Effect of air trapped under pressure transducer diaphragm

In article , Rob wrote: [...]

Making sure I understand the drawing:

The bubble of air is open at its bottom to the water, its top is blocked by the transducer and it is held from the sides by the tube leading into the transducer.

Is that right?

Thought experiment #1:

The "air" has no weight at all and the pressure at all points in the "air" is equal. Therfore the pressure in the "air" is equal to the water pressure at the depth where the air touches the water.

Though experiment #2:

The "air" has the same weight as water. The pressure in the "air" varies with depth at the same rate as it would in water. The pressure at the transducer is equal to the pressure in the water at the depth the transducer is.

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kensmith@rahul.net   forging knowledge

The air bubble will be at ambient pressure approximately 14.69595 psi (1 atmosphere) at sea level. When the pictured SENSOR is submersed in water The air bubble volume will decrease with depth. Water is for all practical purposes un-compressible. For every 32.8083 ft (10 meters) of depth the air bubble will half in volume due to compression. An object (in this case the air bubble) will displace the same volume of water as it's self. This displaced volume of water will be heaver than the volume of air that displaced it. That boyle's law in my words.

Therefore as the SENSOR is lowered into the water, the air bubble will start to compress. The water will be applying the same pressure to the air bubble as it applies to the sensor's diaphragm (even the top of the air bubble). The diaphragm will move with applied pressure, and the air bubble will compress. I have purposely negated the temperature effects from this discussion. Draw your own conclusions.

I hope this helps.

Best Regards,

William R. Hightower Jr. CEO Air Certain Inc.

"Rob" wrote in message news:43be7db9$0$15769$ snipped-for-privacy@per-qv1-newsreader-01.iinet.net.au...

A little OT - hydrostatic pressure sensors in environmental data logging.

We're trying to settle a difference of opinion... for a vertically oriented vented low pressure transducer immersed in water, what practical effect will entrapped air have on the measured pressure?

I've come across a few users that are of the opinion that the trapped air will change the indicated pressure. Typical application depths are 10 centimetres --> 20 metres, a vented gauge pressure sensor is usually used to eliminate atmos. pressure changes.

vent AIR || || \\/\\/\\/\\//\\/\\/\\/\\||/\\//\\/\\/\\//\\/\\/\\/ || WATER |------||------| | | | | | SENSOR | WATER | | | | |/\\/\\------/\\/\\| | air "bubble" | WATER

Theoretically it does not have any affect on the pressure/depth seen by the sensor. I imagine in some environments where there is rapid flow or vibration the trapped air may change the dynamic response of the sensor.

Any ideas / comments?

regards rob

Yes, indeed - read up on buoyancy by all means. The buoyant force on an object partially or completely immersed in a fluid is equal to the weight of fluid displaced (the NET buoyant force is the vector sum of the buoyant force and the weight of the object).

Since water is incompressible, the weight of fluid displaced is directly proportional to the volume of fluid displaced. Since air is compressible, the size of the bubble (=volume of fluid displaced) is governed by the gas law PV=nRT, where n, R and (for the sake of argument) T are constant.

As you descend, ambient pressure increases proportional to the specific gravity of the fluid through which you are descending and g. Since P is increasing as we descend, and PV=a constant, clearly volume is decreasing.

The deeper you go, the smaller the air bubble and the _smaller_ its buoyancy. This is why submarines (at least, some submarines) have to adjust the contents of their ballast tanks continuously during descent

- if you just flood enough to achieve neutral buoyancy at the surface, then you use the planes to descend, the displacement of the submarine will decrease as the vessel descends, and it will accelerate faster and faster towards the bottom.

The error in the OP's reading will therefore be worst at the surface, where the positive buoyancy of the bubble is greatest, and it can be calculated very accurately if the size of the bubble and the density of the water are known.

The OP could eliminate the error by inverting the measuring device so the bubble is not pressing on the diaphragm. This way the transducer will be measuring ambient pressure only, instead of ambient pressure + net buoyancy of bubble.

Hi Ken - your understanding of the arrangement is correct.

I think I agree with your point #1 - I tend to think of it as; the pressure results from the conditions above the point of measurement - ie the above column of fluid.

I like your #2.

regards rob

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Thanks William. All is clear. I would expect temperature would have no effect, as the air changes volume with temperature it would simply "displace" some of the water with all the other points you made remaining valid. regards rob

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Hi Rich - I read your reply last, I think it explains the pressure offset error.

The trapped bubble could be about 20mm diamter x say 2mm maximum tall with the sides and top of the bubble constrained by the sensor diaphragm and front recess wall. In effect the sensor will report a depth of d+2mm - the offset is pretty insignificant in the application in question.

Minimum depths are likely around 100mm, so its not a huge problem - sensors are sometimes used in sewage without compensating for a density change from water. I'm no expert on sewage but I imagine the density may change depending on the time of day, industrial waste discharges, Chilli Festivals etc. Maybe the errors from this factor compare with or exceed the air bubble offset error.

cheers rob

Air wants to rise, and the deeper it's entrapped the more it wants to rise. This means it exerts a force on the diaphragm that adds to the hydrostatic pressure, giving an error. If the area and height below the diaphragm are known this error can be calculated and corrected for. Read up on buoyancy in some physics text-book. Even better is to eliminate it completely if possible.

If you have a reasonably clean air supply handy you could use a bubbler tube and have the sensor on the topside out of harm's way. IME submerged sensors always give trouble and are a hassle to maintain.

- YD.

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Saving the best for last, of course! ;-D

I'd think if you're measuring something whose density could change dramatically, that the difference in the reading for the depth error would be accounted for by the fact that you're probably controlling your pumping system based on the pressure at the sensor - if there's more pressure, you have to pump harder, so denser stuff would be less deep but you'd move a controlled amount of material.

Hope this makes sense. ;-)

Good Luck! Rich

You don't need the area so long as it is not microscopic.

I've deployed a few hundreds submerged sensors and have had fewer problems with them than ones in aircraft or automotive environments.

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kensmith@rahul.net   forging knowledge