{"product_id":"janssena-silo-pressure","title":"Janssena – The Janssen Effect \/ Silo Pressure Saturates Physics Sticker","description":"\u003cp\u003eJanssena, a stone giant, guards a glowing bin of grain whose floor feels far less weight than the grain above it.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn 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).\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ep(z) = p\u003csub\u003e∞\u003c\/sub\u003e(1 − e\u003csup\u003e−z\/λ\u003c\/sup\u003e), λ = R\/(2μK)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ep(z): vertical pressure at depth z (Pa)\u003c\/li\u003e\n\u003cli\u003ep\u003csub\u003e∞\u003c\/sub\u003e: saturation pressure, ρgλ (Pa)\u003c\/li\u003e\n\u003cli\u003ez: depth below the grain surface (m)\u003c\/li\u003e\n\u003cli\u003eλ: saturation length (m)\u003c\/li\u003e\n\u003cli\u003eR: silo radius (m)\u003c\/li\u003e\n\u003cli\u003eμ: wall friction coefficient\u003c\/li\u003e\n\u003cli\u003eK: ratio of horizontal to vertical stress\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThis 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.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e 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.\u003c\/p\u003e\u003ch3\u003eOn the sticker\u003c\/h3\u003e\u003cp\u003eJanssena, a stone giant, holds a glowing grain bin; the pressure curve itself is not drawn. Printed text: \u003cstrong\u003eJANSSENA\u003c\/strong\u003e with the line \u003cstrong\u003ep SATURATES\u003c\/strong\u003e. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50964003258471,"sku":"13646733390686753444","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50964003291239,"sku":"18349300816672497031","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50964003324007,"sku":"88479958355741094851","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50964003356775,"sku":"31149168358270318792","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/13526934923732840832_1200.jpg?v=1793657918","url":"https:\/\/pixelatedphysics.com\/nl\/products\/janssena-silo-pressure","provider":"Pixelated Physics","version":"1.0","type":"link"}