Flow Measurement – Fluid Mechanics

Name ******** Class DME2 Title period Measurement Date 11/02/2013 Lecturer Mr Higgins Summary In this examine m from each one different meters were use to measure fluid unravel direct the hatchway home base, the ship meter, the rota meter and the weigh cooler. Each meter full treatment by its ability to alter a certain physical position of the comeing fluid and past allows this alte symmetryn to be measured. The measured alterations ar linked directly to the operate rate and these measurements argon subbed in to correct equalitys to solve for it. Each method actings pop outcome is then analysed, comp atomic number 18d over against apiece other. . Objectives * To introduce the bookman to three typical methods of measuring he play rate of an incompressible fluid namely 1- Venturi metre 2- Orifice plate 3- Rotor metre * To compare the accuracy of each device. * To give insight into appropriate industrial finish for each device. 2. Theory Water enters and first geo logical periods by dint of the Venturi metre, then through the Orifice plate and then through the Rotor meter. On leaving the Rotor meter the urine campaigns via a control valve to the weigh-tank of the hydraulic bench.At the inlet and the outlet of each flow measuring device is a connection to the manometer board, this allows the head loss to be chanced across each device. For an incompressible fluid flowing through a pipe the following(a) equations apply Continuity, Q=V1A1=V2A2(1) Bernoullis P1? g+V122g+z1=P2? g+V222g+z2(2) Venturi Rewriting Bernoullis equation for the testal frame-up PA? g+VA22g+zA=PB? g+VB22g+zB Since weapon is horizontal ZA=ZB therefore, PA? g+VA22g=PB? g+VB22g Rearranging VB22g+VA22g=PA? g+PB? gSince P/? g is the hydrostatic (pressure) head, h at any given rase we spate rewrite the above equation as, VB22g+VA22g=hA-hB(3) Where hAand hB are articulate directly from the apparatus. To solve for velocities, we rear wander equation (1), VA=VBABAA cream into equation (3), VB22g+VBABAA22g=hA-hB(4) Hence the only unknown asVB. Therefore, to find the flow rate, determine VB from equation (4) and then Q is given by. Q=VBAB (5) Orifice Q is calculated using the selfsame(prenominal) procedure as the Venturi meter using ports E and F as opposed to A and B.However, because the orifice plate is less ideal, it causes turbulence in the flow it requires a correction gene known as the coefficient of discharge, K. For this apparatus K=0. 601 therefore, the calculated Q must be multiplied by K, Qactual=Qtheoretical? K Rotor meter The flow rate is examine directly sour the rotor meter calibration curve as seen in the interpret h below. 3. Apparatus * The bulk of the apparatus used in this experiment is as shown below on a labelled diagram. * The flow of water was manually varied by a screw type tap. The freight balance is not shown merely is acted on a counter equilibrise weight system. In this experiment a 4kg weight was dropped and the meter was started. The duration of time was determined by how long it would take for the water to filch the weight. This (with a 13 weight is to water ratio) allowed the sens flow rate to be calculated. Rotameter Rotameter Manometers Manometers 4. Orifice Orifice Venturi Venturi Procedure 1. Set flow rate to maximum. 2. Record the monometer readings A, B, E and F. 3. Measure the discharge using the weigh-tank. 4. accept the steps 2 and 3 for 6 other flow rates. 5.Draw a graph of volumetric flow rate measured by the weigh-tank versus volumetric flow rate measured by the other three devices (all on one graph). 6. Discuss the advantages and disadvantages of each device from an installation view. 5. Experimental Results Amm Bmm Emm Fmm Rota-meter fertilize rate (weigh tank) 4kg (s) 1 378 131 349 86 21. 4 25 2 345 162 326 one hundred thirty 18. 4 31. 8 3 320 188 304 165 15. 2 37 4 298 202 288 191 12. 3 47. 5 5 282 222 274 211 9. 3 59. 4 6 266 236 262 232 5. 4 91. 5 Position A B E F diam (m) 0. 026 0. 016 0. 051 0. 020 6.Sample Calculations Venturi As Q=VA, the volume (V) and the area (A) must be calculated first. volume is found from the equation (4) as shown in system being rearranged VB22g+VBABAA22g=hA-hB VB2-VB2AB2AA2=hA-hB2g VB21-AB2AA2=hA-hB2g VB2=hA-hB2g1-AB2AA2 VB2=hA-hB2g1-AB2AA2 VB=hA-hB2g1-AB2AA2 From this equation, V notify now be calculated using the emergences from the experiment. Calculation carried out for first instance AA=? 0. 02624AB=? 0. 01624 AA=5. 3093? 10-4m2AB=2. 0106? 10-4m2 h = the height read from the manometer in the experiment. VB=0. 378-0. 131(29. 8)1-(2. 0106? 10-4)2(5. 3093? 10-42)2 VB=4. 4120. 85659 VB=5. 6517 VB=2. 3773m/s Now that the velocity at point B and the area of point B is calculated, Q can now be worked out QB=VBAB QB=2. 3773? (2. 0106? 10-4) Volumetric conflate RateB=4. 7799? 10-4m3/s To convert into kg/s QB=(4. 7799? 10-4)? 1000 Mass blend rate B=0. 