Unsteady Drag Coefficient of a Falling Sphere in Water

概要

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The purpose of this study is to know differences between steady and unsteady drag coefficients of a sphere. Though we often have to estimate unsteady drag-forces acting on a moving obstacle, we are obliged to use the well-known steady drag coefficient for the first estimation because of lack of information about effects of unsteadiness on the drag coefficient. The usual way to take account of unsteadiness is an added mass. However, its application is restricted within the simple shape of an obstacle. We propose a way based on the equation of motion to obtain the unsteady drag coefficient. To confirm validity of the way, we measured and analyzed the motion of the falling sphere in water by using a high-speed camera and a motion capture method. The drag coefficients as a function of time were obtained by substituting measured values of velocity and acceleration into the equation of motion. The drag coefficient was 0.52 when the sphere attains the terminal velocity, being quite large at the beginning of motion. Comparing with the values obtained by the other previous studies, our result is reasonable.