Week 3 - Pitot tube
A pitot tube is a flow measurement device used to measure fluid velocity. It is widely used to determine the air speed of an aircraft for instance and also useful to measure the velocities of air and gas in a certain flow field.
If fluid flows and we place a tube in its path, water raises to a certain height in that tube. This pressure of the fluid that has raised by a certain height is the static pressure.
Now if a pitot tube which is just as the shape in the given geometry is placed in the path of the fluid, the fluid is bought to rest at the stagnation point. Now the height which the water raises = static pressure + dynamic pressure
Stagnation pressure = static pressure + dynamic pressure
The stagnation point, velocity of the fluid is equal to zero and this is converted into the form of dynamic pressure of the fluid.
The solver setup in a brief manner:
1) Pressure based solver
2) Laminar and viscous
3) Inlet Velocity outlet pressure
|
Inlet Velocity |
Outlet gauge pressure |
|
240 |
-2817 |
|
100 |
33287 |
|
62 |
65780 |
The simple principle of bernoulis is applied to the pitot tube to obtain the velocity of the fluid at a particular point in the flow.
`P1 + (1/2)*rho*V1^2 + z1 = P2 + (1/2)*rho*V2^2 + z2`
where z1=z2 and V2 =0
On simplification, the velocity V1 = `sqrt((p1-p2)*2/rho)`
where `rho` is the density of the fluid
`V 1` is the flow velocity
Case 1:
For velocity = 240 m/s, gauge pressure = -2817 Pa
tube_walls-fff_total_measure_small_fluid_volume = 32305.022 Pa
tube_walls-fff_static_measure_big_fluid_volume = -3977.7444
V1 = `sqrt((p1-p2)*2/rho)` on substituting the above obtained pressure values, we get
V1 = 243.386 m/s
Case 2:
For velocity = 100 m/s, gauge pressure = 33287 Pa
tube_walls-fff_static_measure_big_fluid_volume = 33159.7 Pa
tube_walls-fff_total_measure_small_fluid_volume = 39451.265
On substituting the above pressure values we obtain V1 = 101.350 m/s
Case 3:
For velocity = 62 m/s, gauge pressure = 67580 Pa
tube_walls-fff_static_measure_big_fluid_volume = 67512.546
tube_walls-fff_total_measure_small_fluid_volume = 69940.765
V1 = 62.96 m/s
Contour of static pressure looked on a plane passing through the mid plane of the geometry
Contour of velocity looked on a plane passing through the mid plane of the geometry
It can be observed that the velocity reduces to zero at the point where the fluid strikes the pitot tube and hence static pressure at this point is the highest.