4779kg/s Orifice To calculate the mussiness flow rate us ing the orifice method, calculations very similar to the venture method are used. The positions are now different so therefore the diameters are changed in finding Q. AA/VA and AB/VB are now obviously changed to AE/VE and AF/VF but otherwise the exact same method is used to find VF.However, the overall mass flow rate has to be corrected by a factor of K=0. 0601 due to a less efficient apparatus being tested. AE=? 0. 05124AF=? 0. 02024 AE=2. 0428? 10-3m2AF=3. 1416? 10-4m2 VF=hE-hF2g1-AF2AE2 VF=0. 349-0. 08629. 811-3. 1416? 10-42. 0428? 10-32 VF=5. 16. 97635 VF=5. 2851 VF=2. 298m3/s Q=VFAF Q=2. 2983. 1416? 10-4 Q=7. 223? 10-4 Now multiplied by correction factor and converted to kg/s Q=7. 223? 10-4)(0. 601)(1000) Q=0. 43406 kg/s Rota-meter The mass flow of water is worked out in this method by feeding the results read from the rotor meter into the graph as shown below enumerate TankThe ratio of weight of the load to the weight of the water in this lab is 13. A weight was applied to t he time the discharge was 4kg. Therefore the time taken for this discharge can allow us to calculate the mass flow rate as Mass flow Rate = KG/S. So for the first test Q=4325 Q=0. 48kg/s 7. Calculated results Venturi (kg/s) Orifice (kg/s) Rota meter(kg/s) Weigh tank(kg/s) 1 0. 4779 0. 4341 0. 463 0. 48 2 0. 4116 0. 3747 0. 404 0. 3773 3 0. 3496 0. 3156 0. 341 0. 3243 4 0. 2981 0. 2636 0. 284 0. 2526 5 0. 2357 0. 2124 0. 224 0. 202 6 0. 1667 0. 1466 0. 152 0. 1312 8. DiscussionsThe measurement of fluid flow can present very essential in day to day applications. For example the measurements of blood-flow rates in human artery or the measurement of liquid oxygen in a rocket are amplely important in their field of work. Although the methods used in this lab may not all work in these cases, the selection of the proper instruments for a particular application is hugely important. Flow-rate-measurement devices much require accurate pressure and temperature measurements in order to ca lculate the end product of the instrument so choosing the correct method of measurement is hugely important.Each of the flow measurement devices used had its own advantages and disadvantages. Comparing the venturi meter the orifice plate there are some noticeable differences. Although both are fitted for clean or dirty fluids the orifice plate has a comparatively low cost compared to the venturi meter. But on the other hand the orifice plate does require a smaller diameter in compared to the venture meter. In day to day applications these two factors could have huge power on the choice in application. Cost is always a huge factor in any application decision and depending on the requirements for the application size could also play a vital role.The weigh tank is a somewhat more basic approach to measuring the mass flow rate of fluid. The human element of error in the measure of the weights displacement can be easily corrected by machinery and could prove very effective for applic ations measuring flow. The rota meter is also a transparent but effective method of flow measurement. The simple effects of parallax are a disadvantage to this application but again in day to day modern applications, computerised sensory machines can correct this very easily. 9. end Overall this lab was a success.The results are all within the range of having explainable errors such as * The main error predicted is due to the sweet sand verbena effect in calculations, where a rounding off of results at the graduation exercise of a number of equations has a greater effect with the end result. This rounding error can have greater effects than thought and can drastically vary the end result. * Parallax is another error caused across each application. The heights read across the manometers and the rotameter can be easily read wrong. Along with the meniscus of the fluid giving a false take and a wrong angle at the result reading can change the end result also. Human error is always a small error to be taken into account, especially when using the stem watch in the weight tank method of measuring the flow rate. The likelihood of reading the exact time needed is very small. This again can have huge effect on the accuracy of the result achieved. By carrying out this science laboratory students were able to become comfortable with calculations and equations that were ran through in class. The hands on approach of this lab allows students to understand the theory better and this in turn results in easier revision when studying for exams.Overall this laboratory and its results proved successful, with results accurate with an explainable percentage of error and with students having a greater understanding in this area. 10. Bibliography 1. CIT laboratory manual Fluid mechanics-B. S. Massey, Applied mechanics J. D. Walker, Fluid mechanics Irfan A. Khan, Mechanical Engineering Science- J. Hannah and M. J. Hiller. 2. Wikipedia formulas / units confirmation 3. http/ /fetweb. ju. edu. jo general instruction on each measuring meter used.