Chapter 7

# Barrel drilled

Take 15 minutes to prepare this exercise.

Then, if you lack ideas to begin, look at the given clue and start searching for the solution.

A detailed solution is then proposed to you.

If you have more questions, feel free to ask them on the forum.

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.

Data :

and .

## Question

At what rate (in liters per second) should you fill the barrel to succeed in the overflow ?

### Solution

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 :

Either :

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  :