A Semi-Empirical Determination of the Shape of Cloud and Rain Drops

Abstract

A physical model which predicts the shape of water drops falling at terminal velocity in air is presented. The model is based on a balance of the forces which act on a drop falling under gravity in a viscous medium. The model was evaluated by numerical techniques and the shape of water drops of radii between 170 and 4000 μ (equivalent to Reynolds numbers between 30 and 4900) was determined. The results of our investigation show that the drop shapes predicted by the model agree well with those experimentally observed in our wind tunnel. Both theory and experiment demonstrate that: 1) drops with radii ≲170 μ are very slightly deformed and can be considered spherical, 2) the shape of drops between about 170 and 500 μ can be closely approximated by an oblate spheroid, 3) drops between about 500 and 2000 μ are deformed into an asymmetric oblate spheroid with an increasingly pronounced flat base, and 4) drops ≳2000 μ develop a concave depression in the base which is more pronounced for larger drop sizes. The relevance of these findings to the process of drop breakup is discussed.