A settling pond is m deep and its water is perfectly still

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluids and Continuum Physics, Ch The Navier-Stokes equations and exact viscous solutions

Problem

A settling pond is 1.51.5 m deep and its water is perfectly still. Suspended in it are silt grains that may be modelled as smooth spheres of radius a=10a = 10 μ\mum and density ρs=2600\rho_s = 2600 kg m−3^{-3}. The water has μ=1.0×10−3\mu = 1.0\times10^{-3} Pa s and ρ=1000\rho = 1000 kg m−3^{-3}; take g=9.8g = 9.8 m s−2^{-2}. Assume the grains are small and slow enough that the Stokes drag law F=6πμaUF = 6\pi\mu a U holds, that each grain settles alone without disturbing its neighbours, and that the terminal velocity is reached almost at once. ((a)) Estimate the terminal settling velocity of a grain. ((b)) Estimate how long a grain released at the surface takes to reach the bottom.

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