Why the straw gives up.

This is a fixed-flow model: it calculates the pressure needed to maintain the representative Q shown above, not the smaller flow a real person would achieve after reaching their pressure limit. The highlighted equation follows the current regime. The Hagen–Poiseuille equation covers laminar flow; water can cross into transition or turbulence, where the calculation uses Darcy–Weisbach with a smooth-pipe friction factor. Milkshake and honey remain laminar across the controls, but their results still assume Newtonian fluids with fixed representative viscosities; real mixtures can change viscosity with temperature, composition, and shear rate. Air uses the full one-dimensional isothermal momentum balance, p₁²−p₂²−2G²RT ln(p₁/p₂)=G²fLRT/D, solved numerically with the exit at atmospheric pressure. Results at Mach 0.3 or above are flagged because heat transfer and entrance details become more important. The mouth limits are rough estimates based on clinical maximal-mouth-pressure measurements, not a straw study; blowing and sucking have different limits. A suction-driven liquid cannot sustain a pressure drop of a full atmosphere: larger displayed values describe pressure that would have to be supplied by pushing from the source side. The gauge uses a log scale. This models horizontal, straight, smooth tubing; it omits gravity and local losses at entrances, bends, kinks, and taped joints. Those joint losses likely mattered more in Tim Vine's real chained-straw attempt than wall friction alone.