Presentation on theme: "Pre-measurement class I."— Presentation transcript:
1Pre-measurement class I. Budapesti University of Technology and EconomicsDepartment of Fluid MechanicsPre-measurement class I.Csaba Horváth2009.
2General information Department webpage: www.ara.bme.hu Student information page:(materials, test scores, etc.)Schedule: 2 pre-measurement classes + 3 measurements (A,B and C) + 2 presentations1. For the first presentation, the A and half of the B measurement leaders will make presentations2. For the second presentation, the second half of the B and all of the C measurement leaders will make presentationsThe measurement reports are due within one week of the measurement date, on Friday at noon. The submitting student must send an to the faculty member checking the report, to notify them that they have submitted the report. The faculty member will correct the report within 3 days and send a message to the student, through the Poseidon network, to let them know if the report has been accepted, corrections need to be made or if the measurement needs to be repeated. If corrections need to be made, the students can consult the faculty member. The corrected reports need to turned in within 2 weeks from the measurement, at noon. An must once again be sent to the faculty member correcting the report.
3Measuring pressure U tube manometer Betz manometer Inclined micro manometerBent tube micro manometerEMB-001 digital handheld manometer
4H g > D pB pJ Measuring pressure / U tube manometer I. Pipe flow Butterfly valveAverage the pressure on pressure taps around the perimeterThe manometers balance equation:HgD>rny <<rm(For example> measuring air with water)Or(Measuring water with mercury)pBpJNotice that
5D Measuring pressure / U tube manometer II. The manometers balance equation:DDensity of the measuring fluid rmf (approximately)mercurywateralcoholDensity of the measured fluid: rny (For example air)plevegő = pair -atmospheric pressure [Pa] ~105PaR - specific gas constant for air 287[J/kg/K]T - atmospheric temperature [K] ~293K=20°C
6Measuring pressure / U tube manometer III. Example: the reading:The exactness ~1mm: The absolute error:How to write the correct value with the absolute error(!)The relative error:Disadvantages:Reading error (take every measurement twice)Exactness~1mmWith a small pressure difference, the relative error is largeAdvantages:ReliableDoes not require servicing
7Measuring pressure / upside down U tube micro manometer The manometer’s balance equationSince the upside down U tube manometer is mostly used for liquid measured fluids, the measurement fluid is usually air. The density of air is13.6 times smaller than mercury and therefore the results are much more exact.
8Measuring pressure / Betz micro manometer The relative error is reduced using optical tools.Exactness ~0,1mm: The absolute error is:The relative error:
9Measuring pressure / inclined micro manometer The manometers balance equationDExactness ~1mm,The relative error:It is characterized by a changing relative error.
10Measuring pressure / bent tube micro manometer Is characterized by a constant relative error and not a linearly scaled relative error.
11Measuring pressure / EMB-001 digital manometer List of buttons to be used during the measurementsOn/Off Green buttonReset the calibrations „0” followed by the „STR Nr” (suggested)Changing the channel „CH I/II”Setting 0 Pa „0 Pa”Averaging time(1/3/15s) „Fast/Slow” (F/M/S)Measurement range:Measurement error:
12Velocity measurement Pitot tube/probe or Static (Prandtl) tube/probe
13Velocity measurement / Pitot tube/probe Pitot, Henri ( ), French engineer.Determining the dynamic pressure:Determining the velocity:
14Velocity measurement / Prandtl tube/probe Prandtl, Ludwig von ( ), German fluid mechanics researcher
15Measuring volume flow rate Definition of volume flow rateMeasurement method based on velocity measurements in multiple pointsNon-circular cross-sectionsCircular cross-sections10 point method6 point methodPipe flow meters based on flow contractionVenturi flow meterThrough flow orificeInlet orificeInlet bell mouth
16Measurement method based on velocity measurements in multiple points Very important: the square root of the averages ≠ the average of the square roots(!)Example: Measuring the dynamic pressure in multiple points and calculating the velocity from it22.214.171.124.
17Volume flow rate / based on velocity measurements I. Non-circular cross-sectionsAssumptions:126.96.36.199.
18Volume flow rate / based on velocity measurements II. Circular cross-sections, 10 point (6 point) methodThe velocity profile is assumed to be a 2nd order parabolaSteady flow conditionsPrandtl tube measurements of the dynamic pressure are usedSi/D= 0.026, 0.082, 0.146, 0.226, 0.342, 0.658, 0.774, 0.854, 0.918, 0.974
19Volume flow rate / based on velocity measurements III. Circular cross-sections, 10 point (6 point) methodAssumptions:The advantage of this method as compared to methods based on flow contraction is that the flow is not disturbed as much and is easy to do.The disadvantage is that the error can be much larger with this method. For long measurements it is also hard to keep the flow conditions constant. (10 points x 1.5 minutes = 15 minutes)Si/D= 0.026, 0.082, 0.146, 0.226, 0.342, 0.658, 0.774, 0.854, 0.918, 0.974
21Volume flow rate / flow contraction methods Through flow orifice Standard orifice size- pressure differenceb = d/D Cross-section ratiod [m] Diameter of the smallest cross/sectionD [m] Diameter of the pipe upstream of the orificeReD = Dv/n Reynolds number’s basic equation (characteristic size x velocity)/ kinematic viscosityv [m/s] The average velocity in the pipe of diameter Dn [m2/s] kinematic viscosityp1 [Pa] The pressure measured upstream of the orificep2 [Pa] The pressure measured in the orifice or downstream of itExpansion number (e=e(b,t,k)~1 For air the change in pressure is small)a Contraction ratio, a=(b,Re) (When using the standard it is 0.6)k Heat capacity ratio or Isentropic expansion factort=p2/p1 Pressure ratio
22Volume flow rate / flow contraction methods Inlet orifice (not standard)Not a standard contraction – pressure difference
23Example: Pipe volume flow rate uncertainty Determining the uncertainty of the results (error calculation) I.Example: Pipe volume flow rate uncertainty188.8.131.52.Pressures measured withthe Prandtl tube:p1 =486,2Pap2 =604,8Pap3 =512,4Pap4 =672,0PaAmbient conditions:p =1010hPaT=22°C (293K)R=287 J/kg/K0,1m2Uncertainty of the atmospheric pressure measurements, dp=100PaUncertainty of the atmospheric temperature measurements, dT=1KUncertainty of the Prandtl pressure measurement with thedigital manometer (EMB-001) dDp=2Pa
24Example: Pipe volume flow rate uncertainty Determining the uncertainty of the results (error calculation) I.Example: Pipe volume flow rate uncertaintyTypical absolute error184.108.40.206.(dp, dT, dDp)The absolute error for volume flow rate measurements:The relative error of volume flow rate measurements:The results for the volume flow rate:
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