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### HARDWARE SET

COMPONENTS NEEDED:The hardware needed to complete this project can be bought as a PROJECT SET by clicking HERE.

### Operation

QUICK FACTS

• Wind speeds from 32 km/h (20mph) up to 97 km/h (60mph)
• Install it on the lateral mirror of any car.
• Design your own support and mount PITOT on to a bicycle (…speedy riders only)
• Uses water for pressure differential indication

HOW IT WORKS

PITOT consists of two concentric ducts that get pressurized at different values when air flows through and around them. The level of pressure on each duct is determined by the direction of entrance relative to the flow mainstream speed. In the high pressure duct, the entrance is perfectly aligned with the mainstream and sees the flow “impinging” at full speed.  In the low pressure duct, small entrances or taps are perpendicular to the flow and no impingement occurs. In reality, both ducts are made circular but here they somewhat square to guarantee an easy 3D printing without supports.

At the end of the ducts, high pressure and low pressure connection ports are provided for flexible hose K1-H7 to be pressure-fitted. The hoses are arranged into two parallel columns in a platform and connected to nozzles at the bottom joined by a U-bend. When filled with water, two parallel columns of the fluid sit side to side at the same level under static conditions. The column on the left is connected to the high or “total” pressure duct and the column on the right to the low or “static” pressure duct.

When the PITOT is sped through air (attached to a moving vehicle) the air pressure at the top of the left water column will be higher than on the right and a difference in column heights will be seen (left will have a lower level).  This difference indicates the exact difference in air pressure between the high and the low pressure duct.

The scale attached between the two water columns, is physically graded at different values of column level displacement. If one column level displacement is known (left in this case) then the value of the air pressure difference can be computed and so the speed of the flow (see LEARN section). Pre-computed values of speeds at equal intervals (ie: 30, 40, 50 mph…) are then printed at known displacement values. All there is left to do is to watch where the left column level is and get an instant reading of wind speed. Like a true pilot!

The PITOT can be attached to the lateral mirror of a car on the passenger side. It attaches through the tensioning of two O-Rings of ID=100 mm (K1-OR100) and two platforms mounted on the lips of the mirror at top and bottom. A third platform at the back of the mirror is provided with multiple grooves to hook the O-Rings from top and bottom at different length combinations making it possible to attach to most mirror sizes. Tension is achieved by the action of the nut pulling the carriage that slides in the dovetail  groove of the bottom platform.

The PITOT is provisioned with alignment features to change pitch, roll and yaw angles:

Yaw: align the PITOT to be parallel to the car direction and not perpendicular to the mirror. The bolt/nut inside the arched groove at the top platform helps lock it in place.

Pitch: use both bolts in the top mirror fixture (04-PITOT) to change the pitch angle and give the tube a streamlined orientation. Also, when mounted in a car, make sure the platform is aligned vertically as operation relies on alignment with gravity (see LEARN and also Mounting to a Bicycle).

Roll: when at rest, both columns of water must be of the same height. Adjust the platform angle if this is not the case.

The closer the PITOT remains aligned with the car direction, the closer the match between wind and ground speed. You must note that when mounting pitot onto a lateral mirror of a car, the driver’s visibility of other vehicles will be decreased. Operation IN traffic should be avoided!

MOUNTING TO A BICYCLE

As explained in the LEARN section, column displacement depends on the square root of the speed. At slow speeds, pressure differential can be quite small and the height difference between the columns of water barely noticeable. A normal cyclist will achieve speeds of 32km/h (20mph) on fast days, which would correspond to only 2.5 mm of water displacement. One way to get around this problem is to change the angle of the platform with respect to the vertical. For the exact height difference in the direction of gravity, a larger displacement of the columns will be needed. The static pressure side (right) of the PITOT is graded in angle increments of 15ᵒ. If set to 75ᵒ with respect to the horizontal, a 32 km/h (20mph) run would correspond to a column displacement of 9.5mm, which is a lot easier to read! Of course, and as you may have guessed it, a different scale would be needed. Do you think you could compute and make your own given the information you have here?

This figure helps to represent it

Another way to get around the problem would be to use a fluid lighter than water (why?). But here we won’t attempt that…

For a bike mount, you will need a support. It is our hope that you can design your own and apply all what you learn in here to take PITOT for a ride!

### LEARN ABOUT THE BERNOULLI'S PRINCIPLE

To understand the operational principles of a pitot tube, you need to be familiar with three variants of pressure: static, dynamic and stagnation (or total) pressure. Whereas our immediate thinking reduces the concept of pressure to “force per unit area”, in fluids, pressure is used to describe the amount of energy per unit volume that a flow has. The Pitot tube is a device that measures these variants to mechanically compute flow speed.

The static pressure describes the energy a fluid particle has to potentially flow. Air statically trapped within a balloon is under pressure exerted by the stretching walls of the balloon. It will flow as soon as the opening is released. Another way is to think of a water dam. A particle right at the bottom of the dam is under great pressure due to the weight of the column of water (and the atmosphere that sits on top). When the dam gate is opened, the particle will flow, trading slowly its static energy for dynamic motion. The deeper in the dam, the larger the static pressure and the stronger the flow to be expected. We can know the value of static pressure at any depth by computing the weight per unit area of the water column standing above, plus any other additional pressure (atmospheric in this case).

