An oceanographic sonde is a sealed cylinder of length and diameter

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

An oceanographic sonde is a sealed cylinder of length

0.80\ \mathrm{m}

and diameter

0.12\ \mathrm{m}

. On deck it is calibrated by drawing sea-level air through a straight bore of diameter

0.15\ \mathrm{mm}

in its pressure port; the mean free path of sea-level air is

70\ \mathrm{nm}

. It is then lowered on a thin cable until it hangs fully submerged in sea water of density

1025\ \mathrm{kg\,m^{-3}}

. Take

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

, treat the sonde as a perfect cylinder and ignore the volume of the cable. Treat the continuum description as reliable when

Kn \le 0.01

, doubtful when

0.01 < Kn < 1

and failed when

Kn \ge 1

. ((a)) The sonde's length and the bore's diameter are both lengths you might use for the air drawn through the bore. Say which one sets the Knudsen number of that flow and why, estimate

Kn

, and say whether a continuum description of that flow is allowed. ((b)) Estimate the buoyant force on the fully submerged sonde.

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