Experiments on the drag coefficient of a sphere with a variable velocity

Abstract

The drag coefficient plays a dominant role in the particle motion. The main objective of the present study is to extract a mathematical correlation between the total drag coefficient and the particle motion parameters. To this end, the total drag coefficient of a sphere with a variable velocity in a water tank was studied experimentally using a high-speed camera. An expression was developed to simulate the correlation between the total drag coefficient, the Reynolds number, and the acceleration coefficient. Then the developed expression for calculating the total drag coefficient based on the Reynolds number was improved. Moreover, the correlation between the Froude number and the acceleration coefficient was analyzed and an expression was developed in this regard. A formula for calculating the total coefficient based on the Froude number was established. The obtained results show that the total drag coefficient has a complex change with an increasing Reynolds number at a determined acceleration coefficient. Furthermore, it is found that at a constant Reynolds number, the total drag coefficient decreases as the acceleration coefficient increases. The performed analyses demonstrated that the established expression based on the Froude number has high accuracy and low computational complexity. HIGHLIGHTS The total drag coefficient of a sphere with a variable velocity by analyzing the affecting forces on the sphere is calculated.; The correlation between the total drag coefficient and the particle motion parameters is investigated.; The established expression for calculating the total drag coefficient based on the Froude number has high accuracy and low computational complexity.;

Keywords

• drag coefficient
• drag force
• froude number
• reynolds number
• sphere
• variable velocity motion