Here it is in all it's splendour...if such a term can be used to describe it 😂
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| The newly printed Venturi Tube! |
It didn't print too badly although my printer has room for improvement! I may well tweak the settings and print another as one of the ports for the tubes broke off. The design may need improving anyway. It will work for now...
Here is a poor diagram for the venturi tube. For some inexplicable reason I cannot easily export 2D images with dimensions from Fusion 360.
In order to write the firmware and calculate the required values from the sensor measurements we need to calculate the volume of each of the shaded sections of the venturi tube and apply the Bernoulli Venturi formula:
An is the blue shaded area which is made up of three cylinders: A1, A2 and A3. The volume area of a cylinder is found by the following formula:
If we now use the dimensions from the diagram we have the following for the blue shaded area (An):
The area of the blue section (An) is 14547.5675 mm^2 or 0.01455 m^2
Lets calculate the volume of the green section (Am):
The area of the green section (Am) is 4432.305 mm^2 or 0.0044 m^2
Note: I used a value of 3.142 for Pi...
Lets now attempt to calculate Q, the volumetric flow rate. We will use a value of 320 for P1 and 200 for P2, The density of air (µ) at 20 °C is 1.204:
Applying the values calculated above:
This simplifies to:
Which finally gives:
Therefore Q is:
The volumetric flow rate of air (Q) in the blue section, with a pressure differential of 120 has been calculated to be 65702.79 mm^3/s or 0.0657 m^3/s.
Lets calculate the volumetric flow rate of air (Q) in the green section:
This simplifies to:
Which finally gives:
Therefore Q is:
The volumetric flow rate of air (Q) in the green section, with a pressure
differential of 120 has been calculated to be 65702.79 mm^3/s or 0.0657 m^3/s.
Thankfully the calculations match for the different sections - It means theoretically the operations performed were correct...
We can now calculate the velocity of flow using the formula:
Using the values calculated:
which calculates to:
The velocity of flow in the blue section with a pressure differential of 120 has been calculated to be 0.4516 metres / second.
If we repeat for the green section:
Using the values calculated:
which calculates to:
The velocity of flow in the green section with a pressure differential
of 120 has been calculated to be 14.82e^-9 metres / second.
We can check our results are correct by applying Bernoulli's formula:
If we apply the values we have calculated:
This simplifies to:
Which finally calculates to:
As the pressure differential was set to 120 and calculating back came to 119.94 I think we are close enough! With long decimal numbers and rounding there will always be some errors which creep in - I'm happy that our method is correct.
We can know turn this into some firmware. We needed to perform the calculations to obtain the volume of the blue section and the volume of the green section. These will be used as constants in our firmware along with the constants used for the density of air at 20 °C.
The more astute among my readers will notice that the venturi formula uses µ as the symbol for the density of air. This is incorrect and it should be ρ.
Please accept my notational errors but I haven't the will or patience to change the µ symbol to ρ....
Please also accept my apologies for the really long and possibly boring post...It had to be done to get to the firmware writing stage.
If anyone is curious as to how I have obtained the formulae used these are applications of the Venturi Equation. I wrote about this in my previous post:
In the next post I will write some firmware for the STM32 Blue Pill and connect up the differential air pressure sensor, 16 bit ADC and test the venturi tube...right now I need some sleep...
That's all for now - take care always - Langster!
Sorry for interrupting
ReplyDeleteI think that you made two mistakes the first one is that you used the volume formula to calculate the area (pi*r^2*l) and apply that answer to calculate areas An and Am. Unfortunately those values are not areas those are volumes which do nothing with Bernoulli equation.
In Bernoulli equation we use the area of the section that perpendicular to the flow and adjacent to the pressure sensor output which has to be in your example A2 = (pi*D^2)/4 = 3.14*20^2/4 and A4 = 3.14*15^2/4
Second thing is that the Venture design is not accurate. The Venture walls has to change gradually in the form of cone to decrease the hydraulic losses that occur when you change the area so you have to change the design
Another hint that you can print a better venture by printing it vertically the printer could handle that better
Thank you for commenting.
DeleteI partially agree with your comments. I can find no information that a venturi tube has to have gradually changing walls. I grant you they are often depicted this way but I cannot find any resource that says they must be. However I suspect they work better when this is the case and I will be redesigning the venturi tube shortly. I will update the post once I have gained more information.
What was printed did work, I was able to detect my breathing with a differential pressure sensor but not as efficiently as I had hoped...I accept the comment about the application of the equations. Using wikipedia as my resource two years without checking the application has come back to haunt me...I will update the post to reflect the correct formulae to prevent issue. I will also give you credit for your input.
If you have any resources on how to design a venturi tube please share them. I'm also interested in Lilly pneumotachs or fleishcman pneumotachs...particularly if you have any knowledge on how to design them...I can find little information on this.