Beeminder Forum

Torricelli's Law: Calculus problem hidden in the last blog post

I have despaired of anyone noticing it in the hovertext of the image so I’m putting it here:

Torricelli’s Law says that if there’s a hole with radius r at the bottom of a vat then fluid flows out at a rate of

1/2\tau r^2\sqrt{2gh}

where g is 9.81 \text{m}/\text{s}^2 and h is the depth of the hole. If the vat is a cylinder with height H and radius R, how long does it take for the vat to drain?