Physics unit 1

An engineer studies spherical beads settling in a deep, still liquid. The bead density is ρb, liquid density ρl, bead radius r, viscosity η and downward speed v. Weight minus buoyancy is (4πr³/3)(ρb−ρl)g. In the slow-flow regime, upward drag is 6πηrv. At terminal speed these forces balance. The regime is considered valid only when R = 2ρlrv/η < 1. All beads in the following measurements have the same density. In liquid L, the measured terminal speeds for radii r0, 2r0 and 3r0 are v0, 4v0 and 6v0 respectively. The measured R for the r0 bead is 0.10. Temperature and density are constant unless stated otherwise. Treat these measurements as exact for model comparison.