Acceleration length and time of falling spherical particles

Acceleration length and time are required for various aspects of system design. However, simple and accurate equations that can be used by designers are lacking. Therefore, in this study, we used previously conducted tests and the simple exponential model to describe particle velocity and acceleration and thereby calculate the acceleration length, which is the length required for a particle to achieve 99% of the terminal velocity. Results indicated that the acceleration length can be well described by a function of the Archimedes number, density ratio, and particle diameter. Several new tests were conducted to measure the particle velocity as a function of time. These tests confirmed the newly developed model that describes the particle location, velocity, and acceleration as functions of time. Based on the new model, the acceleration time was calculated and found to be well described by the acceleration length and terminal velocity.