Volume Meassurement (Dry Method)

I still have to work more on this Project, sorry.

The biggest difficulties I see with the problem, as you mentioned are

  1. Making the container air-tight (which is an annoying problem), Do you have access to a decent machine shop where you can talk to someone about this? It might be more complicated than you think
  2. Adding a fixed amount of air. The basis for your measurement, similar to the 'wet' method, is there is a fixed and known amount of fluid entering the system. Then based on this known amount, the object inside the measurement then affects the fluid, in the case of water (non compressible) increasing the measured volume of the liquid, and in the case of air (compressible), it increases the pressure. This does however rely on a very accurate measurement of the amount of gas inside the container. I'm not an expert on this, but I've been working with gas flow controllers for a while now, and that seems like a very expensive thing.

However, in writing this, I had a thought:
Take 2 containers that have a valve in between each other, Both with known volumes, and a pressure sensor inside each (Or maybe not). One you can place an object whose volume is to be measured. Place the object in, and purge gas down to atmospheric pressure, and make sure the two are at equal pressure before sealing them off from each other. Now feed air into the one with the object. This will increase the pressure in the object's container by some amount. The amount is not important at the moment, but it will stabilize and equal something. Record it. Now open the valve between the two containers. The pressure in the two containers will equalize to some other value. What I believe (though I do not have good knowledge of fluid dynamics to be sure), is that depending on the size of the object in the first container, which will reduce the volume of the first container by some unknown amount, and by measuring the change in pressure between the two volumes (Container 1 - Object, and Container 1+2-Object), you should be able to calculate the volume of the object, because the amount of air inside the container did not change between the two volumes. Assuming that the temperature stays the same (This might be unreasonable), or by measuring it and including it in your calculations, wouldn't this be true?

Yes, making the container leak free has been really difficult. The main problem is the leaks change every time it is opened to place the sample inside. However, once the container is sealed and the test repeated, it looks the repeatability of the results is good (if temp does not changes significantly). I already checked a local machine shop with a proposed container to be built; but since my goal for now is to find if the method could be used, I have been delaying that.
The fixed amount of air looks a good assertion; but I'm using the air pressure drop in the vessel as an indirect method of finding the volume. The initial pressure from which deflation occurs is measured on every test. The time it takes to reach 36.7% of the initial value is recorded and the volume calculated. I have changed the initial pressure at which the container is filled and the time to reach 36.7% of the new initial Pr. appears to be about the same.
Another problem affecting the results is temp drift. The air volume required to reach the required initial Pr changes at different temps, and that affects the calculated volume. This is possible to solve (I think) and I have been trying to find the relationship between the measured volume and temp, (by also measuring the temp); but that has proven to be really difficult.
I don't know much about fluids dynamics either; but I wanted to test if this method could work.
I'm still working on this.

I've been thinking on the 2 containers method you suggested and seems very feasible too; but perhaps, I will have the same 2 problems again: containers leak and temp dependency of the amount of air entering the first container (the one with the object) and it will basically be the same thing; but I really don't know either??. So far, the results I've obtained with one container, apparently indicate the method is working; but I still have to solve these two problems, that I think are the reasons for (greater) inaccuracies, which only appear, once I open the container or the temp changes substantially. The results repeat, when temp is about the same and leaks are about the same, which I can observe by repeating the test over and over without opening the container.
Thanks.

This is a screen picture after one of my latest tests. The repeatability looks really good while the container is kept sealed and temp does not changes substantially. I definitely has to seek professional help to solve the container leaks problem; but that costs real $$$ and not just my personal time on this. Please beware I'm still working on this; but anyhow if you have any ideas, let me know.

Interesting project ... I do see some similarities when comparing this with the testing of diaphragm gas meters by using a bell prover (something I used to do many moons ago). With the bell prover, a measured volume of room temperature air at only 2 oz pressure is passed through the meter. A photo-electric sensor monitors the test dial and starts/stops the test, then the true volume delivered is read from the prover. In both cases here, measuring temperature and pressure with high precision and accuracy is important.

