Sample Pitot Calculation in Pi-Space

Let’s do a simple calculation to solve for velocity knowing pressure.  In Pi-Space, Energy is an area loss of a Pi-Shell.  Velocity is a diameter line change.

Pressure is an energy calculation and is therefore an area loss.

We use an imperial system example

Where we have PSI

Let’s take an example where the dynamic pressure is 1.040 lb/ft^2

Also the density of air is 0.002297 slug/ft^3

Using the classic formula, Using Mathematica

Sqrt[2∗(1.04)/(0.002297)] = 30.092 ft/s

Now let’s use the Pi-Space formula

This formula requires that we use the speed of light in feet per second

the speed of light = 983,571,056 foot per second

Sin[ArcCos[1 - (((1.04)/(0.002297))/(983571056^2))]]*983571056 = 29.3127

Now we can see this is not the same as the Classical Result.

The Pi-Space Theory maintains that this is a “more accurate” result than the classical approach.

The Classical Approach is just an approximation.

Let’s make Pi-Space match the Classical approach.

For the speed of light, we set it to 9835710 foot per  second (incorrect!) instead of 983571056 foot per second

Sin[ArcCos[1 - (((1.04)/(0.002297))/(9835710^2))]]*9835710 = 30.092

Therefore, the more accurate the speed of light calculation, the more accurate the Pitot Velocity result in the Pi-Space Theory and it diverges from the Classical Result.

Note: This would have to be proven/disproven by actual experimentation.  I do not have the equipment for this.

Here is a table showing the range of values which are approximate to one another.

Table[Sin[
   ArcCos[1 - (((psi)/(0.002297))/(983571056^2))]]*983571056, {psi, 1,
   30, 1}]

{29.3127, 41.4544, 50.7711, 58.6254, 65.5452, 71.8012, 77.5541, \
82.9088, 87.9381, 93.8464, 98.3178, 102.594, 106.7, 110.653, 114.47, \
118.163, 121.745, 125.224, 128.609, 131.907, 135.125, 138.268, \
141.341, 144.348, 147.295, 150.183, 153.017, 155.799, 159.209, \
161.885}




Table[Sqrt[2*(psi)/(0.002297)], {psi, 1, 30, 1}]

{29.5076, 41.7301, 51.1087, 59.0153, 65.9811, 72.2787, 78.0699, \
83.4602, 88.5229, 93.3114, 97.8658, 102.217, 106.391, 110.407, \
114.283, 118.031, 121.663, 125.19, 128.621, 131.962, 135.221, \
138.403, 141.514, 144.557, 147.538, 150.46, 153.326, 156.14, 158.904, \
161.62}