All Problems

Hydrodynamics

Problem 1.339

A steel ball of diameter d=3.0 mmd=3.0 \mathrm{~mm} starts sinking with zero initial velocity in olive oil whose viscosity is η=0.90P\eta=0.90 \mathrm{P}. How soon after the beginning of motion will the velocity of the ball differ from the steady-state velocity by n=1.0%?n=1.0 \% ?

Reveal Answer
t=ρd218ηlnn=0.20 st=-\frac{\rho d^{2}}{18 \eta} \ln n=0.20 \mathrm{~s}