However, I think there is a problem with precision ... it could be mathematical, poor matching of sensor range to ADC range, or perhaps higher ADC resolution is required. If its mathematical, sometimes 6 digits of precision is needed in order to get several digits of precision in the results (you're using exponential equations).

From your data in reply#10;
Start Pressure (hPa) jumps from 134.41 to 134.16 and back, indicating 0.25 hPa resolution.
Pressure @ TC (hPa) has many readings the same ... they change by 0.05 or 0.10 hPa.
Its good to know how much these changes are affecting your volume calculations.
Also, in all calculations, try using at least 6 digits of precision.

Referring to the operation I can't find a convincing explanation for these 2 facts:

  • ...
    -The slight difference during the first half of deflation between the ideal exponential decay curve (pink) and the real pressure measured (top of the blue area). After that they are almost identical.

Perhaps the compressibility factor (Z) of air is playing a role here.

First of all, thanks for your interesting comments.

I do see some similarities when comparing this with the testing of diaphragm gas meters by using a bell prover

I’m trying to measure the volume of the object not the gas. I have no idea about these tests you are mentioning or the diaphragm gas meters; but I will search as it seems to be very interesting. If you have a link to a website, please post it.

In both cases here, measuring temperature and pressure with high precision and accuracy is important.

That's very true. My intention so far was just to test if this could work, high accuracy is not the goal yet. These are just preliminary tests and results. I'm using some good enough sensors (I guess) for this trial; but perhaps in a future stage of this, I will need to use better ones. I didn't want to go for expensive ones without making sure it could be done, find out practical problems and details by testing, writing the code and making a prototype.
I'm using:
-For Pressure Honeywell SSCDRNN250MGAA5 datasheet (Safety and Productivity Solutions | Honeywell)
-For temp LM35DZ (http://www.ti.com/lit/ds/symlink/lm35.pdf)
I chose this sensors mainly because of the simplicity of use and also because they are linear and should not introduce much problems other than constant errors which could be canceled by adding or subtracting a correction factor (if present). I placed means in the code for that. There could be small calibration issues and errors added as I don’t have precise standards to check; but they will be systematic and possible to cancel. I’m more interested in "behavior" of the physical variables at this point than their exact values. Later on it all needs precise adjustment and you are right about that.

However, I think there is a problem with precision ... it could be mathematical, poor matching of sensor range to ADC range, or perhaps higher ADC resolution is required.

That I don’t see very well; but I’ll check your suggestions carefully.
-I’m rounding the results just for display on the screen; but calculations are done without rounding with full floats before displaying the results. I’ll check anyway, there maybe some cases where its not. I though approximating 3 decimal digits was enough for display for now.
The AD conversion I’m using which includes averaging among other things, is resolving more than the 1024 normal steps the Arduino ADC can resolve (using it). I’ve been working on achieving this for a while now (you can check some of my previous Projects). That creates the 0.05hPa steps in the 0-250mbar range which will otherwise won’t be possible to achieve and constitute a very good observation from you which I haven’t noticed. Anyhow, the jumps and their differences in both cases (Start Pr and Pr@TC) are more because of other factors, I think. The fact that Arduino takes time to read the values and the code takes time to find the thresholds as there are other things that need to be done also (communication, etc). As example, deflation starts by time 20 000 milliseconds after the inflation is stopped at 150hPa (that’s what I set it for). Inflation is stopped by finding when the Pr surpasses that threshold and there is a small error involved there. Since time elapsed is the trigger, perhaps the resolution in the differentiation of time originated by the loop duration is creating the impression of the 0.25hPa. The loop duration is not fixed though, it depends on what needs to be done and that could be another factor. The 0.25hPa jumps you have observed, could be just this particular test. I have to observe if that repeats in others. On the other hand, Arduino finds the TC by looking for the Pr to drop to 36.7% of the initial value, then sends the value to the computer (the TC which is what I’m after and the Start Pr recorded). This is a true threshold comparison, different than the time elapsed triggering and the recording of the Start Pr and perhaps the reason for the diffrences in the resolutions you have observed in both cases (This could be more precise; but I don’t know???).

