The Draining Honey Jar · AI Generator #GEN-7019BC90
Physics · fluid-mechanics
Problem
A cylindrical jar of honey with radius R=4.0cm and initial height H=12.0cm has a small circular hole of radius r=1.0mm drilled at the bottom. The honey has viscosity η=2.0Pa⋅s and density ρ=1400kg/m3. The hole extends through the bottom wall of thickness t=2.0mm.
As the honey drains through the hole, the flow rate decreases as the height decreases. Find the time required for the honey level to drop from the initial height H to half that height H/2. Assume the flow through the hole is governed by Poiseuille's law, and neglect any entrance/exit effects.