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GVSU EGR 365 - EGR365 Determining Drag from an Integrated Pressure Distribution

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Drag On a Cylinder from Integrated Pressure DistributionbyDan SchwarzSchool of EngineeringGrand Valley State UniversityEGR 365 – Fluid MechanicsSection 01Instructor: Dr. S. FleischmannJuly 3, 2007OutlineI. Purpose Statementa. The drag force on a cylinder was determined experimentally by integrating the surface pressure distribution.II. Backgrounda. 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.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.   LRdppFdragcos(1)c. The drag force can be non-dimesionalized to produce the drag coefficient described by Equation 2. See Appendix A for details. dCCpDcos2120(2)d. Experimental Methodi. 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.III. Results / Discussiona. 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 sideθ dF= PRdθ Flow Directionof 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 thecylinder 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(θ) 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(θ) to determine CD.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 detailsIV. Conclusionsa. The drag coefficient of the cylinder was experimentally determined form the approximate area under the Cpcos(θ) 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.V. Appendicesa. Appendix A – Develop an equation for the coefficient of dragi. Relate force to pressure. PdAPAFii. The drag force only acts perpendicular to the flow direction shown in Figure 1.   LRdppFdragcosiii. The drag coefficient is non-dimensionalized drag force.   2221cos21ULRdppUFCdragDiv. For an ideal flow the velocity is  sin2 UU. Substitute this into Bernoulli’s equation.      pCUppUppUUppUUppUpUp2222222222222sin4121sin4121sin221sin4212121sin421v. Substitute   pp into the drag coefficient equation.    dCULRdUCpDcos2121cossin412120222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.     0472.16.12219.03211621smoothAreaii. Approximate the area under the curve in Figure 3 for the rough side of the cylinder.     7854.016214.13216.1221roughAreac. Appendix C – Calculate the Reynolds number of the experimental systemi. Calculate the Reynolds number of the experimental system.5551034.111034.11034.1Re  Zd. Appendix D – Calculate U∞.i. Find an equation for velocity in terms of pressure difference.  2122122222122221211225.05.05.0PPVPPVVPPgzVPgzVPii. Calculate air density, ρ.   3333332002269.010940.117.117.1273229.28699000ftslugmkgftslugmkgmkgKKKkgJmNRTPRTPiii. Calculate  PP where the air flow comes to rest on the cyclinder.232.54.62121ftlbftlbfthPP iv. Find U∞.  sftftslugftlbUPPU1.6638.22.52232e. Appendix E – Spreadsheet CalculationsPosition Angle, θ (°) Manometer (in) P-P∞ (lb/ft2) Ideal CpMeasured Cp% Discrepancy Measured Cpcos(θ)0 0 1.00 5.35 1.00 1.03 2.9% 1.031 15 0.78 4.17 0.73 0.80 9.6% 0.782 30 0.02 0.11 0.00 0.02 - 0.023 45 -0.94 -5.03 -1.00 -0.97 3.3% -0.684 60 -1.72 -9.20 -2.00 -1.77 11.5% -0.885 75 -1.65 -8.83 -2.73 -1.70 37.9% -0.446 90 -1.60 -8.56 -3.00 -1.65 45.1% 0.007 105 -1.58 -8.45 -2.73 -1.63 40.5% 0.428 120 -1.60 -8.56 -2.00 -1.65 17.7% 0.829 135 -1.65 -8.83 -1.00 -1.70 69.8% 1.2010 150 -1.67 -8.93 0.00 -1.72 - 1.4911 165 -1.59 -8.51 0.73 -1.64 323.5% 1.5812 180 -1.53 -8.19 1.00 -1.57 257.4% 1.5713 195 -1.55 -8.29 0.73 -1.59 317.9% 1.5414 210 -1.60 -8.56 0.00 -1.65 - 1.4315 225 -1.55 -8.29 -1.00 -1.59 59.5% 1.1316 240 -1.50 -8.03 -2.00


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