This is something I might need to try to improve as it adds uncertainty to the results; but honestly, I don’t think this is a major influential factor. The leaks and temp issues are, I guess. It will be good to be able to quantify how much uncertainty they add though, as you pointed out.

Also, much of the info such as Start Pr, Pr at TC is there as I placed all that from the very beginning of the Project trying to solve the exponential equation as you thought. They are still there in case any calculations are needed; but in reality I’m not using them in the calculations or solving the exponential equation to find the volume. To do that, I needed to precisely know the flow restrictor value I used, which is a constant in the equation. The restrictor is just an obstruction I placed inside the bleeding hose, which value I don’t know. I tried to calculate that and was difficult, so I opted for another more simple method. Since the container volume is a constant, the flow restrictor is a constant (assuming no leaks) and from the equivalences for a given volume there should be a Time “Constant” regardless of the initial Pr (as the TC concept suggests) the only factor affecting the TC (TC=R*C) is (C) the Volume of the container (affected by the volume of the object). In other words, the volume the air occupies. So I set up tests using fairly equal batteries as standards for which I measured the volume and presumed each of them equal. Ran the test with 0, 1, 2, 3, 4 and 5 batteries inside the container (each test 10 times) and then plotted expected Object Volume (determined by the batteries) vs. average TC measured in Excel, with the data being logged automatically. From there, I got an equation which relates Object Volume vs. TC which is fairly linear as expected.
Since the TC is the only factor I really need to have precisely measured, I concentrated on that and did not place much emphasis on the rest of the values (not needed). That’s probably why, you may have observed some precision problems; but they may not be affecting the results. Calculating the volume this way, gives much better results and accuracy than solving the exponential equation. This way any other factors influencing are contained in the equation by means of the TC. If the TC measurement is affected by anything constant (I'm aware of or not), the effect is present in the equation and effectively canceled. If trying to solve the exponential equation no other factor will be cancelled, unless I know about it and added it somehow to the calculations, if I can do that (probably not). Of course, all this procedure must be repeated precisely using a container and pneumatic system with zero leaks, real volume standards and at precise temperature. The repeatability should be improved considerably when all that and temp compensation are added. That’s why I think this is apparently working fine. I’m consistently obtaining excellent repeatability, like the one shown, given the container is not opened and temp. does not changes substantially (stays within about 1 Celsius). As you can see, I still have to work more on this to get there. Now is when $$$ is required.
Thanks.

Perhaps the compressibility factor (Z) of air is playing a role here.

Perhaps, yes. This could also be influencing. I've been thinking maybe its a combination of factors, some of which I have no idea about.

It is important to mention that Relative Humidity and Atmospheric Pr are not being measured at this time and RH in particular, could be influencing the results also. That is pending.

I think, the results so far prove this is possible and the method is valid, however fine tuning is required. To be honest, I can't continue from this point on with this by myself, as it is a matter of resources to build the container(s) and perform precise measurements and adjustments with precise standards I don't have access to. Perhaps, someone here has access to these things or maybe a University or Institution is willing to help with this as a research Project with real practical applications. Any help or suggestions will be much appreciated.

Thank you so much.

I’m trying to measure the volume of the object not the gas. I have no idea about these tests you are mentioning or the diaphragm gas meters; but I will search as it seems to be very interesting. If you have a link to a website, please post it.

Most all the same considerations are needed. In both cases we have temerature, pressure, flow and volume.

Some of the specifications and procedures are documented here(A, B, C) however, I wish I had kept my notes - it was pre-internet days.

Re: The compressibility factor (Z) of air - the curve is similar to the deviations you have found. It would only take some simple mathematics or use values from a look up table to correct for this.

