Effect of air trapped under pressure transducer diaphragm

[Rob]

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

 

[Ken Smith]

[...]

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.

 

[William Hightower]

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.
http://www.math.montana.edu/frankw/ccp/before-calculus/function/boyle/body.htm
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.
http://www.aircertain.com

 

[Rich Grise]

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?

It will measure the pressure that's against the diaphragm, which will be
the pressure against all sides of the bubble, so, yeah, I suppose if it's
a real tall bubble, you'd get an error proportional to the height of the
bubble. Air is a fluid, right? And the pressure is equal on all sides of
its enclosure, right? So, calibrate the bubble, and you can compute the
correction factor.

Hope This Helps!
Rich

 

[Rob]

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

[...]

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.

Thought 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.

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

 

[Rob]

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

 

[Rob]

It will measure the pressure that's against the diaphragm, which will be
the pressure against all sides of the bubble, so, yeah, I suppose if it's
a real tall bubble, you'd get an error proportional to the height of the
bubble. Air is a fluid, right? And the pressure is equal on all sides of
its enclosure, right? So, calibrate the bubble, and you can compute the
correction factor.

Hope This Helps!
Rich

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

 

[[email protected]]

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

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.

 

[YD]

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

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.

 

[Rich Grise, but drunk]

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

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

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.

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

 

[Ken Smith]

hydrostatic pressure, giving an error. If the area and height below
the diaphragm are known this error can be calculated and corrected

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

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.

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