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GVSU EGR 365 - Drag Force on a Cylinder

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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 2006Introduction 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. 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. = 1/10 (pt-ps) Velocity profile of fluid Pitot-Static Tubes Cylinder (12” x 0.5”) Control Volume Uinfinity x y V(y)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. ∫−∞∞−=HHdyVULUD )1(222ρ (1) Where ρ 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: )5.0/(2AVDragCDρ= (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. µρ/)(ReVdd= (3) Where d is the diameter of the cylinder, and µ is the dynamic viscosity. Results& Discussion 0.005.0010.0015.0020.0025.0030.0035.0040.0045.000369121518Pitot)Static tube locationVelocity (ft/s)Low SpeedHigh Speed Figure 2: Velocity Profile for Wake of a Cylinder In Flow-Field of Different VelocityFigure 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. 0.002000.004000.006000.008000.0010000.0012000.0014000.0016000.0018000.0020000.006559.496597.515789.735293.164243.973536.643606.684744.905569.505875.50Reynold's Num berDrag Coefficient 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 h (in) P (psi) V (ft/s) CD Re Integral 0 0.086 0.0055 24.74 5239.74 6559.49 0.006801 1 0.075 0.0048 23.10 6008.24 6125.64 0.006780 2 0.087 0.0055 24.88 5179.52 6597.51 0.006803 3 0.071 0.0045 22.48 6346.73 5960.05 0.006771 4 0.067 0.0043 21.84 6725.64 5789.73 0.006760 5 0.063 0.0040 21.17 7152.66 5614.24 0.006748 6 0.056 0.0036 19.96 8046.75 5293.16 0.006724 7 0.048 0.0031 18.48 9387.87 4900.51 0.006687 8 0.036 0.0023 16.01 12517.16 4243.97 0.006600 9 0.027 0.0017 13.86 16689.55 3675.38 0.006485 10 0.025 0.0016 13.34 18024.72 3536.64 0.006448 11 0.025 0.0016 13.34 18024.72 3536.64 0.006448 12 0.026 0.0017 13.60 17331.46 3606.68 0.006467 13 0.036 0.0023 16.01 12517.16 4243.97 0.006600 14 0.045 0.0029 17.90 10013.73 4744.90 0.006669 15 0.055 0.0035 19.78 8193.05 5245.68 0.006720 16 0.062 0.0040 21.00 7268.03 5569.50 0.006745 17 0.067 0.0043 21.84 6725.64 5789.73 0.006760 18 0.069 0.0044 22.16 6530.69 5875.50 0.006766 0 0.085 0.0054 24.59 5301.39 6521.24 0.006799 Total Drag


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