That I don’t see very well; but I’ll check your suggestions carefully.
-I’m rounding the results just for display on the screen; but calculations are done without rounding with full floats before displaying the results. I’ll check anyway, there maybe some cases where its not. I though approximating 3 decimal digits was enough for display for now.

Approximating 3 decimal digits might be enough for the display, but its how the numbers are determined that can influence the effective precision in the results. Certain equations can have a precision reducing effect.
For example, P = I2R where I = 1A and R = 1 ohm and both have been measured with 5% precision (not accuracy).
At the low end, we would get P = (0.95)2*0.95 = 0.857 Watt
At the high end, we would get P = (1.05)2*1.05 = 1.157 Watt
So, using numbers with 5% precision here affects the results by more than 15%

As mentioned, using floats is good - I would make sure all partial calculations do not truncate valid information. For some statistical MADT calculations, 6 digits of precision is required, for the meter testing I've performed, 12-bit ADCs were used - higher precision was desired but not available at the time.

From your link to the sensor, its pressure range is 1 psi to 150 psi (60 mbar to 10 bar) (69 hPa to 10,342 hPa). The datasheet notes High resolution (min. 0.03 %FSS), so this represents 3.1 hPa resolution. Note you are only using this at the very low end (0.5-2 psi range). Would a different low-cost sensor be available, say within 0-10 psi range?

I'm not sure how you have pre-conditioned the signal levels into the 10-bit ADC. Perhaps resolution could be improved as follows. If ADC code 0 represents the lowest pressure you'll ever measure, say 40 hPa, and ADC code 1023 represents the highest pressure you'll ever measure, say 140 hpa, then the resolution becomes only 0.09765625 hPa per step. You may only need an op-amp or 2 to achieve this.

$$$ may not be required at this point yet ... there may be still room for low-cost or no-cost improvements.

EDIT:

The AD conversion I’m using which includes averaging among other things, is resolving more than the 1024 normal steps the Arduino ADC can resolve (using it). I’ve been working on achieving this for a while now (you can check some of my previous Projects). That creates the 0.05hPa steps in the 0-250mbar range which will otherwise won’t be possible to achieve and constitute a very good observation from you which I haven’t noticed.

Oops - missed this. If averaging (sensor resolution 3.1 hPa) among other things can get 0.05 hPa steps, then perhaps averaging readings with 0.098 hPa resolution could result in 0.01 hPa steps.

As example, deflation starts by time 20 000 milliseconds after the inflation is stopped at 150hPa (that’s what I set it for). Inflation is stopped by finding when the Pr surpasses that threshold and there is a small error involved there. Since time elapsed is the trigger, perhaps the resolution in the differentiation of time originated by the loop duration is creating the impression of the 0.25hPa.

Yes - possible. All time values should also be floats (numbers like 20 could be expressed as 20.0 in calculations)

Valve Timing:
If the solenoid valves have AC coils and if your using a zero-crossing type relay there could be +/- 8.3 ms timing variance (@60Hz AC), if the relays are phase-type, this would be improved. Anyhow, for any type of solenoid (AC or DC coil) there is its response time to activate or deactivate that might have to be considered if the solenoids are controlling the testing start/stop.

Volume determination:
I'm wondering if the object's volume could be determined by looking at just a portion of the decompression test. Then using certain pressure readings within a window of the test to be the trigger points. Say for example 120 hPa as a start trigger and 80 hPa as a stop trigger. That way, more time could be allowed after pressurizing, after the valve opens and before the valve closes. This could be done just by taking data from a more stabilized, but definite portion of the results to determine volume.

Leaking problem:
What if the pump just pre-charges a small tank to around 5 psi. Then the check valve (I think this is the leak source) is replaced with an on/off solenoid control valve (which is inherently leak-free). Another benefit would be air that is much more stabilized with temperature and humidity for performing the tests.

(just some random and perhaps crazy thoughts in case something was missed)

Most all the same considerations are needed. In both cases we have temerature, pressure, flow and volume.

I just did not know about this procedures you are mentioning and its really interesting to know about them. I'll make some time and check the links. Thanks.

