Drag Force on a Cylinder EGR 365 Fluid Mechanics Section 03 Grand Valley State University Padnos College of Engineering Instructor Dr Blekhman Author Matt Brower 19 June 2006 Introduction The purpose of this lab was to determine the force acting on a cylinder in a steady flow field using a momentum balance in the wake of the cylinder By placing a cylindrical rod into a flow field and measuring the velocity of the fluid both before and after the cylinder it is possible to find the force acting on the cylinder as it resists the flow and causes a wake For this lab velocity was estimated by direct measurement of dynamic pressure along the wake and before the cylinder Apparatus Flow field set up in GVSU wind tunnel 0 5 inch diameter rod 1 foot long Velocity profile of fluid y x Pitot Static Tubes Uinfinity V y 1 10 pt ps Cylinder 12 x 0 5 Control Volume Figure 1 Control Volume for Cylinder in Flow Field Array of Pitot static tubes to read dynamic pressure distribution in wake see Fig 1 Procedure First the dynamic pressure was read by a Pitot static tube placed well outside of the wake of the cylinder This was used as a reference The air was turned on until the gage read 0 75 inches Readings of dynamic pressure Patm Pstatic were taken from each tube in the wake see Fig 1 The airspeed was increased until the gage read 2 75 inches Readings were again taken for dynamic pressure from each tube in the wake Theory When an object is placed in a fluid experiencing steady state flow the object will create a wake behind it The wake is essentially an area where the velocity of the fluid is disturbed and it increases as it flows around the object swirling behind it This velocity change creates a force on the object in the flow field since the object is restrained from moving and the fluid flowing around it is experiencing viscous shear as it flows over the surface of the object disturbing it To measure the force the velocity in the wake must first be determined experimentally The Pitot Static tubes in the wind tunnel measure dynamic pressure in the wake This pressure can be used to find the velocity See Appendix A for derivations of the equations and Appendix B for sample calculations Putting velocity into Eq 1 will yield the force on the cylinder H U2 2 D LU 1 2 dy 1 V H Where is the density of the fluid L is the length of the object U is the velocity well away from the wake V is the velocity in the wake and H to H are the width of the wake Drag measurements can be presented non dimensionally in the form CD Drag 0 5 AV 2 2 Where CD is the drag coefficient A is the cross sectional area opposing the flow and V is the fluid speed relative to the body Flow speed can be non dimensionalized in the form of Reynolds Number which is useful in determining the theoretical drag force on an object based on its geometry and the properties of the fluid in the flow field Re d Vd 3 Where d is the diameter of the cylinder and is the dynamic viscosity 45 00 40 00 35 00 30 00 25 00 20 00 15 00 10 00 5 00 0 00 Low Speed 18 15 12 9 6 High Speed 3 0 Velocity ft s Results Discussion Pitot Static tube location Figure 2 Velocity Profile for Wake of a Cylinder In Flow Field of Different Velocity 0 5 0 75 5 58 69 9 55 44 47 36 06 6 0 8 4 6 7 35 36 9 6 43 42 52 93 1 7 1 89 5 57 97 4 65 59 65 3 20000 00 18000 00 16000 00 14000 00 12000 00 10000 00 8000 00 6000 00 4000 00 2000 00 0 00 9 Drag Coefficient Figure 1 shows the typical velocity distribution in the wake after the cylinder as was measured by the Pitot static tubes Figure 2 shows a plot of Reynolds Number compared to the Drag coefficient Refer to Appendix B for sample calculations and Appendix C for data tables It can be seen from Figure 1 that the velocity was the greatest directly behind the cylinder and became less as the distance went out towards infinity Figure 2 shows that the drag coefficient was the highest while Reynolds Number was the lowest directly behind the cylinder Reynold s Num ber Figure 3 Drag Coefficient vs Reynolds Number for Air Flow Around a Cylinder The drag force found on the cylinder was 158 lb with a wind speed of 25 ft s and 477 lb with a wind speed of 42 ft s in front of the cylinder Refer to Appendix B for sample calculations Interpretations and conclusions When an object is immersed in a flowing fluid and restrained from moving it experiences a drag force This drag force was found to increase exponentially as the wind speed increased This increase was due to the fluid interacting with the surface of the obstructing object and creating shear force due to the viscosity of the fluid With a lower viscosity fluid or a smoother surface the drag force could be decreased The drag coefficient could be used to find the theoretical force on the cylinder based on the fluid properties and the obstructing object s geometry If he drag coefficient were known beforehand it could be used to find the force on a cylinder based on its geometry and the velocity of the fluid downstream of the object This could be helpful in decreasing the amount of measurements required Reynolds number can serve the same function as the drag coefficient as they are similarly related Appendix C Data Tables h infinity 0 75 U 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 h in 0 086 0 075 0 087 0 071 0 067 0 063 0 056 0 048 0 036 0 027 0 025 0 025 0 026 0 036 0 045 0 055 0 062 0 067 0 069 0 085 P psi 0 0055 0 0048 0 0055 0 0045 0 0043 0 0040 0 0036 0 0031 0 0023 0 0017 0 0016 0 0016 0 0017 0 0023 0 0029 0 0035 0 0040 0 0043 0 0044 0 0054 U 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 h in 0 233 0 204 0 221 0 188 0 185 0 165 0 150 0 125 0 095 0 085 0 065 0 058 0 065 0 098 0 121 0 145 0 169 0 179 0 186 0 233 P psi 0 0149 0 0130 0 0141 0 0120 0 0118 0 0105 0 0096 0 0080 0 0061 0 0054 0 0041 0 0037 0 0041 0 0062 0 0077 …