Terminal Velocity and Shape of Cloud and Precipitation Drops Aloft

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Abstract
The terminal velocity of cloud and precipitation size drops has been analyzed for three physically distinct flow regimes: 1) slip flow about a water drop treated as rigid sphere at negligible Reynolds numbers, 2) continuum flow past a water drop treated as a rigid sphere with a steady wake at low and intermediate Reynolds numbers, and 3) continuum flow around a non-circulating water drop of equilibrium shape with an unsteady wake at moderate to large Reynolds numbers. In the lower regime the effect of slip was given by the first-order Knudsen number correction to Stokes drag. In the middle regime a semiempirical drag relation for a rigid sphere was used to obtain a formula for the Reynolds number in terms of the Davies number. In the upper regime a correlation of wind tunnel measurements on falling drops was used in conjunction with sea level terminal velocities for raindrops to obtain a formula for the Reynolds number in terms of the Bond number and physical property number. The result for the u... Abstract The terminal velocity of cloud and precipitation size drops has been analyzed for three physically distinct flow regimes: 1) slip flow about a water drop treated as rigid sphere at negligible Reynolds numbers, 2) continuum flow past a water drop treated as a rigid sphere with a steady wake at low and intermediate Reynolds numbers, and 3) continuum flow around a non-circulating water drop of equilibrium shape with an unsteady wake at moderate to large Reynolds numbers. In the lower regime the effect of slip was given by the first-order Knudsen number correction to Stokes drag. In the middle regime a semiempirical drag relation for a rigid sphere was used to obtain a formula for the Reynolds number in terms of the Davies number. In the upper regime a correlation of wind tunnel measurements on falling drops was used in conjunction with sea level terminal velocities for raindrops to obtain a formula for the Reynolds number in terms of the Bond number and physical property number. The result for the u...

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