First slide

Viscous flow/Laminar flow

Question

Neglecting the density of air, the terminal velocity obtained by a raindrop of radius 0.3 mm falling through the air of viscosity 1.8 x 10^-5 N/m² will be

Easy

A

10.9 m/s
B

8.3 m/s
C

9.2 m/s
D

7.6 m/s

Solution

The terminal velocity of the spherical raindrop of radius r is given by
$v_{t} = \frac{2 r^{2} (ρ - σ) g}{9 η}$
where $ρ$ is the density of water and $σ$ the density of air and $η$ is viscosity of air.
$Substituting r = 0.3 mm = 0.3 \times 10^{- 3} m, ρ = 10^{3} kg / m^{3}$
$g = 9.8 {ms}^{- 2} and η = 1.8 \times 10^{- 5} Ns / m^{2}$
Compared to water, we can neglect density of air.
$We get v_{t} = \frac{2 \times (0.3 \times 10^{- 3})^{2} \times 10^{3} \times 9.8}{9 \times 1.8 \times 10^{- 5}} = 10.9 m / s$

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