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GVSU EGR 365 - EGR 365 Drag on a Cylinder

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Drag On a CylinderbyDan SchwarzSchool of EngineeringGrand Valley State UniversityEGR 365 – Fluid MechanicsSection 01Instructor: Dr. S. FleischmannJune 26, 2007OutlineI. Purpose Statementa. The drag force on a cylinder was determined experimentally.II. Backgrounda. The experimental system is shown in Figure 1. The control volume contains the test section of a wind tunnel where the cylinder is located. Air flows into the control volume with constant uniform velocity. When the air passes the cylinder its velocity profile is altered. This velocity profile is determined using pressure measurements gathered with the rake.Figure 1: The experimental system is a control volume that contains the cylinder. b. The drag force on the cylinder is determined using Equation 1. Equation 1 was derived using the momentum balance for the control volume as shown in Appendix A.hhdyVuLVD2221(1)c. Equation 1 was converted into a non-dimensional form which is given by Equation 2. See Appendix A for details.dyVudChhD2212(2)d. Experimental Methodi. Increase the velocity of the wind tunnel until the water manometer reads 2 inches when is reading the outermost tube in the rake.ii. Record the manometer readings for each tube in the rake.iii. Measure the local static pressure.iv. Measure the static pressure at the scanivalve.v. Determine the pressure difference between the local and scanivalve static pressure measurements. Subtract the difference from each of the manometer readings taken by the rake.12”12”+h-hu(y) V 1 18CVIII. Results / Discussiona. The pressure measurements taken during the experimental procedure where used to calculate the velocity profile. Table 1 shows the velocities that were calculated from the pressure differences in the control volume.Table 1: The velocity ratio from Equation 1 and Equation 2 was calculated from each pressure difference.PositionManometerOutputManometerAdjusted (in)PressureDifference (Psi)Velocity, u(ft/s)VelocityRatio (u2/V2)0 0.202 2.260 0.0816 100.78 1.0561 0.149 1.730 0.0625 88.18 0.8082 0.147 1.710 0.0618 87.67 0.7993 0.137 1.610 0.0581 85.06 0.7524 0.126 1.500 0.0542 82.11 0.7015 0.113 1.370 0.0495 78.47 0.6406 0.105 1.290 0.0466 76.14 0.6037 0.090 1.140 0.0412 71.58 0.5338 0.085 1.090 0.0394 69.99 0.5099 0.080 1.040 0.0376 68.37 0.48610 0.080 1.040 0.0376 68.37 0.48611 0.085 1.090 0.0394 69.99 0.50912 0.095 1.190 0.0430 73.13 0.55613 0.105 1.290 0.0466 76.14 0.60314 0.114 1.380 0.0498 78.75 0.64515 0.122 1.460 0.0527 81.00 0.68216 0.133 1.570 0.0567 84.00 0.73417 0.145 1.690 0.0610 87.15 0.79018 0.150 1.740 0.0628 88.43 0.813V 0.190 2.140 0.0773 98.07 1.000b. Figure 2 shows the velocity profile of the control volume. Figure 2: The velocity profile is given with respect to the pressure tap position.c. The drag force was approximated using the velocity profile shown in Figure 2. The area between the straight line and the velocity profile is equivalent to the integral in Equation 1. The drag force was found by substituting the approximate area for the integral into Equation 1. The resulting drag force was found to belblbD 149.1477.0 . See Appendix E for detailsd. The drag coefficient was also approximated by substituting the area for the integral into Equation 2. The resulting drag coefficient was found to be408.2000.1 DC. See Appendix E for details.e. For a drag coefficient of 408.2000.1 DC, the accepted Reynolds number could be in the range of 1x101 to 1x106. Since the Reynolds number for the system was 22906, the drag coefficient and drag force approximations appear to be correct.IV. Conclusionsa. The experimental results show that the force on the cylinder was approximatelylblbD 149.1477.0 .b. The Reynolds number and the drag coefficient seemed to match accepted experimental values. Thus, the approximated drag force is considered to be sufficiently accurate.V. Appendicesa. Appendix A – Question 1i. Find an equation that describes the drag on the cylinder.    hhhhhhhhhhycv csydyVuLVDLdyuLdyVDdAnuudAnVVDFdAnVVVdVF222221ˆˆ0ˆ0ii. Find an equation for the drag coefficient.dyVudCLdVDCAVDChhDDD2222125.05.0iii. Find an equation for velocity in terms of pressure difference.  2122122222122221211225.05.05.0PPVPPVVPPgzVPgzVPiv. Calculate the air density.   3333332002314.010940.1193.1193.1273239.286101300ftslugmkgftslugmkgmkgKKKkgJmNRTPRTPb. Appendix B – Question 2i. Calculate Reynolds number for the maximum speed of the wind tunnel.   505601074.304167.067.1901038.2Re2733ftslbftsftftslugVlc. Appendix C – Question 3i. Calculate the length to diameter ratio to be sure it is above 10.245.012inindlii. Calculate the blockage ratio to be sure it is below 10%.  %17.4%10012125.012_ininininAreaTotalBlockaged. Appendix D – Question 4i. Calculate the Reynolds number of the experimental system.   229061074.304167.038.861038.2Re2733ftslbftsftftslugVle. Appendix E – Approximate Experimental i. Find the area between the curve and the straight line in Figure 2. 02084.004167.05.0 Areaii. Find the area of the error region in Figure 2.  10035.00035.11.01.00035.104167.05.0222AreaHieghtLengthiii. Determine the approximate drag force.     lblbDftftftftftslugsDftftLVD149.1477.005018.002084.007.9811038.205018.002084.02332iv. Determine the approximate drag coefficient.  408.2000.105018.002084.004167.0205018.002084.02DDDCftftftCftftdCf. Appendix F – Spreadsheet CalculationsPositionManometerOutputManometerAdjusted (in)Pressure Difference(Psi)Velocity, u (ft/s) Velocity Ratio0 0.202 =10*(B2+0.024) =C2*62.4/(12*12*12) =SQRT(2*D2*12*12/0.002314) =E2*E2/($E$21*$E$21)1 0.149 =10*(B3+0.024) =C3*62.4/(12*12*12) =SQRT(2*D3*12*12/0.002314) =E3*E3/($E$21*$E$21)2 0.147 =10*(B4+0.024) =C4*62.4/(12*12*12) =SQRT(2*D4*12*12/0.002314)


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