The Draining Paint Bucket · AI Generator #GEN-8322BFE3

Physics · fluid-mechanics

Problem

A cylindrical paint bucket of radius

R = 15\;\text{cm}

has a small circular hole of radius

r = 2.0\;\text{mm}

drilled near the bottom. The bucket is initially filled with paint to a height

h_0 = 40\;\text{cm}

above the hole. The paint has density

\rho = 1200\;\text{kg/m}^3

and flows like an ideal fluid. As the paint drains through the hole, the height of paint in the bucket decreases over time. Find the time

t

required for the paint level to drop from the initial height

h_0

to half that height,

h_0/2

. Take

g = 10\;\text{m/s}^2