The Size of Drops

The relation between the diameter of a tube and the weight of the drop which it delivers appears to have been first investigated by Tate, whose experiments led him to the conclusion that “other things being the same, the weight of a drop of liquid is proportional to the diameter of the tube in which it is formed.” Sufficient time must of course be allowed for the formation of the drops; otherwise no simple results can be expected. In Tate's experiments the period was never less than 40 seconds.

The magnitude of a drop delivered from a tube, even when the formation up to the phase of instability is infinitely slow, cannot be calculated à priori. The weight is sometimes equated to the product of the capillary tension (T) and the circumference of the tube (2πa), but with little justification. Even if the tension at the circumference of the tube acted vertically, and the whole of the liquid below this level passed into the drop, the calculation would still be vitiated by the assumption that the internal pressure at the level in question is atmospheric. It would be necessary to consider the curvatures of the fluid surface at the edge of attachment. If the surface could be treated as a cylindrical prolongation of the tube (radius a), the pressure would be T/a, and the resulting force acting downwards upon the drop would amount to one-half (πaT) of the direct upward pull of the tension along the circumference.