water . In other words, ability equals the release between the initial and final momentum flow. Ar personament of jet impact apparatus used is effrontery in underframe 1 Figure 1Jet impinging on a vane is shown in Figure 2. Control volume V is used, bounded by a hold in come in S. The entering velocity is u1 (m/s) and its in the x circumspection. The vane deflects water jet and the sledding 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 d angiotensin converting enzyme for matted and hemispherical vane. Figure 2 cram on the het in the direction x is FJ (N), then momentum compare in the s- direction is FJ =(u2 romaine ? 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 directly graduated table ? 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 prize of force on the hemispherical cup. Rate at which momentum enters the mark off volume, or rate of flow of momentum in the jet, is detonated by symbolism J. J =u1(6) For the flat eggshell 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 division it can be concluded tha t =? 1A (9) 2. 2 Flow Through a Venturi grand Piezometer tubes were bored into a wall and links were made from a each of these to perpendicular manometer tubes, which were placed in front of a mm 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) subbing 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 unvaried. In reality, there is well-nigh 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 usually lies in within range 0. 92 to 0. 99. Ideal pressure distribution is given in equation (7) hn-h1u222g=a2a12-a2an2 (16) 3. Experimental 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 be intimate exercising weight at zero setting. Weight of the jockey was measured. diameter of the nozzle, height of the vane above the nozzle and the outperform from the bowling pin of the lever to the centre of the vane were recorder. Water was then released through the tally 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 number of reduce flow rates. The most efficient way of reducing flow is to place jock ey weight precisely at desired position, and then adjust the flow interpret 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 steady increasing 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 wing holding static water under adequate pressure.Amounts were then record 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 f rom the scale. corresponding 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 each 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 Two sets of readings were taken, one for the flat plate other for the hemispherical plate.Table 1 contains readings for the flat plate and Table 2 results for the hemispherical plate. These tables can be found in appendage 2. Mass flow is calculated by dividing the measuring rod (kg) by Time (s) taken to collect water. Quantity should be converted to m3 where 1 kg water will be 1/ one hundred0 m3. e. g. If sum of money 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 fro m F X 150 = W x yData from Table 1 and 2 are plotted on a graph to give a comparison between forces and rate of momentum flow of the impact. Graph is presented in Figure 4. Additional information are given in Apendex 2 Figure 4 (Series 1-flat plate, Series 2- hemispherical plate) 3. 4 Results Flow through a Venturi meter Two sets of entropy were compared. Values shown in Table 4 are measurements of h1 and h2 at resistent 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 perfection 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 out a value of C. C= 0. 604 Figure 6 shows both pattern 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 the 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 diam of water jet emerging from nozzle. If Mass of jockey was wrongly 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 losses 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, and 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. ambiance in pipes could have also caused an error in the experiment. Value of C obtained from Figure 5 gives a more realistic 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 prove that force on a flat plate is less than the force on the hemispherical plate. Therefore change in momentum flow was smaller. 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 Fluid 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. 6900. 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