PurposeTheory & MethodResultsDiscussionConclusionAppendix ADesign QuestionsGrand ValleyState UniversityPadnos School of EngineeringEGR 365: Fluid MechanicsLab 6:Impact of a JetDale SlotmanPartner:Ian RudnikDr. Fleischmann6-10-03PurposeThe purpose of this lab was to experimentally determine the impact of a jet deflected at aknown angle and to compare the experimental results to predictions from a controlvolume analysis of an inviscid fluid.Theory & MethodThe experimental data measured in this lab was taken by measuring the deflection of acantilever beam which deflected a jet of air 90 degrees at its free end. The controlvolume for the jet is shown in figure 1 and the beam is shown in figure 2. Note that thereaction force to deflect the jet 90 degrees is the same as the force deflecting the beam.Figure 1: Control Volume of JetFigure 2: Cantilever BeamFrom control volume analysis:121AvRy (1)From solid model analysis:IELRyy33 (2)See Appendix A for derivations.Because volume flowrate is fluid velocity times area,12AQRy(3)The area of the nozzle used in lab was 1.346E-5 m2 = 1.449E-4 ft2.Because the cantilever beam was enclosed inside a casing and made of an unknownmaterial, it was known from the beginning of the lab that equation (2) would not be usefulin giving an accurate prediction of the deflection. The length, modulus of elasticity, andmoment of inertia of the beam are unknown. Because predicted values for the deflectioncould not be obtained, predicted values for force were obtained.The beam was loaded with four different, known masses. The deflection caused by each mass was recorded.For each deflection value, the mass flowrate of air to deflect the beam that exact amountwas measured. The pressure and mass flowrates were recorded.ResultsThe results measured in lab are given in table 1.Table 1 : Results (Metric)Deflection(units unknown)Static Load(g)Fluid Flowrate(g/sec)Pressure(kN/m2 gage)13 51 2.62 4027 102 4.02 7540 153 5.25 11067 255 7.78 200The results were converted into English System units.Table 2: Results (English)Deflection(units unknown)Static Load(lbf)Fluid Flowrate(slugs/sec)Pressure(lb/ft2 abs) 13 0.112524 0.000179522 295227 0.225047 0.00027545 368240 0.337571 0.00035973 441367 0.562618 0.000533086 6293The static load results indicate the measured force supplied by the fluid flowrate. The pressure can be used to calculate the predicted force supplied by the fluid. The ideal gas equation is used to calculate the density of the fluid in the jet. The ambient temperature was measured to be 75 deg Fahrenheit. Also, volume flowrate can be calculated from density and mass flowrate.3003217.067.53417162952ftslugRRsluglbftpsfTRpsec055805.0003217.0sec000179522.033ftftslugsslug smQ Table 3: Density and Volume Flowrate ResultsFluid Flowrate(slugs/sec)Pressure(lb/ft2 abs)Density(slugs/ft3)Volume Flowrate(ft3/sec)0.000179522 2952 0.003217 0.0558050.00027545 3682 0.004014 0.0686290.00035973 4413 0.00481 0.0747840.000533086 6293 0.006859 0.077722Equation (3) gives the relationship between the volume flowrate and the force applied tothe cantilever.lbftftftslugsAQRy069134.00001449.0)sec055805.0(003217.0223212Table 4: Forces: Measured and PredictedFluid Flowrate(slugs/sec)Measured Load(lbf)Predicted JetForce (lbf)PercentDifference0.000179522 0.112524 0.069134 38.56%0.00027545 0.225047 0.130451 42.03%0.00035973 0.337571 0.185644 45.00%0.000533086 0.562618 0.285917 49.18%00.10.20.30.40.50.60 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006Flowrate (slugs/sec)Jet Force (lbf)PredictedMeasuredFigure 3 : Predicted and Measured ForcesDiscussionFrom figure 3, the force induced by the air jet (“Measured”) is about twice the forcepredicted by using the line pressure and mass flowrate.Using a constant measurement uncertainty of sec10852.6sec1.06slugsgram, error barscan be put in for the measured values. The predicted force is dependant on themeasurements of mass flowrate, pressure, and diameter, as related by the equationTRdpmAQRy42212From this, a propagated error can be calculated for the predicted values.222)()(4)(4pudumuRupdmRFor instance,lbmkNmkNmmmmgramsgramslbuR006707.0)33.1415()14.401.0(4)sec10795.1sec10852.6(4069134.0222224600.10.20.30.40.50.60 0.0002 0.0004 0.0006Mass Flowrate (slugs/sec)Jet Force (lbf)MeasuredMaximum PredictedMinimum PredictedFigure 4: Measured and Predicted Values with Error BarsThe interesting thing about the discrepancy between the measured and predicted resultsis that the predicted force is actually less than the measured force of the air jet. This isstrange because losses between the point at which the pressure is taken and the pointof applied force on the beam would make the predicted force greater than the measuredforce.If there were leaks in the system, the mass flowrate measured would be less than themass flowrate at the point of impact, as the mass flowrate was measured downstreamfrom the point of impact. To compensate for the discrepancy, however, the leaks wouldhave been great, and in a sealed system, this is unlikely.ConclusionIt is safe to assume that the pressure and flow gages were functioning properly andgiving accurate readings. Therefore, the discrepancy seen between the measured andpredicted forces must be coming from somewhere else. It is my opinion that thediscrepancy comes from fluid effects not taken into account in the control volumeanalysis. These include, but are not limited to, sonic effects, viscous effects, and flowdispersion.The two data sets seem to have the same trend, however, giving credence to the controlvolume approach for analyzing this setup. It seems that there is just a piece missing.Appendix ADesign Questions1) Begin with the approximate control volume in figure A.1 and derive equation (A1).Figure A.1: Control Volume of Jet and ReactionUsing conservation of momentum on the control volume shown in figure 1,- dAnvvvmtamRFycvyyycv)(--22221111)()( dAnvvdAnvvRyyy2221111)()0()()( dAvdAvvRy121AvRy(A1)2) Suppose that you are building this experiment. One