Re: The compressibility factor (Z) of air - the curve is similar to the deviations you have found. It would only take some simple mathematics or use values from a look up table to correct for this.

I did not know about that either and that was the reason for my question. On the other hand, neither the graph nor the compensation is required to find the volume. That's why I did not put much effort on solving that. Thanks for that info also. (another subject to study)

Approximating 3 decimal digits might be enough for the display, but its how the numbers are determined that can influence the effective precision in the results. Certain equations can have a precision reducing effect.

That is absolutely true; but I'm not approximating until the results are send to the display. All calculations are done with the floats without any approximations. On the other hand, none of the results shown are used to calculate the volume with the only exception of the TC which is measured by Arduino and I did not placed any approximations in the Arduino code. In the Processing code, there aren't any approximations in calculating the volume either and its just a simple linear equation linking the TC and the volume as explained above. That's why such repeatability is obtained, which is way better than solving the exponential equation as there would be more measured variables involved, each of them contributing with errors to the results. If you try to solve the exponential equation with the values shown, there will be significant errors not corresponding to the volumes shown, because I did not do it that way. I realized that was a tough proposition. You can find the equation I used though, by simply plotting the Volumes vs. TCs values shown in Excel, (insert graph, add trend line-show equation in the options). I left the other values there because I wanted to calculate the Standard Deviations for them and observe "behavior" of those variables and also to help explain the method. Same as with the Graph; but none of that is really necessary. The screen is probably saturated with information an operator does not need and will just create confusion; but I need it for now, while I get this right.

From your link to the sensor, its pressure range is 1 psi to 150 psi (60 mbar to 10 bar) (69 hPa to 10,342 hPa). The datasheet notes High resolution (min. 0.03 %FSS), so this represents 3.1 hPa resolution.

1psi-150psi is the possible Full Scale Span (FSS) of the sensors in that Series (SSC). In other words, in that particular Series you can find sensors with FSS inside that range; but there are many different ones in there with different FSS and not all of them are 150psi FSS. The FSS for the one I'm using is 250mbar (250MG in the part number) and I believe (could be wrong though) from the table in page 2, that its resolution is 0.03% of its FSS, in this case = 0.075 mbar and not 3.1 hPa.

I'm not sure how you have pre-conditioned the signal levels into the 10-bit ADC. Perhaps resolution could be improved as follows. If ADC code 0 represents the lowest pressure you'll ever measure, say 40 hPa, and ADC code 1023 represents the highest pressure you'll ever measure, say 140 hpa, then the resolution becomes only 0.09765625 hPa per step. You may only need an op-amp or 2 to achieve this.

Perhaps there is another way. The sensor does not provide that output. It is a linear analog sensor providing a voltage output already amplified from certain value above 0V to a little less than 5V (I don't remember exactly; but its in the datasheet somewhere) therefore the range is not 1023 different steps in the ADC as it looks; but less. That output corresponds to Pr values from 0 mbar (referenced to the Atmosphere as it is a gauge sensor and not absolute) to its FSS in this case 250mbar. That's why I chose it, as it requires no additional electronics, just power and ready to go. On the other hand it is a high quality device (check the recommended applications in the datasheet)
Cont...

Continue...

$$$ may not be required at this point yet ... there may be still room for low-cost or no-cost improvements.

That is almost always true also. However, at this point I do certainly believe this has reached a plateau here with no further visible progress, unless real improvements are made, such as the leaks free container and temp compensation. Then I think, new findings will prompt new improvements. The reasoning for that is that I can't find ways of improving the repeatability in the volume calculations significantly more than what they are now. Perhaps its just me, not able to do it. One way or another, help is required though.

Oops - missed this. If averaging (sensor resolution 3.1 hPa) among other things can get 0.05 hPa steps, then perhaps averaging readings with 0.098 hPa resolution could result in 0.01 hPa steps.

