Question

Estimate the speed of vertically falling raindrops from the following data. Radius of the drops = 0.02 cm, viscosity of air = 1.8 × 10−4 poise, g= 9.9 × 10 ms−2 and density of water = 1000 kg m−3.

Answer 1

$v=4.89\ m.s^{-1}$ speed of vertically falling raindrops

Explanation:

Given:

radius of the rain drop, $r=0.02\ cm$

viscosity of air, $\eta=1.8\times 10^{-4}\ poise$

density of water, $\rho=1\ g.cm^{-3}$

acceleration due to gravity, $g=9.9\ m.s^{-2}=990\ cm.s^{-2}$

The forces acting on a raindrop are:

• Downward weight

• upward buoyancy

• upward viscous force

Neglecting the buoyancy force since the density of air is very less, we balance the remaining forces:

$F_v=W$

$6\pi .\eta. r.v=m.g$

$6\times \pi \times (1.8\times 10^{-4})\times 0.02\times v=\frac{4}{3} \times \pi \times 0.02^3\times 1\times 990$

$v=488.89\ cm.s^{-1}$

$v=4.89\ m.s^{-1}$

TOPICS: viscous force, buoyancy, terminal velocity

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