Study of falling water drop in stagnant air

The objective of this work is to propose a mathematical expression for the instantaneous velocity of falling water droplets in air and traveled height versus time. In addition, changes in terminal velocity depending on terminal height are studied. For very small spherical drops, having very low Reynolds number and obeying Stokes law for the drag force, the instantaneous velocity u of the drop with time is a well-known result. From the expression of that speed, it is easy to get the drop height h versus time. By eliminating the time, the displacement h of the droplet as a function of the velocity u is obtained. In the present work, the latter was extended to larger drops. The values predicted by the mathematical equation obtained from the combination of theory and experiment (semi empirical equation) are compared with well known experimental data. The results show good agreement between the values predicted and the experimental data.