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Hagen–Poiseuille

Why the straw gives up.

Push a fluid through a tube and it fights back with viscous drag. Here's the equation behind that — and why one setup below famously failed on live TV.

ΔP = 8ηLQ πr4
10 m
Fluid η η ∝ ΔP
Length L L ∝ ΔP
0.1 mdouble L · double the effort10 m
Diameter r r⁻⁴ ∝ ΔP
1.5 mmhalve r · 16× the effort10 mm
Pressure needed
mouth limit
Try

The Hagen–Poiseuille equation describes slow, steady (laminar) flow through a round tube, where η is viscosity, L is length, r is inner radius (half the diameter set above), and Q is a fixed, representative flow rate. The scale's limits are rough estimates of what a person can sustain by mouth, not hard numbers. This models horizontal flow only — a straw held upright also fights gravity, and no amount of suction can lift water more than about 10 m, since that alone needs a full atmosphere of pressure difference. It's also the reason a long drinking straw is so much harder to use than a garden hose of similar length: on Taskmaster, comedian Tim Vine taped a chain of drinking straws together and couldn't blow a candle out through them, while a garden hose of the same length worked fine — try both presets above. Real chained drinking straws also kink at their joints, choking flow by a mechanism this equation doesn't capture, likely a bigger factor in Tim Vine's attempt than viscosity alone.