Empirical formulae for the terminal velocity of water drops falling through the atmosphere

Abstract From a consideration of experimental measurements of the terminal velocity of water drops and of the drag coefficient of rigid spheres it is suggested that a formula of the type V = A exp bz 1 – exp – (d/a) n may be used to represent the terminal velocity of water drops which are larger than those to which Stokes's law is applicable and which are falling through a standard atmosphere. If V (the terminal velocity) is measured in cm/sec, z (the height) in km and d (the drop diameter) in mm the values of the constants are as follows: — I. C. A. N. atmosphere Summer tropical atmosphere Range of d mm A b a n A b a n 0. 3 to 6. 0 932 0. 0405 1. 77 1. 147 958 0. 0354 1. 77 1. 147 0. 05 to 0. 3 191 0. 0290 0. 316 1. 754 188 0. 0256 0. 304 1. 819 If the drops have diameter less than 0. 05 mm, Stokes's law is applicable and V = A d 2 exp bz where A is 3040 and 2840 in the I. C. A. N. and S. T. atmospheres respectively and b has the values 0. 0191 and 0. 0172 in these two atmospheres.