A freshwater reservoir is open to the atmosphere

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 freshwater reservoir is open to the atmosphere. The water is at rest, of uniform density ρ=1000 kg m−3\rho = 1000\ \mathrm{kg\,m^{-3}}; take g=9.8 m s−2g = 9.8\ \mathrm{m\,s^{-2}} and atmospheric pressure at the free surface p0=1.013×105 Pap_0 = 1.013\times10^{5}\ \mathrm{Pa}. ((a)) Find the absolute pressure at a depth h=12 mh = 12\ \mathrm{m} below the free surface. ((b)) A stone of volume 2.5×10−3 m32.5\times10^{-3}\ \mathrm{m^{3}} is held completely submerged at that depth. Find the buoyant force on it. ((c)) At the same depth, imagine a small flat surface element whose unit normal is n=(0.6, 0.8, 0)\mathbf{n} = (0.6,\ 0.8,\ 0). Using the stress tensor of a fluid at rest, σij=−p δij\sigma_{ij} = -p\,\delta_{ij}, find the three components of the traction t(n)\mathbf{t}(\mathbf{n}) on that element.

Browse the problem library