Bernoulli equation - pitot tubes

[yy205001]

Homework Statement

Homework Equations

P₁+pV₁²/2+pgh₁=P₂+pV₂²/2+pgh₂

The Attempt at a Solution

My thinking: since the pitot tubes measure the stagnation pressure (static + dynamics pressure) and the height of the tubes are the same. By Bernoulli's equation, the total pressure along a streamline is unchanged, therefore there is no pressure change between two tubes which gives h=0.

I just want to check is my thinking correct or not.
Thank you![/B]

 

[andrevdh]

The speed of the airflow at 2 will be higher than at 1 so that P₂ < P₁
so that h will be as indicated in the diagram - the water level higher
on the left than on the right.

 

[yy205001]

but isn't that P only the static pressure? But in this case we also have to include the dynamics pressure as well, so the total pressure
P+(p/2)V² stay the same everywhere on the streamline?

 

[andrevdh]

Bernoulli's equation describes fluid in motion so that P is the pressure in the fluid.
The pressure is transferred to the air and water in the manometer.
The 1/2 ρ v² term is the kinetic energy term of the equation
while the P term is the energy of the pressure (per unit volume of the fluid) and the
ρgh is the potential energy term of the equation.