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A drop of drizzle of radius 0.030 mm falls through air of viscosity 1.8 × 10⁻⁵ Pa s.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A drop of drizzle of radius $0.030\ \text{mm}$ falls through air of viscosity $1.8 \times 10^{-5}\ \text{Pa s}$ . Find its terminal speed, ignoring the air's buoyancy. How long would it take to fall $1.0\ \text{km}$ at that speed? ( $g = 9.8\ \text{m/s}^2$ .)

Need a reminder? The key ideaShow

Viscosity: the force to slide a plate of area $A$ at speed $v$ over a film of thickness $d$ is $F = \eta A\dfrac{v}{d}$ . Stokes' law: a small sphere feels $6\pi\eta rv$ , so it falls at a terminal speed $v_t = \dfrac{2r^2(\rho - \sigma)g}{9\eta}$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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