CYLINDER DRAGEGR 365 – FLUID MECHANICSPURPOSE:THEORY:APPARATUS:ITEMPROCEDURE:RESULTS:ANALYSIS:Using Equation 1, the drag force can be found:Using Equation 2, the drag coefficient can be found:CONCLUSION:Grand Valley State UniversityThe Padnos School of EngineeringCYLINDER DRAGEGR 365 – FLUID MECHANICSBrad Vander Veen June 10, 2003Lab PartnersJulie WatjerPURPOSE:The purpose of this exercise is to experimentally determine the drag on a cylinder in crossflow using a momentum balance in the wake of the cylinder.THEORY:Consider the diagram of the flow in Figure 1 below. Notice that the view is from directlyabove the cylinder.Figure 1 – Experimental SetupUsing the control volume shown above, it is possible to show that the total drag force on the cylinder is:HHVuLVD2221 (1)-where D is the drag force,  is the fluid density, L is the height of the cylinder, V is the undisturbed fluid velocity, u is the disturbed wake velocity, and –H to H is the width of the wake.This result can be put into non-dimensional form:HHVudLdVDCD222125.0 (2)-where CD is the drag coefficient, and d is the diameter of the cylinder.The flow speed can also be put into non-dimensional form:VddRe (3)-where Red is Reynolds Number, and  is the dynamic viscosity of the fluid.The undisturbed air velocity can be calculated using:25.0 Vppst (4)-where pt is the total pressure, ps is the static pressure, and V is the air velocity.APPARATUS:ITEM Wind Tunnel Pressure Measuring Device ManometerScalePROCEDURE:1). Assemble the experimental setup as seen in Figure 1.2). Place rake in the wake of the object.3). Turn wind tunnel on to desired speed.4). Measure and record the pressures in the wake at each rake tine.5). Measure total pressure in the wind tunnel at the entrance to test section and at the rakeRESULTS:tine distance from zero (ft) dynamic pressure (in of H2O) 0 0.000 1.081 0.008 0.922 0.015 0.903 0.023 0.884 0.030 0.825 0.038 0.756 0.045 0.667 0.053 0.578 0.060 0.419 0.068 0.3510 0.075 0.3311 0.083 0.3512 0.090 0.4213 0.098 0.5414 0.105 0.6715 0.113 0.7616 0.120 0.8317 0.128 0.8618 0.135 0.88Table 2 – Experiment ResultsANALYSIS:In Figure 3 below, the experimental results can be seen. This figure plots the undisturbedair velocity (in pink) and the disturbed wake velocity (in blue). The velocity was calculated using Equation 4 from the theory section in the lab report. Notice also the propagated error in yellow.Velocity vs. Position in Wake4.005.006.007.008.009.000.00 0.02 0.03 0.05 0.06 0.08 0.09 0.11 0.12 0.14distance (ft)Velocity (ft/s)Air VelocityConstant VelocityUpper ErrorLow er ErrorFigure 3 – Fluid VelocityFrom Figure 3 above, it is clear that the fluid velocity in the wake is much slower that theundisturbed air velocity. Notice that the fluid velocity is the slowest directly behind the cylinder, and that the fluid velocity on the edge of the wake is very close to the undisturbed fluid velocity.This data can also be shown in non-dimensional form, as seen below in Figure 4.Normalized Velocity vs. Position in Wake00.250.50.7511.250.00 0.02 0.03 0.05 0.06 0.08 0.09 0.11 0.12 0.14distance (ft)U^2/V^2Nomalized VelocityNormalized ConstantUpper ErrorLow er ErrorFigure 4 – Normalized Fluid VelocityNote from Equations 3 and 4, that the area between these two curves is directly proportional to the drag force and the drag coefficient.Using Riemann Sums between to approximate the area between the curves yields:ftftVuHH0048.00446.122It is also known that:300238.ftslugs L = 11 in V = 8.37 ft/s d = .5 inUsing Equation 1, the drag force can be found:lbflbfD 0008.00068.0 Using Equation 2, the drag coefficient can be found:23.014.2 CDUsing Equation 3, Reynolds number can be found:2220Re dCONCLUSION:In this lab, a round cylinder was placed in a wind tunnel. When fluid was forced past the cylinder, a wake was created behind it. This wake was experimentally measured and analyzed. The drag force on the cylinder was found to be 0.0068 lbf ± 0.0008 lbf. The drag coefficient was found to be 2.14 ± 0.23. Reynolds Number was found to be 2220, and since no measuring error is associated with Reynolds Number, there was no propagated