# Fluid Mechanics

# Double Pitot tube

Take 10 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.

Considering steady flow of a gas in a cylindrical pipe provided with a Double Pitot tube.

is the gas density and the density of the liquid filling the U-tube.

It will be recognized that the velocity of the gas has the same value at any point of a right cross section of the pipe.

## Question

Express the velocity and the volume flow rate of the pipe as a function of , , , and , the cross section of the pipe.

### Hint

### Solution

We neglect the difference in level between and .

The Bernoulli's equationbetween and gives : ( is a breakpoint)

Similarly, between and (same altitudes and speeds) :

We can deduce :

Far from the tube, the Bernoulli's theorem gives :

Finally :

In the U-tube, one can write :

Either :

Finally :