Sea water at rest has uniform density and bulk modulus

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

Sea water at rest has uniform density

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

and bulk modulus

K = 2.3\ \mathrm{GPa}

. Take

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

and atmospheric pressure at the sea surface

p_0 = 1.013\times10^{5}\ \mathrm{Pa}

. ((a)) Find the absolute pressure at a depth

h = 40\ \mathrm{m}

. ((b)) A sample of sea water is carried from the surface down to that depth. Using

\Delta V/V \approx \Delta p/K

, estimate the fractional decrease in its volume. ((c)) A sealed, flexible bag holds a fixed mass of air, which stays at the same temperature as it is carried from the surface down to

40\ \mathrm{m}

. Find the ratio of its volume at

40\ \mathrm{m}

to its volume at the surface, and the bulk modulus of the air in the bag at that depth.

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