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

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<jats:title>Abstract</jats:title><jats:p>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 <jats:italic>V = A</jats:italic> exp <jats:italic>bz</jats:italic> { 1 – exp [– (<jats:italic>d/a</jats:italic>)<jats:sup><jats:italic>n</jats:italic></jats:sup>]} 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 <jats:italic>V</jats:italic> (the terminal velocity) is measured in cm/sec, <jats:italic>z</jats:italic> (the height) in km and <jats:italic>d</jats:italic> (the drop diameter) in mm the values of the constants are as follows:— I.C.A.N. atmosphere Summer tropical atmosphere Range of <jats:italic>d</jats:italic> mm <jats:italic>A b a n A b a n</jats:italic> 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 <jats:italic>V = A d</jats:italic><jats:sup>2</jats:sup> exp <jats:italic>bz</jats:italic> where <jats:italic>A</jats:italic> is 3040 and 2840 in the I.C.A.N. and S.T. atmospheres respectively and <jats:italic>b</jats:italic> has the values 0.0191 and 0.0172 in these two atmospheres.</jats:p>

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