Tuesday, June 4, 2019

Flow Through A Venturi Meter

feed in Through A Venturi MeterGiven a Venturi Meter, Cv , the Venturi coefficient throw out be determined to comp atomic number 18 the real and ideal set as per Bernoullis predictions, for a volume flow rate. For better comparisons, two separate running games were analyzed and Venturi coefficients for some(prenominal) were computed. Trial 1 and Trial 2 yielded a Cv of 0.93 and 0.92 respectively. In this try the values calculated were found to be less than 1.0 this relatively high correlation between the experimental and ideal flows for the given Venturi pulsation however when compared to the ideal flow, the actual flow for this Venturi is not tight nor one dimensional. Therefore neither of these assumptions can be applied to any given actual flow.NomenclatureVariable/ Constant/ Symbol/ParameterValuesQVolume flow rate (m3/s)VVelocity (m/s)AArea (m2)air parsimony of air, 1.23 kg/m3waterDensity of water, 1000 kg/m3CvVenturi coefficientPoStagnation insistence (Pa) is Static P ressure plus Dynamic PressurePatm atmospheric pressure, 101.325 KPahHeight difference (m) between readings and PatmgAcceleration, 9.81 m/s2zElevation of Point (m)()V2Dynamic Pressure (Pa)PStatic PressureFlow AnalysisBernoullis Equation relates two points alongside a streamline asP1 + ()airV12+ airgz1 = P2 + ()airV22 + airgz2z is negligible so airgz cancels out on both sides leavingP1 + ()airV12+ = P2 + ()V22RearrangingP1 P2 = ()air(V22 V12) grade thatQideal = V1A1 = V2A2.Solving for V2V2 =Subbing (5) into (3) and solving for V1V1 =ThenQideal = A1Flow Analysis (Contd)For the derivation of Qactual, sufficient distance from the Venturi inlet is fall upond for a fluid particles relative fastness to be taken as zero. The same height (z value) as the Venturi will be taken for the particle.P1 + ()airV12+ airgz1 = P2 + ()airV22 + airgz2z is negligible so airgz cancels out on both sides leavingP1 + ()airV12+ = P2 + ()V22as stated, the fluid particles velocity at point 0 is assumed to be 0m/sPatm = P2 + ()airV22Solving for V2V2 =P2 is defined as the static pressure at the inlet, found to beP2 = Patm + waterghSubbing (9) into (8)V2 =To find QactualQactual = V2A2.Sub (11) into (12) where A2 is the cross sectional areaQactual = A2Flow Analysis (Contd)With values for Qactual and Qideal, Cv can then be calculated with the relationCv =For ideal static pressures combine (8) having solved for P2 and (4) having solved for V2P2 = Patm ()airV22P2 = Patm ()airExperimental Setup and ProcedureThe experiment was carried out per the instructions outlined in the course manual. However due to a problem with the apparatus and a constantly fluctuating Venturi meter, a photographic camera was use to take a photo. Measurements were taken from the scale viewed on say picture.Figure Shows Experimental SetupResultsFor trial 1Qideal = 0.01238 Qactual = 0.01153The Venturi Coefficient, Cv, was calculated by exploitation the values found for Qideal and Qactual and substituting them into eq uation (14). This value obtained was 0.93.To find the stagnation pressure, P = Patm and V = 0 the match pressure at this point is be by P0 = Patm + ()airV2, however since V = 0 , the stagnation pressure is P0 = Patm.The Static Pressure is Patm = Patm watergh where the h used is the value that corresponds with the throat. Therefore Pthroat = 99.206KPaFor Dynamic Pressure, ()airVthroat2 = Patm Pthroat = 2.119KPaResults(Contd)For trial 2Qideal = 0.01238 Qactual = 0.01153The Venturi Coefficient, Cv, was calculated by using the values found for Qideal and Qactual and substituting them into equation (14). This value obtained was 0.92.To find the stagnation pressure, P = Patm and V = 0 the total pressure at this point is represented by P0 = Patm + ()airV2, however since V = 0 , the stagnation pressure is P0 = Patm.The Static Pressure is Patm = Patm watergh where the h used is the value that corresponds with the throat. Therefore Pthroat = 96.871KPaFor Dynamic Pressure, ()airVthroat2 = Patm Pthroat = 4.454KPaDiscussionThe two calculated Venturi Coefficients for both trials of differing flow rates were found to fetch close enough values to assume that said coefficients do not depend on the flow rate but rather on the Venturi meter in use. For ideal calibration methods, an just of values, 0.92 and 0.93 could be taken to compensate for ideal assumptions which have been determined to be inaccurate. This would aid the user to find actual values once ideal ones have been found.Although these values are not 1.0, they are relatively close. However despite this, it can be inferred that the idealistic conditions assumed at the beginning of the experiment are invalid as they do in fact incur a noticeable effect on the results creating an defect. These assumptions included a one dimensional steady flow that existed in a frictionless environment such implies no energy transfers.Dimensions for the outlet and inlet were assumed to be equal however if the graphs are reviewed , there are discrepancies and a certain amount of irregularities. These further outline the existence of friction and energy loss which can be observed by means of the comparison of tables 1 and 2 in the appendix where the values of experimental and ideal static pressures are defined.There was however another source of error that was introduced due to the faulty apparatus as was discussed in the Experimental Setup and Procedure section. Measurements were taken from a photograph to facilitate taking down said measurements from a fluctuating Venturi meter.Bernoullis equation states that when a fluid in flow undergoes a rise in pressure, then its velocity must decrease. Said judgment also applies the other way around. Figure 1 in the appendix illustrates this through a rough sketch.ConclusionVenturi coefficients such as the ones calculated in this experiment, 0.92 and 0.93 imply that the actual flow is lower than the ideal flow. Therefore the ideal conditions that were applied only g ive an approximation to the actual flows. The coefficients can be averaged for a more accurate way to calibrate the Venturi meter. The values found imply that the Venturi meter relates the actual and ideal values relatively well however this may be due to the fluctuating meters. Also very likely, is the presence of a relatively low amount of friction and symmetrical dimensions in the Venturi meter.ReferencesUniversity, Carleton, ed. MAAE 2300 Course Manual. Ottawa, 2011. Print.

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