A cubical box of wine has a small spout located in one of the bottom corners. When the box is full and placed on a level surface, opening the spout results in a flow of wine with a initial speed of $v_0$ (see figure). When the box is half empty, someone tilts it at $45^o $ so that the spout is at the lowest point (see figure). When the spout is opened the wine will flow out with a speed of
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According to Torricelli's Theorem velocity of efflux i.e. the velocity with which the liquid flows out of a hole is equal to $\sqrt{2 g h}$ where $h$ is the depth of the hole below the liquid surface.
Lets say side of the cube is $a,$ so we have
$v_{o}=\sqrt{2 g a}$
When cubical box is half empty, height of wine surface above the spout is half of the diagonal of the cube's face, i.e. $\frac{\sqrt{2} a}{2}=\frac{a}{\sqrt{2}}$
Now the speed of the wine from the spout is
$v^{\prime}=\sqrt{2 g\left(\frac{a}{\sqrt{2}}\right)}=\frac{v_{o}}{\sqrt[4]{2}}$
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