$P_{s} = P_{o} +\rho_{w}gh$
Ps = static pressure [Pa], Po = Pressure at water-air interface (usually atmospheric) [Pa], ρw = water density [kg/m3], g = Earth’s gravity acceleration [m/s2], h = depth of interest [m]

What about the atmospheric pressure Po? Is it also static? Yes, air particles are also subject to the pressure exerted by the weight of the atmosphere and its intensity depends on altitude.  From time to time, we see the transformation of this pressure into dynamic motion in the form of strong winds. Wind will flow from a zone of high static pressure to one where it is low due to weather and temperature. At sea level and at temperature of 15ᵒC, Po is constant and has the value of 101.3 MPa. At altitudes that airplanes fly at however, atmospheric pressure can be as low as Po =26 MPa

In a continuum of water (as well as air), static pressure is the same for any particles at the same depth (or altitude) regardless of how far apart they remain.

Dynamic pressure is the term used to quantify the amount of energy per unit volume a flow has due to its motion/velocity. To compute it, we need to know the fluid density and speed and relate them by the equation below. Unlike static pressure, there is no way to physically measure dynamic pressure (…in reality, we want to deduct the dynamic pressure of a flow and from this, compute its velocity)

$P_{d} = \tfrac{1}{2}\rho V^{2}$
Pd = dynamic pressure [Pa], ρ = density of the fuild in question [kg/m3], V = fluid velocity [m/s]

We conclude then, that in a fluid, pressure transformations from static to dynamic and vice versa may continually occur as the flow speeds up, slows down stops and flows again. An excellent solid body analogy is that of a pendulum where potential energy transforms back and forth into kinetic energy. In order to know the total energy or total pressure of the fluid at any point in time we must add instant values of static and dynamic pressures. Note that in the absence of any mechanisms leading the fluid to loss of its original amount of energy, the total pressure will remain constant. That is what Bernoulli (XVIII century) proposed through his famous equation, which in a simplified form can be written as:

$P_{t} = P_{s} + P_{d} = P_{o} + \tfrac{1}{2}\rho V^{2}=constant\,if\,no\,losses$
Pt = total pressure [Pa]

From the above equation it is easy to understand why total pressure is also called stagnation pressure. If we were to measure the static pressure of a stream of air flowing with a certain level of total pressure like in the equation above (static + dynamic) we would register different values: low values for when the flow has high speeds, high values for when it slows down. But what if it came to a complete stop? The value of the static pressure would be at its maximum and equal that of the total pressure (dynamic pressure is zero). Hence, all we need to do in order to know the total pressure of any given flow, is to stagnate it into a full stop and take static pressure readings.

Furthermore, if the total pressure value of a stream is known and the static pressure reading is known, the value of dynamic pressure can be determined by subtracting static pressure from total. This is what PITOT does and we use water to do it! Both ducts of the PITOT connect to parallel clear hoses that will be filled with water to the same level. The high pressure (or stagnation) duct connects to the hose on the left and the low (static) pressure duct to the hose on the right. We know we’ll be measuring stagnation pressure at the high pressure duct because the flow will enter the duct and come to a full stop when reaching the water inside the hose. In static conditions, two columns of water of equal height will rest side to side. During a run, the air pressure on top of each column will be different, producing a difference in column height that will yield the value of dynamic pressure:

$P_{d} = P_{t} - P_{d} = \rho_{w}g(2_{d})$
d = column displacement [mm]

Since both hoses are of equal diameter, the displacement of the water column level from the reference position will be equal and in the opposite direction. We only need to look for the downward displacement of the stagnation pressure hose to compute the difference in heights. With the mechanically determined value of the dynamic pressure, the velocity of the free air stream is computed by:

$\tfrac{1}{2}\rho_{a}V^{2}=P_{t}-P_{d}=\rho_{w}g(2d)\,\to\,V=\sqrt{\frac{2\cdot\rho_{w}g(2d)}{\rho_{a}}}$

Pw = water density = 999.97 [kg/m3] ρa = air density = 1.225 kg/m3

From the equation above, if a fluid less dense than water was to be employed for the column readings, we would notice that a larger difference in column heights would be produced for the same levels of flow dynamic pressure.The tables below show: i) the values of velocity for some common types of motion and ii) the corresponding stagnation column displacement d in mm:

Concept:mphKm/hm/s
Pace of average marathon runner7113
Approximate wind speed required by wind turbine15247
Fast bicycle ride20329
Car speed limit on a busy road304813
Maximum allowable car speed (UK)7011331
Cruise speed small jetliner580933259

It is important to understand how the grading is produced. The idea is to place marks from a reference point at different pre-computed values of displacement that correspond to round numbers of speed. In this case the chosen units have been mph and the scale has been marked from 30 to 70 at increments of 5 (see sheet 3 of the drawing).

Distance "d" from reference [mm][mph][km/h][m/s]
2.4620.031.98.9
5.5530.048.013.3
10.0040.264.417.9
15.5050.180.222.3
22.5060.469.626.8
30.2570.0112.031.1

It is worth noting, that at a bicycle’s velocity, the displacement is very small (2.46 mm) and most likely not to be noticed.  We can amplify the displacement by setting the platform at an angle with respect to the vertical. See this figure to understand

Table A is reproduced for a platform angle of 75 deg with respect to the vertical. This could perhaps be more readable while peddling hard on your bike!

V [mph]45°60°75°
20.02.143.494.949.54
30.05.565.575.585.63
40.210.0210.0210.0210.02
50.115.7315.7315.7315.73
60.423.4023.4023.4023.40
70.032.9632.9632.9632.96

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