Impact of a Fluid Jet by Dan Schwarz School of Engineering Grand Valley State University EGR 365 Fluid Mechanics Section 01 Instructor Dr S Fleischmann June 19 2007 Outline I II Purpose Statement a 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 Background a 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 Nozzle A 1 28x10 5 m3 CV A 2 A 2 Cantilever Beam Ry 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 2 m A R y v 2 A A c Experimental Method i 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 R y 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 III vi The calibration curve was used to determine the reaction forces based on the beam deflection Results Discussion a 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 Mass Flow Rate kg s 0 002 0 003 0 004 0 005 0 006 0 007 0 008 0 009 Air Velocity m s Deflectio n m Predicted Force N Experimental Force N Discrepancy 135 399 203 098 270 797 338 497 406 196 473 895 541 594 609 294 0 008 0 017 0 026 0 035 0 046 0 056 0 067 0 079 0 271 0 609 1 083 1 692 2 437 3 317 4 333 5 484 0 306 0 650 0 994 1 338 1 759 2 141 2 562 3 021 13 0 6 7 8 2 20 9 27 8 35 4 40 9 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 Conclusions a The experimental results show that control volume analysis can successfully predict the impact reaction force produced by a fluid jet However this prediction becomes inaccurate when the fluid velocity approaches the speed of sound V Appendices a Appendix A Question 1 i Find the reaction force using control volume analysis 1 Begin with the general conservation of momentum equation F y d dt v dV v v n dA cv cs 2 Unnecessary terms drop out dA v v n F y 0 R y cs 3 Simplify Ry v v n dA v cs 2 A b Appendix B Question 2 i Find the density of the air at room temperature 1 Begin with the ideal gas law P RT 2 Solve for density P RT 3 Substitute values into the equation and solve numerically 990mbar 100 Pa mbar 286 9 J kg K 26 273 K 1 154 kg m3 c Appendix C Question 3 i Relate air velocity to the mass flow rate of air through the nozzle 1 Begin with the mass flow rate equation Av m 2 Solve for velocity v m A d Appendix D Question 4 i Create a calibration curve to relate the reaction force to the beam deflection e Appendix E Spreadsheet Calculations Mass Flow Rate kg s 0 002 0 003 0 004 0 005 0 006 0 007 0 008 0 009 Mass kg Force N Deflection m 0 000 0 051 0 102 0 204 0 408 0 000 0 500 1 001 2 001 4 002 0 000 0 012 0 026 0 052 0 105 Mass kg Force N Deflection m 0 0 051 0 102 0 204 0 408 A2 9 81 A3 9 81 A4 9 81 A5 9 81 A6 9 81 0 0 012 0 026 0 052 0 105 Air Velocity m s Deflectio n m Predicted Force N Experimental Force N Discrepancy 135 399 203 098 270 797 338 497 406 196 473 895 541 594 609 294 0 008 0 017 0 026 0 035 0 046 0 056 0 067 0 079 0 271 0 609 1 083 1 692 2 437 3 317 4 333 5 484 0 306 0 650 0 994 1 338 1 759 2 141 2 562 3 021 13 0 6 7 8 2 20 9 27 8 35 4 40 9 44 9 Mass Flow Rate kg s Air Velocity m s Deflection m Predicted Force N Experimental Force N Discrepancy 0 002 A31 0 0000128 1 154 0 008 B31 B31 0 0000128 1 154 C31 38 239 ABS D31 E31 D31 0 003 A32 0 0000128 1 154 0 017 B32 B32 0 0000128 1 154 C32 38 239 ABS D32 E32 D32 0 004 A33 0 0000128 1 154 0 026 B33 B33 0 0000128 1 154 C33 38 239 ABS D33 E33 D33 0 005 A34 0 0000128 1 154 0 035 B34 B34 0 0000128 1 154 C34 38 239 ABS D34 E34 D34 0 006 A35 0 0000128 1 154 0 046 B35 B35 0 0000128 1 154 C35 38 239 ABS D35 E35 D35 0 007 A36 0 0000128 1 154 0 056 B36 B36 0 0000128 1 154 C36 38 239 ABS D36 E36 D36 0 008 A37 0 0000128 1 154 0 067 B37 B37 0 0000128 1 154 C37 38 239 ABS D37 E37 D37 0 009 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 32 239N m