A refreshing gusher

A lemonade vat is essentially a big cylinder that rests on its end with a spigot on the very bottom. One particular vat is a cylinder with radius \(0.1~\mbox{m}\) and a spigot of radius \(0.01~\mbox{m}\). Initially the lemonade is at a height of \(0.5~\mbox{m}\) in the vat. You then open the spigot. How long does it take for all the lemonade to flow out of the vat in seconds?

Details and Assumptions:

  • The vat is open to the air at the top.
  • The acceleration due to gravity is \(-9.8~\mbox{m/s}^2\).

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