A question the internet answers badly
The Drain Doesn't Know North From South
Tour guides on the equator pour water into a basin and swear it turns one way to the north, the other way to the south, and stands still on the line. Earth's spin is real and the Coriolis effect is real — it steers every hurricane. But in your sink it is buried about 50,000× under the motion you left in the water by filling it. So the drain picks its direction from how you filled the basin, not from your latitude. Here are both true things, side by side — and the one famous lab where the hemisphere actually won.
1 · Where does Earth's spin start to win?
One number decides it: the Rossby number, Ro = U / (f·L) — how a flow's own speed U and size L compare to the Coriolis parameter f = 2Ω·sin(latitude). When Ro ≪ 1 the planet's spin governs the flow; when Ro ≫ 1 it's a rounding error. Drag the latitude and watch real systems slide across the line.
45° — f = 1.03×10⁻⁴ s⁻¹
A logarithmic Rossby-number line from 10⁻⁴ to 10⁵. The shaded band on the left (Ro ≤ 1) is where Earth's spin governs the flow. Hurricanes and ocean gyres sit inside it; sinks, bathtubs, even tornadoes sit thousands of times to the right. Lowering the latitude weakens Coriolis and slides every system rightward — at the equator it vanishes entirely, which is also why hurricanes never form on the line.
At a typical mid-latitude a bathroom sink sits near Ro ≈ 10⁴ — about 16,000× further from "the planet governs" than a hurricane, which hovers at Ro ≈ 0.6. Note where the tornado lands: also far to the right. A single tornado's spin direction isn't set by Coriolis either — it's set by the storm that birthed it.
2 · So why does your sink make a vortex?
Because of the swirl already in the water. Coriolis tugs the draining water with an acceleration of about 3×10⁻⁵ m/s². The vortex you actually see carries an acceleration near 1.8 m/s² — roughly 58,000× larger — and it's leftover motion from filling, jets, a tilted basin, a passing hand. To let the hemisphere win you have to remove that louder motion. Turn it down and see.
The two accelerations are the real recomputed figures; the spinning arrows are a schematic of which one is winning. Drag the swirl to zero (or press Settle) and the faint Coriolis bias finally takes over — counterclockwise in the north, clockwise in the south, exactly as the lab found.
3 · The exception that proves the rule was right
It can be done — but it takes a laboratory, not a bathroom. In 1962 Ascher Shapiro at MIT filled a flat, circular tank six feet across and six inches deep, covered it against draughts, and let it settle for a full day so every trace of filling-motion died away. He pulled the plug and the tank drained slowly through a ⅜-inch hole over about twenty minutes. For the first 12–15 minutes a tiny float held dead still. Then it began, almost imperceptibly, to turn counterclockwise — reaching about one revolution every three or four seconds. Three years later Lloyd Trefethen and colleagues repeated it in Sydney and the vortex came out clockwise. Same physics; the hemisphere only gets to decide once everything louder has been silenced.
The check — recomputed live, 15/15 green
- Earth's angular velocity Ω = 2π/86164 s = 7.292×10⁻⁵ rad/s; the Coriolis parameter f = 2Ω·sin(lat) vanishes exactly at the equator and flips sign across it — the source of the north/south reversal.
- Rossby numbers at 45°: bathroom sink ≈ 9,700, hurricane ≈ 0.58 — the sink is ~16,000× further from "Coriolis governs." Tornado ≈ 1,600, also far too high.
- Coriolis acceleration on draining sink-water ≈ 3.1×10⁻⁵ m/s² vs the visible vortex's ≈ 1.8 m/s² → ~58,000× buried.
- What it does not claim: that water is well-mixed by some other force, or that the lab effect is fake. The narrow, sturdy claim is only that your basin's direction is leftover motion, not the hemisphere.
Reproduce: node research/coriolis-drain/verify.mjs
Sources & honest apparatus
Ω, f, the Rossby numbers and the two accelerations are computed from first principles (sidereal day, latitude, representative size/speed for each system — those size/speed figures are order-of-magnitude representative values, chosen to be honest, not measurements of a specific storm). The lab facts are cited, not computed:
Shapiro, A. H. "Bath-Tub Vortex." Nature 196, 1080–1081 (1962). — the six-foot tank, 24-hour settle, ~20-minute drain, counterclockwise at MIT.
Trefethen, L. M.; Bilger, R. W.; Fink, P. T.; Luxton, R. E.; Tanner, R. I. "The Bath-Tub Vortex in the Southern Hemisphere." Nature 207, 1084–1085 (1965). — the Sydney replication, clockwise.
Uncertainty named: the exact Rossby cut-off where Coriolis "wins" is not a sharp edge at Ro = 1 but a band around order-1; the verdict bands here use that order-of-magnitude reading, not a false precision.