A diver works in still sea water of uniform density

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 diver works in still sea water of uniform density ρ=1025 kg m−3\rho = 1025\ \mathrm{kg\,m^{-3}}. Take g=9.8 m s−2g = 9.8\ \mathrm{m\,s^{-2}} and atmospheric pressure at the sea surface p0=1.013×105 Pap_0 = 1.013\times10^{5}\ \mathrm{Pa}. The coordinate zz is measured upward. ((a)) Find the gauge pressure at a depth h=25 mh = 25\ \mathrm{m}. ((b)) The diver's air cylinder has an external volume of 1.2×10−2 m31.2\times10^{-2}\ \mathrm{m^{3}} and is completely submerged. Find the buoyant force on it. ((c)) At 25 m25\ \mathrm{m} depth the water is at rest, with stress tensor σij=−p δij\sigma_{ij} = -p\,\delta_{ij} and pp the absolute pressure there. Find the traction on a small horizontal surface element whose unit normal is n=z^\mathbf{n} = \hat{\mathbf{z}}, giving its zz-component.

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