The resolution of the 250mbar FSS sensor is not 3.1hPa as explained before and I was referring to the AD conversion process.
Please take a look at this: Glass Cockpit for Flight Simulator Game - YouTube
Arduino and its ADC are resolving 10000 different values to drive the Gauges in that video.

Yes - possible. All time values should also be floats (numbers like 20 could be expressed as 20.0 in calculations)

I did not do it like that, I used a long type variable and micros() to improve precision in the detection; but perhaps it can be improved by using interrupts. That's possible. However, the Standard Deviation as % of Avg for the TC is really low already (as shown in the picture). There is margin for improvements there, sure; but I don't think I can use floats for time??.

Valve Timing:

The solenoids are DC type and I’m driving them with transistors (way faster than relays), so there is a negligible delay in the switching. If you look, I extended the deflation time to decrease the error added by the valves response time among other things. In other words, a few ms delay for the valve to open, are almost negligible in 40000-50000 msec aprox range of the TC. The valves I’m using have a response time of 5-10ms@ 100 psi (probably lower at 250mbar) which represent 0.0125-0.025% of 40000ms (in the lower TC where the effect is greater). This is a very low added error and enough for now. Furthermore, since this error is almost constant it is probably cancelled by the way the volume is calculated.

Volume determination:

I think I tried that already long ago when I was solving the exponential equation; but there were not visible improvements, I think because of the fact that the valve commutation time is negligible and lower than the intrinsic error in finding the TC.
I tried even more, I calculated the area under the curve and also played with the slope of the curve with no improvements observed; on the contrary worst results.

Leaking problem:
What if the pump just pre-charges a small tank to around 5 psi. Then the check valve (I think this is the leak source) is replaced with an on/off solenoid control valve (which is inherently leak-free). Another benefit would be air that is much more stabilized with temperature and humidity for performing the tests.

Very possible, I already thought about that as you can see in reply #2. Actually that's what I'm doing on the video on reply#5 where I use a tank and everything is smoother there and more stable. The inflation is more precise than with the one piston compressor I'm using now. I did not implemented that because I had to either build it myself or buy one (which I have not found so far for such low pressures) and that was not really necessary for this proof of concept stage. This is another area where $$$ is required. Also, I reduced the error in the Start Pr by placing another flow restrictor in the inflation circuit as you can see in the schematic, right after the check valve. That slows down inflation and Arduino can detect the 150hPa more precisely. It also helps reduce leaks back to the compressor through the check valve (which may appear) and helps reduce the pulsation effects from the one piston compressor. I'm also driving the compressor with PWM to reduce the voltage and speed and therefore increase the inflation time. When I was testing that part I needed the Inflation time in the table to be able to compare as I adjusted things. That's why its still there. Furthermore, the concept of the TC suggests it is independent of the Start Pr.
There is more on this:
The Functions Generator I built was a consequence of this Project. I'm planning to use that to control a temp chamber where I can test temp dependency for this Project precisely; but to do that I need to correct the leaks problem first. Although I don't have the exact equation or certainty on this, preliminary observations suggest there is an almost linear dependency with temp. I want to test the whole thing inside a temp chamber to be able to find the temp dependency of everything combined which will produce a much more effective cancelation and allow to use this device in a wide range of temps. That's is pending.

Well really thanks for your interesting observations and comments.

I can see you really have this project well thought out. I tend to gloss over some things and miss some details ... I see now that you are using a 250mbar sensor. The 160mbar version's range is somewhat better suited, but I see there are 0 available at Digi-Key and minimum order is 20. The closest type available is this, but it may not provide enough benefit.

I'm not sure what types of containers you've already tested, but have you tried a pressure cooker? Might be easy to retrofit to your project and hopefully be leak free. However, I still believe the check-valve to be the main culprit, as its very susceptible and influenced by contamination and has very low pressure (less than 2 psi) trying to keep it closed.

Anyhow, good luck with your research and progress.

P.S. That video and also your Functions Generator is really incredible!

