Drag On a Cylinder by Dan Schwarz School of Engineering Grand Valley State University EGR 365 Fluid Mechanics Section 01 Instructor Dr S Fleischmann June 26 2007 Outline I II Purpose Statement a The drag force on a cylinder was determined experimentally Background a 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 12 h CV 1 V 12 u y 18 h 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 h D LV 2 2 1 u V2 h dy 1 c Equation 1 was converted into a non dimensional form which is given by Equation 2 See Appendix A for details CD 2 d h 2 1 u V2 h dy 2 d Experimental Method i 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 III Results Discussion a 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 Manometer Manometer Pressure Velocity u Velocity Position Output Adjusted in Difference Psi ft s Ratio u2 V2 0 0 202 2 260 0 0816 100 78 1 056 1 0 149 1 730 0 0625 88 18 0 808 2 0 147 1 710 0 0618 87 67 0 799 3 0 137 1 610 0 0581 85 06 0 752 4 0 126 1 500 0 0542 82 11 0 701 5 0 113 1 370 0 0495 78 47 0 640 6 0 105 1 290 0 0466 76 14 0 603 7 0 090 1 140 0 0412 71 58 0 533 8 0 085 1 090 0 0394 69 99 0 509 9 0 080 1 040 0 0376 68 37 0 486 10 0 080 1 040 0 0376 68 37 0 486 11 0 085 1 090 0 0394 69 99 0 509 12 0 095 1 190 0 0430 73 13 0 556 13 0 105 1 290 0 0466 76 14 0 603 14 0 114 1 380 0 0498 78 75 0 645 15 0 122 1 460 0 0527 81 00 0 682 16 0 133 1 570 0 0567 84 00 0 734 17 0 145 1 690 0 0610 87 15 0 790 18 0 150 1 740 0 0628 88 43 0 813 V 0 190 2 140 0 0773 98 07 1 000 b Figure 2 shows the velocity profile of the control volume Figure 2 The velocity profile is given with respect to the pressure tap position IV V 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 be D 0 477lb 1 149lb See Appendix E for details d The drag coefficient was also approximated by substituting the area for the integral into Equation 2 The resulting drag coefficient was found to be C D 1 000 2 408 See Appendix E for details e For a drag coefficient of C D 1 000 2 408 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 Conclusions a The experimental results show that the force on the cylinder was approximately D 0 477lb 1 149lb 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 Appendices a Appendix A Question 1 i Find an equation that describes the drag on the cylinder F y 0 V dV cv V V n dA cs h Fy 0 D h V V n dA u u n dA h D V 2 Ldy h u 2 h Ldy h h D LV h h 2 2 1 u V2 h dy ii Find an equation for the drag coefficient CD CD CD D 0 5 AV D 2 0 5 LdV 2 2 d h 2 1 u V2 h dy iii Find an equation for velocity in terms of pressure difference P1 0 5 V12 gz1 P2 0 5 V 22 gz 2 P1 P2 0 5 V 22 V 22 2 P1 P2 V 2 2 P1 P2 iv Calculate the air density P RT P RT 101300 N m2 kg 1 193 3 286 9 J kg K 23K 273K m 1 193 3 kg 3 slug ft 1 940 10 m 3 kg m 3 0 002314 slug ft 3 b Appendix B Question 2 i Calculate Reynolds number for the maximum speed of the wind tunnel Re 2 38 10 3 slug ft 3 190 67 ft s 0 04167 ft Vl 50560 3 74 10 7 lb s ft 2 c Appendix C Question 3 i Calculate the length to diameter ratio to be sure it is above 10 l 12in 24 d 0 5in ii Calculate the blockage ratio to be sure it is below 10 Blockage 12in 0 5in 100 4 17 Total Area 12in 12in d Appendix D Question 4 i Calculate the Reynolds number of the experimental system Re 2 38 10 3 slug ft 3 86 38 ft s 0 04167 ft Vl 22906 3 74 10 7 lb s ft 2 e Appendix E Approximate Experimental i Find the area between the curve and the straight line in Figure 2 Area 0 5 0 04167 0 02084 ii Find the area of the error region in Figure 2 Length 2 0 5 2 0 04167 2 1 0035 Hieght 0 1 Area 0 1 1 0035 0 10035 iii Determine the approximate drag force D LV 2 0 02084 ft 0 05018 ft slugs 1 ft 98 07 ft 2 0 02084 ft 0 05018 ft D 2 38 10 3 3 ft D 0 477lb 1 149lb iv Determine the approximate drag coefficient 2 0 02084 ft 0 05018 ft d 2 0 …