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Discussion: As shown in the result section, the drag force increases steadily with increasing wind speed. However, for high wind speeds with largest sphere, this is not true. There is a region that the sphere experiences a large drop of drag force. The drag coefficient remains relatively constant for most cases. However, when a Reynolds number reach about 300,000, and the sphere is the largest one; for this case, the drag coefficient drops abruptly. We also found that for the same wind speed, the larger sphere has larger Reynolds number. The figure below illustrates the relationship between Reynolds number and drag coefficient. The results obtained from this experiment also tend to show the same relationship.

Stoke’s Theory predicts that the drag coefficient decreases as the Reynolds Number less than 1000. However, in the truth, the decrease of drag coefficient is not as quickly as predicted by Stoke’s Theory due to turbulent and low pressure wake that formed on the rear of the sphere. There is a pressure difference between the back and front of the sphere because of the low pressure wake, and the pressure difference causes the most drag force in this region. For Reynolds number between 1000 and 100,000 the drag coefficient remains almost constant. This is because the wake on the rear of the sphere has now consumed the entire rear half of the sphere, and the pressure drop from the front to rear of the sphere is larger. At the Reynolds number of about 300000 the drag coefficient drops abruptly. This is because the turbulent wake consumes the front of the sphere and the pressure drop becomes smaller. When comparing the experimental drag coefficient and the theoretical drag coefficient. The smaller sphere had better accuracy, while the middles size sphere has slightly worse, and the largest size has the worst accuracy. This may be caused by the increases of the Reynolds Number, since higher Reynolds Numbers means more turbulence in the flow. Turbulence has a higher shear force at the boarders of the object than laminar flow does, which will increase the force observed on the object, producing higher drag coefficients. Although this experiment is pretty similar as the values predicted by, there are still errors in the drag coefficient. Those errors come from the uncertainty of the measurements from the pressure and temperature of the air, and drag force. The drag force was measured using a load cell measuring the force on the lever arm applied by the drag force of the sphere. What’s more, the assumption was made that the vibrations in the wind tunnel due to the fan are negligible to the readings from the load cell. Actually, the vibrations will affect the readings that specifically give a larger range of load values. The error of Reynolds Number will also introduce some errors in the result. The error of Reynolds Number mainly comes from the diameter of the sphere, dynamic pressure, and temperature. The surface of the sphere is also assumed perfectly smooth, however, the surface of the sphere is not perfectly smooth, and this will also affect the drag coefficient. To improve this experiment, we can isolate the fan from the wind tunnel to reduce vibrations, and thus, the readings will be more accurate.

Conclusion: Three spheres with difference sizes are put in the wind tunnel to perform this experiment with different air speed. By analyzing the data obtained from this experiment, it is found that drag forces increase with an increase in wind speed in general cases regardless of the size of the sphere. Larger sphere has more sensitive response than small sphere does. However, the largest sphere has large Reynolds number, that causes turbulent wake separation downstream from the sphere, and thus, there is an obvious drag force drop in this case. Finally, the experimental values have been compared to the theoretical values, although those two numbers are pretty close to each other, there are still some errors exist in this experiment.