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GVSU EGR 365 - EGR365 Impact of a Fluid Jet

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Impact of a Fluid JetbyDan SchwarzSchool of EngineeringGrand Valley State UniversityEGR 365 – Fluid MechanicsSection 01Instructor: Dr. S. FleischmannJune 19, 2007OutlineI. Purpose Statementa. The impact force of a jet of air striking a perpendicular surface was calculated using control volume analysis.b. An experimental system was used to verify the calculation.II. Backgrounda. The experimental system is shown in Figure 1. Air is blown at a constant mass flow rate into the control volume. The air jet strikes the beam and then leaves the control volume in two different directions. The mass flow rate of the air leaving the control volume is equal to the mass flow rate of air entering the control volume.Figure 1: The experimental system is a cantilever beam that deforms from the impact force of the air jet. b. The impact reaction force was determined using the conservation of momentum principal. Equation 1 was used to calculate the reaction force as a function of the mass flow rate. See Appendix A for details. Appendix B and C show how the air density and velocity was calculated.AAmAvRy22c. Experimental Methodi. The air nozzle was removed from the system and its inner diameter was measured.ii. Four different masses were placed on the top of the cantilever beam and the deflections were measured. These deflections where used to create a calibration curve that relates beam deflection to the resultant force, yR.iii. The air nozzle was replaced and the air valve was opened until the mass flow rate reached 2 grams/second.iv. The deflection of the beam was measured.v. Steps iii and iv were repeated with mass flow rates ranging from 3 to 9 grams/second. NozzleCantilever BeamCVRy A=1.28x10-5 m3 A/2 A/2vi. The calibration curve was used to determine the reaction forces based on the beam deflection.III. Results / Discussiona. The reaction forces measured in the experimental procedure are compared with the forces predicted using Equation 1.Table 1: Predicted and experimental reaction forces are compared. MassFlow Rate(kg/s)Air Velocity(m/s)Deflection (m)PredictedForce (N)ExperimentalForce (N)%Discrepancy0.002 135.399 0.008 0.271 0.306 13.0%0.003 203.098 0.017 0.609 0.650 6.7%0.004 270.797 0.026 1.083 0.994 8.2%0.005 338.497 0.035 1.692 1.338 20.9%0.006 406.196 0.046 2.437 1.759 27.8%0.007 473.895 0.056 3.317 2.141 35.4%0.008 541.594 0.067 4.333 2.562 40.9%0.009 609.294 0.079 5.484 3.021 44.9%b. The discrepancy begins to grow as the air velocity approaches the speed of sound.At the room temperature of 26°C the speed of sound was approximately 346 m/s. Table 1 shows that the discrepancy increases dramatically at 338.497 m/s and continues to grow as the velocity increases.c. The divergence of experimental and predicted reaction forces is shown in Figure 2.Figure 2: Predicted and experimental reaction forces are compared graphically.IV. Conclusionsa. The experimental results show that control volume analysis can successfully predict the impact reaction force produced by a fluid jet. However, this predictionbecomes inaccurate when the fluid velocity approaches the speed of sound. V. Appendicesa. Appendix A – Question 1i. Find the reaction force using control volume analysis.1. Begin with the general conservation of momentum equation. cscvydAnvvVdvdtdFˆ2. Unnecessary terms drop out. csyydAnvvRFˆ03. Simplify. AvdAnvvRcsy2ˆb. Appendix B – Question 2i. Find the density of the air at room temperature.1. Begin with the ideal gas law.RTP2. Solve for density.RTP3. Substitute values into the equation and solve numerically.    3154.1273269.286100990mkgKKkgJmbarPambarc. Appendix C – Question 3i. Relate air velocity to the mass flow rate of air through the nozzle.1. Begin with the mass flow rate equation.Avm2. Solve for velocity.Amvd. Appendix D – Question 4i. Create a calibration curve to relate the reaction force to the beam deflection.e. Appendix E – Spreadsheet CalculationsMass(kg)Force(N)Deflection(m)0.000 0.000 0.0000.051 0.500 0.0120.102 1.001 0.0260.204 2.001 0.0520.408 4.002 0.105Mass(kg)Force(N)Deflection(m)0 =A2*9.81 00.051 =A3*9.81 0.0120.102 =A4*9.81 0.0260.204 =A5*9.81 0.0520.408 =A6*9.81 0.105MassFlow Rate(kg/s)Air Velocity(m/s)Deflection (m)PredictedForce (N)ExperimentalForce (N)%Discrepancy0.002 135.399 0.008 0.271 0.306 13.0%0.003 203.098 0.017 0.609 0.650 6.7%0.004 270.797 0.026 1.083 0.994 8.2%0.005 338.497 0.035 1.692 1.338 20.9%0.006 406.196 0.046 2.437 1.759 27.8%0.007 473.895 0.056 3.317 2.141 35.4%0.008 541.594 0.067 4.333 2.562 40.9%0.009 609.294 0.079 5.484 3.021 44.9%Mass FlowRate (kg/s)Air Velocity (m/s) * **Deflection(m)Predicted Force (N) * **ExperimentalForce (N) ***% Discrepancy0.002 =A31/(0.0000128*1.154) 0.008 =B31*B31*0.0000128*1.154 =C31*38.239 =ABS(D31-E31)/D310.003 =A32/(0.0000128*1.154) 0.017 =B32*B32*0.0000128*1.154 =C32*38.239 =ABS(D32-E32)/D320.004 =A33/(0.0000128*1.154) 0.026 =B33*B33*0.0000128*1.154 =C33*38.239 =ABS(D33-E33)/D330.005 =A34/(0.0000128*1.154) 0.035 =B34*B34*0.0000128*1.154 =C34*38.239 =ABS(D34-E34)/D340.006 =A35/(0.0000128*1.154) 0.046 =B35*B35*0.0000128*1.154 =C35*38.239 =ABS(D35-E35)/D350.007 =A36/(0.0000128*1.154) 0.056 =B36*B36*0.0000128*1.154 =C36*38.239 =ABS(D36-E36)/D360.008 =A37/(0.0000128*1.154) 0.067 =B37*B37*0.0000128*1.154 =C37*38.239 =ABS(D37-E37)/D370.009 =A38/(0.0000128*1.154) 0.079 =B38*B38*0.0000128*1.154 =C38*38.239 =ABS(D38-E38)/D38*Nozzle Area = 0.0000128 m3**Air Density = 1.154 kg/m3***Calibration Curve Slope =


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