Grand Valley State University Padnos School of Engineering EGR 365 Fluid Mechanics Lab 6 Impact of a Jet Dale Slotman Partner Ian Rudnik Dr Fleischmann 6 10 03 Purpose The purpose of this lab was to experimentally determine the impact of a jet deflected at a known angle and to compare the experimental results to predictions from a control volume analysis of an inviscid fluid Theory Method The experimental data measured in this lab was taken by measuring the deflection of a cantilever beam which deflected a jet of air 90 degrees at its free end The control volume for the jet is shown in figure 1 and the beam is shown in figure 2 Note that the reaction force to deflect the jet 90 degrees is the same as the force deflecting the beam Figure 2 Cantilever Beam Figure 1 Control Volume of Jet From control volume analysis From solid model analysis 2 R y v1 A1 1 y See Appendix A for derivations R y L3 3 E I 2 Because volume flowrate is fluid velocity times area Ry Q 2 A1 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 unknown material it was known from the beginning of the lab that equation 2 would not be useful in giving an accurate prediction of the deflection The length modulus of elasticity and moment of inertia of the beam are unknown Because predicted values for the deflection could 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 amount was measured The pressure and mass flowrates were recorded Results The results measured in lab are given in table 1 Table 1 Results Metric Deflection Static Load units unknown g 13 51 27 102 40 153 67 255 Fluid Flowrate g sec 2 62 4 02 5 25 7 78 Pressure kN m2 gage 40 75 110 200 The results were converted into English System units Table 2 Results English Deflection Static Load units unknown lbf 13 0 112524 27 0 225047 40 0 337571 67 0 562618 Fluid Flowrate slugs sec 0 000179522 0 00027545 0 00035973 0 000533086 Pressure lb ft2 abs 2952 3682 4413 6293 The 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 p R T 1716 2952 psf slug 0 003217 3 ft lb ft 534 67 R slug R slugs 0 000179522 sec m ft 3 Q 0 055805 slugs sec 0 003217 3 ft Table 3 Density and Volume Flowrate Results Fluid Flowrate Pressure Density Volume Flowrate slugs sec lb ft2 abs slugs ft3 ft3 sec 0 000179522 2952 0 003217 0 055805 0 00027545 3682 0 004014 0 068629 0 00035973 4413 0 00481 0 074784 0 000533086 6293 0 006859 0 077722 Equation 3 gives the relationship between the volume flowrate and the force applied to the cantilever Ry Q 2 A1 slugs ft 3 2 0 055805 sec ft 2 0 069134lb 0 0001449 ft 2 0 003217 Table 4 Forces Measured and Predicted Fluid Flowrate Measured Load Predicted Jet slugs sec lbf Force lbf 0 000179522 0 112524 0 069134 0 00027545 0 225047 0 130451 0 00035973 0 337571 0 185644 0 000533086 0 562618 0 285917 Percent Difference 38 56 42 03 45 00 49 18 0 6 Jet Force lbf 0 5 0 4 Predicted Measured 0 3 0 2 0 1 0 0 0 0001 0 0002 0 0003 0 0004 0 0005 0 0006 Flowrate slugs sec Figure 3 Predicted and Measured Forces Discussion From figure 3 the force induced by the air jet Measured is about twice the force predicted by using the line pressure and mass flowrate gram slugs 6 852 10 6 error bars sec sec can be put in for the measured values The predicted force is dependant on the measurements of mass flowrate pressure and diameter as related by the equation Using a constant measurement uncertainty of 0 1 Q 2 m 2 4 R T A1 p d 2 From this a propagated error can be calculated for the predicted values Ry u R R 4 up u m 2 u 4 d 2 2 m d p For instance u R 0 069134lb 4 6 852 10 6 1 795 10 4 kN grams 5 2 sec 2 4 0 01mm 2 m 2 0 006707lb grams kN 4 14mm 141 33 2 sec m 0 6 Jet Force lbf 0 5 0 4 Measured 0 3 Maximum Predicted Minimum Predicted 0 2 0 1 0 0 0 0002 0 0004 0 0006 Mass Flowrate slugs sec Figure 4 Measured and Predicted Values with Error Bars The interesting thing about the discrepancy between the measured and predicted results is that the predicted force is actually less than the measured force of the air jet This is strange because losses between the point at which the pressure is taken and the point of applied force on the beam would make the predicted force greater than the measured force If there were leaks in the system the mass flowrate measured would be less than the mass flowrate at the point of impact as the mass flowrate was measured downstream from the point of impact To compensate for the discrepancy however the leaks would have been great and in a sealed system this is unlikely Conclusion It is safe to assume that the pressure and flow gages were functioning properly and giving accurate readings Therefore the discrepancy seen between the measured and predicted forces must be coming from somewhere else It is my opinion that the discrepancy comes from fluid effects not taken into account in the control volume analysis These include but are not limited to sonic effects viscous effects and flow dispersion The two data sets seem to have the same trend however giving credence to the control volume approach for analyzing this setup It seems that there is just a piece missing Appendix A Design Questions 1 Begin with the approximate control volume in figure A 1 and derive equation A1 Figure A 1 Control Volume of Jet and Reaction Using conservation of momentum on the control volume shown in figure 1 F y R y m a ycv m v cv v y v n dA t R y v y1 v1 n dA1 v y 2 v 2 n dA2 1 2 R y v1 v1 dA1 0 v 2 dA2 1 2 2 R y v1 A1 A1 2 Suppose that you are building this experiment One of your first choices will be a choice …