One often hears the claim that water in a bathtub or basin swirls down a drain clockwise

Question:

One often hears the claim that water in a bathtub or basin swirls down a drain clockwise in the northern hemisphere and counterclockwise in the southern hemisphere. In fact, on YouTube you are likely to find video demonstrations of this (e.g., by searching on “water down drain at equator”). Show that for Earth-rotation centrifugal forces to produce this effect, it is necessary that the water in the basin initially be moving with a speed smaller than

Here Ω_⊕ is Earth’s rotational angular velocity,Ω_* is its vertical component (Box 14.5), R_⊕ is Earth’s radius, a is the radius of the basin, and ℓ is the distance of the basin from the equator. Even for a basin in Europe or North America, this maximum speed is ∼3mm min⁻¹ for a 1-m-diameter basin—exceedingly difficult to achieve. Therefore, the residual initial motion of the water in any such basin will control the direction in which the water swirls down the drain. There is effectively no difference between northern and southern hemispheres.