Drag On a Cylinder from Integrated Pressure Distribution by Dan Schwarz School of Engineering Grand Valley State University EGR 365 Fluid Mechanics Section 01 Instructor Dr S Fleischmann July 3 2007 Outline I II Purpose Statement a The drag force on a cylinder was determined experimentally by integrating the surface pressure distribution Background a The experimental system is shown in Figure 1 Air approaches the cylinder at constant velocity but as it flows around the cylinder the velocity must increase The increase in velocity produces a decrease in pressure around the cylinder The pressure difference creates a force on the cylinder as shown in Figure 1 dF PRd Flow Direction Figure 1 The experimental system is a cylinder with pressure taps located in 15 increments b The drag force on the cylinder is created by the force component that is parallel with the flow direction Equation 1 gives the drag force on the cylinder See Appendix A for details Fdrag p p cos LRd 1 c The drag force can be non dimesionalized to produce the drag coefficient described by Equation 2 See Appendix A for details CD III 1 2 2 C p cos d 2 0 d Experimental Method i Increase the velocity of the wind tunnel until the number 0 pressure tap reads 1 inch on the water manometer ii Record the manometer readings for each pressure tap around the circumference of the cylinder Results Discussion a The pressure measurements taken from each pressure tap were used to compute pressure coefficients See Appendix E for the raw data The pressure coefficients were plotted with respect to the angular position of the pressure taps in Figure 2 The curve is not symmetrical because a strip of sand paper was placed on one side of the cylinder The sand paper causes the flow to separate from the cylinder earlier than it would on a smooth surface The early separation produces a larger pressure change and more negative pressure coefficients Figure 2 shows that the right side has early flow separation caused by a rough surface The left side of the cylinder was completely smooth b Error in the pressure measurements was fairly small This produced a curve that tends to follow the ideal pressure coefficient curve Figure 2 The pressure coefficient is shown as a function of the pressure tap angles c The pressure coefficients from Figure 2 were multiplied by cos to create the curve shown in Figure 3 The area under this curve was used to determine the drag coefficient of the cylinder in accordance with Equation 2 Figure 3 The experimental pressure coefficient curve was multiplied by cos to determine C D IV V d The drag coefficient for the smooth side of the cylinder was determined to be 1 0472 Other experiments with the same Reynolds number have a drag coefficient of approximately 1 1 which confirms the experimental results See Appendix B and Appendix C for details e The drag coefficient of the rough side of the cylinder was determined to be 0 7854 See Appendix B for details Conclusions a The drag coefficient of the cylinder was experimentally determined form the approximate area under the Cpcos curve b The drag coefficient for the smooth cylinder was 1 0472 which was supported by other experimental data c The drag coefficient for the rough cylinder was 0 7854 d The pressure measurement had little error and produced nearly ideal pressure coefficient curves Appendices a Appendix A Develop an equation for the coefficient of drag i Relate force to pressure F PA PdA ii The drag force only acts perpendicular to the flow direction shown in Figure 1 Fdrag p p cos LRd iii The drag coefficient is non dimensionalized drag force CD Fdrag 1 U 2 2 p p cos LRd 1 U 2 2 iv For an ideal flow the velocity is U 2U sin Substitute this into Bernoulli s equation p p 1 2 1 U 4 sin 2 U 2 2 2 p p 1 2 1 2 U U 4 sin 2 2 2 1 p p U 2 2 U 2 sin 2 2 1 p p U 2 1 4 sin 2 2 p p 1 4 sin 2 C p 1 U 2 2 v Substitute p p into the drag coefficient equation 1 2 U 2 1 4 sin 2 cos LRd 1 2 CD C p cos d 1 2 2 U 0 2 b Appendix B Approximate the coefficient of friction of the cylinder i Approximate the area under the curve in Figure 3 for the smooth side of the cylinder 1 1 1 Area smooth 1 0 9 1 6 1 0472 2 6 2 3 2 2 ii Approximate the area under the curve in Figure 3 for the rough side of the cylinder 1 1 1 Area rough 1 6 1 4 1 0 7854 2 2 2 3 2 6 c Appendix C Calculate the Reynolds number of the experimental system i Calculate the Reynolds number of the experimental system Re 1 34 10 5 Z 1 34 10 5 1 1 34 10 5 d Appendix D Calculate U i 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 ii Calculate air density P RT P RT 99000 N m2 kg 1 17 3 286 9 J kg K 22 K 273K m 1 17 3 kg 3 slug ft 1 940 10 m 3 kg m 3 iii Calculate P P 0 002269 slug ft 3 where the air flow comes to rest on the cyclinder lb lb 1 P P h ft 62 4 3 5 2 2 12 ft ft iv Find U U 2 P P U 2 5 2 lb ft 2 2 38 slug ft 3 66 1 ft s e Appendix E Spreadsheet Calculations Angle Manometer in P P lb ft2 Ideal Cp Measured Cp Discrepancy Measured Cpcos 0 0 1 00 5 35 1 00 1 03 2 9 1 03 1 15 0 78 4 17 0 73 0 80 9 6 0 78 2 30 0 02 0 11 0 00 0 02 0 02 3 45 0 94 5 03 1 00 0 97 3 3 0 68 4 60 1 72 9 20 2 00 1 77 11 5 0 88 5 75 1 65 8 83 2 73 1 70 37 9 0 44 6 90 1 60 8 56 3 00 1 65 45 1 0 00 7 105 1 58 8 45 2 73 1 63 40 5 0 42 8 120 1 60 8 56 2 00 1 65 17 7 0 82 9 135 1 65 8 83 1 00 1 70 69 8 1 20 10 150 1 67 8 93 0 00 1 72 1 49 Position 11 165 1 59 8 51 0 73 1 64 323 5 1 58 12 180 1 53 8 19 1 00 1 57 257 …