Janssena

Janssena, a stone giant, guards a glowing bin of grain whose floor feels far less weight than the grain above it.

The Physics

In a tall column of water, pressure at the bottom keeps rising with depth. In a silo full of grain it does not. The grains push sideways on the walls, and friction with the walls carries part of the weight. Below a few silo diameters, the pressure at the bottom levels off. H. A. Janssen measured this with grain in model silos (“Versuche über Getreidedruck in Silozellen”, Zeitschrift des Vereines Deutscher Ingenieure 39, 1045, 1895).

p(z) = p_∞(1 − e^−z/λ), λ = R/(2μK)

• p(z): vertical pressure at depth z (Pa)
• p_∞: saturation pressure, ρgλ (Pa)
• z: depth below the grain surface (m)
• λ: saturation length (m)
• R: silo radius (m)
• μ: wall friction coefficient
• K: ratio of horizontal to vertical stress

This is why an hourglass flows at a nearly steady rate whatever its fill height, and why silos are designed for wall loads rather than for a hydrostatic floor load.

Honest caveat: The Janssen model assumes K is a constant and the friction is fully mobilised everywhere. Real silos, especially while being filled or emptied, can show sudden higher pressures.

On the sticker

Janssena, a stone giant, holds a glowing grain bin; the pressure curve itself is not drawn. Printed text: JANSSENA with the line p SATURATES. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.