Tubbin

Meet Tubbin, a wide pipe who carries a gush while his thin friend manages only a drip.

When a thick liquid flows slowly through a narrow pipe, the layer touching the wall barely moves and the middle flows fastest. Viscosity, the liquid's internal friction, resists that sliding between layers. The pressure difference along the pipe is what keeps the liquid moving.

Poiseuille's law gives the flow rate as Q = πr⁴Δp/(8ηL). Water has η ≈ 1.0 × 10⁻³ Pa·s. Through a pipe 1 m long with a 1 mm radius and a pressure difference of 1,000 Pa, Q ≈ 3.9 × 10⁻⁷ m³/s, about 1.4 litres per hour.

The fourth power is the surprise. Double the radius and the flow goes up 16 times. Halve it and the flow drops to a sixteenth.

This is why slightly narrowed arteries matter so much. A small loss of radius forces the heart to push much harder to keep the same blood flowing.