Using the following data, estimate the speed of vertically falling raindrops: radius of the drops = 0.02 cm , viscosity of air = 1.8 10⁻⁴ poise , g = 10 m/s ^2 , and density of water = 1000 kg/m ^3 .

Step-by-step solution

The terminal velocity v_t of a spherical drop falling through a viscous medium is given by Stokes' law: v_t = 2 9 r^2 ( - ) g Given: Radius of the raindrop, r = 0.02 cm = 2 10⁻⁴ m Density of water, = 1000 kg/m ^3 Density of air, 0 (negligible compared to water) Viscosity of air, = 1.8 10⁻⁴ poise = 1.8 10⁻⁵ Pa s (since 1 poise = 0.1 Pa s ) Acceleration due to gravity, g = 10 m/s ^2 Substituting the values into the formula: v_t = 2 9 (2 10⁻⁴)^2 1000 10 1.8 10⁻⁵ v_t = 2 9 4 10⁻⁸ 10^4 1.8 10⁻⁵ v_t = 8 10⁻⁴ 16.2 10⁻⁵ v_