A cubical wine box has a tiny spout at one bottom corner. When full and standing flat on a level surface, opening the spout lets wine emerge with initial speed v0. Later, when the box is half empty, it is tilted by 45 deg so the spout becomes the lowest point. With the spout opened in this

Question

A cubical wine box has a tiny spout at one bottom corner. When full and standing flat on a level surface, opening the spout lets wine emerge with initial speed v0. Later, when the box is half empty, it is tilted by 45 deg so the spout becomes the lowest point. With the spout opened in this tilted position, the wine's exit speed is:

Accepted Answer

v0/sqrt(2). Torricelli gives v = sqrt(2*g*H). Full box: H = L, so v0 = sqrt(2*g*L). When half full and tilted 45 deg with the spout at the bottom corner, the wine (volume L³/2) forms a prism whose vertical height above the spout works out to L/2. Then v = sqrt(2*g*(L/2)) = sqrt(g*L) = v0/sqrt(2).

Solution

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