EGR 365 Lab 6bPerformed by: Lee C. GroenewegOutlineI. Purpose: To measure drag coefficient of a sphere as a function of Reynolds numberII. BackgroundA. Drag is Primarily form dragFv = ½  A CD V2B. Force balance on a sphere (Figure 1)C. Force balance equationFw - Fb = ½  A CD Vt2III. ProcedureA. Equation to determine drag coefficientB. Table of values used (data)IV. ResultsA. ExperimentalB. TheoreticalC. Propagated error assessmentV. ConclusionsBackgroundProcedureA. ResultsDrag Coefficient of a SphereEGR 365 Lab 6bPerformed by: Lee C. GroenewegProfessor: Dr. FleischmannOutlineI. Purpose: To measure drag coefficient of a sphere as a function of Reynolds numberII. BackgroundA. Drag is Primarily form drag Fv = ½  A CD V2B. Force balance on a sphere (Figure 1)C. Force balance equationFw - Fb = ½  A CD Vt2III.ProcedureA. Equation to determine drag coefficientCD = mg - gVol/(½ AVt2)B. Table of values used (data)IV. ResultsA. Experimental B. TheoreticalC. Propagated error assessmentV. ConclusionsPurposeTo measure the drag coefficient of a sphere as a function of Reynolds numberBackgroundWhen an object falls in a viscous fluid it experiences a gravity force, Fw, a buoyant force Fb, and a viscous drag force, Fv. The gravity force is constant and acts upwards, and the buoyant force is also constant and acts upwards. The viscous force acts against the direction of motion and is an increasing function of the speed of the object. The drag force is primarily form drag and can be written as:Fv = ½  A CD V2(1)Figure 1 shows a free body diagram that is used in determining the force balance on the sphereFigure 1. FBD for force balance on sphere.Considering a sphere that sinks in a viscous fluid (Fw > Fb), if it is released from rest it will accelerate until the viscous plus buoyant force balance the gravity force. At this pointa force balance yieldsFw - Fb = ½  A CD Vt2(2)If the weight of the sphere in the fluid is known, if the density of the fluid is known and the sphere dimensions are know, then the drag coefficient, CD, can be determined from the force balance. In this experiment the drag coefficient of the sphere was determined at terminal velocity. Staring with a force balance on the sphere it is possible to show that the velocity as a function of time with the initial condition being at rest is:V= (Fw - Fb)/½  A CD [(1-e-2t/m½  A CD (Fw - Fb))/(1+e-2t/m½  A CD (Fw – Fb) )] (3)The derivation for this equation is attached as Appendix A1ProcedureBefore any data could be collected, the path length to reach terminal velocity had to be determined. Using equation 4, assuming CD = 0.45, the path length could be estimated.L0.9Vt = (m ln 19)/( A CD) (4)Solving equation 2 for CD yields the following equation used to experimentally determine the drag coefficient, CD. CD = mg - gVol/(½ AVt2) (5)Table 1 contains the data values used to determine the CD for three differently weighted spheres. Mass Time (avg.) Length Diameter Area Volume density31.5 g 2.56 s 1.0414 m 37.35 mm 0.0011m22.75e-3 m31000 kg/m328.5 g 3.26 s 1.0414 m 37.35 mm 0.0011m22.75e-3 m31000 kg/m329.7 g 2.81 s 1.0414 m 37.35 mm 0.0011m22.75e-3 m31000 kg/m3Table 1. Data to calculate CD using equation 5.A. ResultsTable 2 contains the values for the drag coefficients using equation 5 and the Reynolds number, Re =VtD/.CD CD1 CD2 CD3Experimental 0.4522 0.210 0.311Theoretical 0.55 0.55 0.55Table 2. Experimental and Theoretical Values for CD.For this lab, since there were many measurable data values propagated error was introduced, and had to be calculated. The propagated error was found to be 0.88%. The calculation for the propagated error is found in Appendix A4.ConclusionsAs shown in Table 2 there is a discrepancy in the 2nd and 3rd values for the drag coefficient. It is worth noting that the initial entrance length was determined using a CD equal to 0.45, which is agreement for the first value of CD. There may have been some error in the data collection that may have propagated through the results, but with an errorpropagation calculated to be 0.889%, it may not have that large of an effect. Thetheoretical values may be off slightly since they were read from a log-log graph in the textbook, with a limited amount of readability and