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A cylindrical barrel of radius and height is provided with holes.
At the altitude (from the base), the holes occupy a fraction of the wall of the barrel.
Water is a perfect incompressible fluid.
At what rate (in liters per second) should you fill the barrel to succeed in the overflow ?
It is assumed that the searched volume flow rate (that of an external valve) allows to maintain constant the height of the water in the barrel (at the value ).
By neglecting the speed of the free surface of the water, Bernoulli's theorem between the surface and a hole (at ) gives :
On the elementary lateral surface , the holes occupy the surface .
Therefore, the outgoing flow rate of all these holes is :
The searched flow rate must then be :
Either with :
Numerical Application gives about .