As an option you could push a fluid into the chamber. Keep your object out of the fluid of course, or use a separate tank to hold the fluid and connect it to the object's tank with a pipe. The advantage being that the fluid compresses less than air and can be moved into the chamber in a more precisely measurable amount if you used a syringe/hydraulic cylinder/etc.

A mason jar would make a cheap pressure container and you could add your air/wire connections through the replaceable lid. On a larger scale I'd suggest perusing larger jars used for storing dry goods (flour, rice, etc.) or even larger would be a five gallon bucket -- add your own silicone caulk gasket if needed.

As an option you could push a fluid into the chamber...

That is a brilliant solution!. I'll keep that in mind if the temp compensation does not work or proves to be really tough to achieve. Changing everything now can get pretty messy; but that is a real possibility. Thanks.
In regards to the container size, I placed means in the code to use (for now) at least 4 different container sizes to be able to achieve "ranging" and measure a wider range of object sizes. Making the container much bigger than 1000mL (for now) with the set up I have, is kind of out of the spectrum as it will increase the required inflation and deflation times too much. It could be done at any scale I think; but will required different scaled compressors, pipes, valves, etc, to accommodate for the higher flows needed to reduce the times. The purpose for now is to proof the concept at this scale. In my other Project (video on reply #5) the scale of the thing is much bigger as I'm using 100psi as the filling Pr.
There are multiple possible solution for the container (pressure chamber); but all of them cost real money. I have tried several cheap ones already and it has been a waste of money and time.
Really thanks.

(https://www.google.com/search?q=pressure+chamber&hl=en&qscrl=1&rlz=1T4TSNO_enUS463US463&biw=1366&bih=612&tbm=isch&imgil=TUB0CMyAvmlKoM%253A%253Bhttps%253A%252F%252Fencrypted-tbn0.gstatic.com%252Fimages%253Fq%253Dtbn%253AANd9GcQS_n9kBD0v0fN9rk7wG7coBpXQw_DfvbFSq7l-Oxnr1O5KwC9z%253B640%253B480%253Buxo0fz5kD4i_iM%253Bhttp%25253A%25252F%25252Fwww.smooth-on.com%25252FTools-Supplies-and%25252Fc1_1273%25252Findex.html&source=iu&usg=__Os61OAr2D-7kiNUDY3gSJ7DG8LU%3D&sa=X&ei=K8NoU6baO6zIsASBuYHgDQ&sqi=2&ved=0CEYQ9QEwAg#facrc=_&imgdii=e-g8Xp5XladNRM%3A%3BdfEvYTkKR8IlWM%3Be-g8Xp5XladNRM%3A&imgrc=e-g8Xp5XladNRM%253A%3Bq9Wsj_xxUD-qFM%3Bhttp%253A%252F%252Fpeople.timezone.com%252Fimg%252Farticles%252Farchives631703133992922740%252Fpress-chamb.jpeg%3Bhttp%253A%252F%252Fwww.timezone.com%252Flibrary%252Farchives%252Farchives631703133992922740%3B361%3B252

Also, if the thing is scaled up, to reduce the times the Pr needs to be increased and not all objects can be submitted to high pressures without damage. That will seriously limit the application scope of this. In reality, as very often the case in practice, there is no universal instrument capable of measuring at all ranges with the same accuracy. This will have to be adapted to particular cases, as required by the nature of the objects to be measured.

@dlloyd. Sorry, I missed your reply and only looked at the last one (Chagrin's one). Really sorry for that. I really appreciate your thoughts and suggestions and I know you were trying to sincerely help. I'lll carefully consider everything you've said and perhaps there is room for improvement with some of your thoughts about this. Discussion is always good and your points helped me explain better what I've have done here.
Thank you so much!!

Absolutely no problem ... I'll be watching here (and discussing) with great interest. After looking at your signature, I can see there's no room for failure! :wink:

Well, not so much though... That's and "idealistic statement" very hard to follow as humans and perhaps another reason why we all fail so often.

Hi:
I prepared a video showing how the results on the previous screen picture (of the same test) were obtained and others also.

Thanks.