A spherical instrument package of diameter and mass hangs beneath a balloon at an…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Fluid statics and the continuum picture · Fluid statics and the continuum picture

Fluids and Continuum Physics, Ch The continuum hypothesis, pressure and the stress tensor

Problem

A spherical instrument package of diameter

0.30\ \mathrm{m}

and mass

2.0\ \mathrm{kg}

hangs beneath a balloon at an altitude of

35\ \mathrm{km}

. There the air density is about

8.2\times10^{-3}\ \mathrm{kg\,m^{-3}}

and the mean free path of the air molecules is about

8\ \mathrm{\mu m}

. Take

g = 9.8\ \mathrm{m\,s^{-2}}

and treat the air around the package as being at rest and of uniform density on the scale of the package. ((a)) Estimate the Knudsen number of the air around the package, using the package diameter as the macroscopic length, and say whether a continuum description of that air is admissible. ((b)) Estimate the buoyant force of the air on the package. ((c)) Estimate that force as a fraction of the package's weight, and comment on whether the buoyancy of the air matters for the package.

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