The Answer is 42!!: More work with the Venturi Tube (Mark 4)

In order to test the latest venturi tube properly I have had to recalculate the areas of the different tube sections. I performed several calculations to find out the areas of the first and second sections of the tube.

2D Cross Section of the Venturi Tube Design (Mark 4)

The blue shaded area is a cylinder. The formula for calculating the cross sectional area of a cylinder is:

$Area(mm^{2})=\pi \cdot r^{2}\cdot l$

The area of the blue shaded section is therefore:

$Area(mm^{2})=\pi \cdot 13^{2}\cdot 26.1$

$Area(mm^{2})= 13859.0478$

Which in metres is 0.0138590478.

The area of the red shaded section is a conical frustrum. The formula for calculating the area of a conical frustrum is (really complicated!) :

$Area(mm^{2})=\pi \cdot \left ( r_1^{2} +r_2^{2} + (r_1+r_2)\cdot s \right )$

I used an online calculator:

https://www.calculatorsoup.com/calculators/geometry-solids/conicalfrustum.php

$Area(mm^{2})= 1898.6256693642$

Which in metres is 0.00189862567

The red and blue shaded areas combined make up A1:

$A_1(m^{2})= 0.0138590478 + 0.00189862567$

$A_1(m^{2})= 0.00328453045$

The grey shaded section is a cylinder. Its cross sectional area (A2) is therefore:

$A_2(mm^{2})= \pi \cdot 4.5^{2}\cdot 18$

$A_2(mm^{2})= 1145.259$

$A_2(m^{2})= 0.001145259$

We can now apply the formula for the venturi tube:

$Q = A_{1}.\sqrt{\frac{2}{\mu}.\frac{P_{1}-P_{2}}{(\frac{A_{1}}{A_{2}})^{2}-1}}= A_{2}.\sqrt{\frac{2}{\mu}.\frac{P_{1}-P_{2}}{1-(\frac{A_{2}}{A_{1}})^{2}}}$

We will of course just insert these values into the previously written arduino code.

One of the requirements for this project is to display real time graphs on a small graphical display. The display I intend to develop with has not arrived yet. In preparation I thought it would be a good idea to look at using Python and matplotlib.

I have been playing with Python and installed Python 3.8.2 and got it added to my path (Windows 10). I then installed the matplotlib (library for plotting graphs) and watched a few youtube videos and read some tutorials.

I need to create these graphs:

I have the data being delivered from the sensor so this should not be too difficult to achieve. Helpfully the graphs have scales and axes...

Many people have been requesting access to the 3D print design files:

Venturi Mark 4 Design Files

Well that is enough for now - Take care...Langster!

The Answer is 42!!

Sunday, 7 June 2020

More work with the Venturi Tube (Mark 4)

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