Development and validation of mathematical modeling for terminal velocity of cantaloupe

Abstract Terminal velocity is an important factor, which is useful for designing different unit operations such as hydro transport and sorting of fruits. The current investigation is aimed to propose a new dimensionless model for terminal velocity of cantaloupe fruit. For this purpose, 30 fruits from three different varieties commonly known as Jana, Gerdabadi, and Shahabadi randomly were collected and, then, the physical properties, which may affect terminal velocity, were determined. On the basis of Buckingham theorem, six dimensionless groups were recognized and established to be used for dimensionless modeling of terminal velocity of cantaloupe fruit. Dependent pi‐term versus each independent pi‐term was drawn, and regression analysis was applied to draw the curves to produce linear equations, which can be used in the construction of the dimensionless model. In order to evaluate the obtained model, terminal velocity of six randomly selected fruits from each cantaloupe variety were measured and compared with the predicted terminal velocity values. A good agreement was achieved between the experimental and the predicted terminal velocities. Also, the coefficient of determination, mean bias error, and mean relative deviation of the comparison were calculated as 0.90, 7.9, and 10.35%, respectively. In this context, the obtained model can be used as an appropriate procedure for the prediction of terminal velocity of cantaloupe fruit as well as other similar fruits with good accuracy. Practical applications Development of a generalized dimensionless model describing terminal velocity of cantaloupe fruit as a function of various physical characteristics can be used in different units of food industries such as fruit compote preparation and juicer industries. It may also be used for the designation of sorting units and hydro transport of different fruits. In other words, the obtained model could be used to sketch unit operations, which involve some postharvesting activities for cantaloupe fruits.