Exploring the Design of the Bourdon Gauge

[Nauhaie]

Hi all,

I am having some issues understanding the design of the Bourdon Gauge, used to measure primary vacuum. Here is how we were told it works:

http://xuneo.com/bourdon.png

A tube is closed on one side, and linked to the vacuum enclosure on the other. When pressure drops, each surface part receives some perpendicular force, which is proportional to the difference between the environment pressure and the enclosure pressure. Then, because of the tube's shape, the external part of the curve has more surface, thus receives more force than the inner part. Thus, the tubes gets more bent, and we measure this shift.

However, I do not agree with this theory. Indeed, if it were true, it would be very easy to create some incurved empty wire, which would, because of the outter surface being bigger, receive a non-zero resultant force, and we would have perpetual motion!

In fact, what I think is wrong is that we do not consider the force applied on the end of the wire, which, as far as I can see, exacly compensates the resultant force my teacher was talking about. And then we would have no motion at all, because the resultant force on the inner curve, outer curve AND end of the wire would be zero.

Am I getting something wrong? Or is this surface difference theory totally wrong?

Thank you for your help!

Nauhaie

PS: I do know that in fact, a Bourdon tube works with the section's geometry being changed by the pressure, but I would like to know if this other theory really is wrong!

 

[physical1]

Old post but good question.

What all the teachers, books, and websites fail to clearly explain is that the bourdon tube is just a special balloon.

The bourdon tube becomes larger in volume when pressure is applied inside. Flow occurs into the gauge tube. Volume is lost from what you were measuring - water, air, etc. Therefore it is not actually just measuring pressure alone, rather it is storing potential energy and volume. New volume moves into the tube, just as volume is lost from your lungs when you blow into a balloon. Not one website or book that I could find out of about 50 that I went over explained clearly that the most important factor in making the bourdon tube work is the significant volume change (for a tiny tube it is significant, and very visible through experiment). A lot of websites mislead people into thinking that the bourdon tube simply changes shape, not volume.

Therefore a bourdon tube works due to a change of volume (displacement) just as when you blow air into a balloon it moves outward.

If you had a curved balloon and you blew air into it, the balloon would elongate, expand, and straighten out, and finally try to turn into a sphere in order to naturally find the most efficient use of space - similar to how round water drops form instead of bent rectangles, zig zags, or squares. However the bourdon tube is a special balloon in that it has a memory of a general curved solid shape, whereas a balloon is far more flexible and tends not to retain a specific shape as metal does.

Under vacuum the bourdon tube loses volume and therefore contracts. When a curved thin metal tube is under vacuum the metal shrinks inward just like when a balloon contracts, and this causes movement. It is again due to volume change, not just shape.

 

[sir-pinski]

Hi Nauhaie,

Thank you for bringing up this interesting topic. The design of the Bourdon Gauge can be a bit confusing, but I believe your understanding of the surface difference theory is correct.

The Bourdon Gauge works on the principle of elastic deformation. When pressure is applied to the closed end of the tube, it causes the tube to deform, specifically in the curved section. This deformation is directly proportional to the pressure applied. The greater the pressure, the more the tube will deform.

The surface difference theory is not entirely wrong, but it is not the complete explanation for how the gauge works. The force applied on the end of the wire does indeed counteract the resultant force on the inner and outer curves, resulting in no motion. However, the key factor here is the elastic deformation of the tube. This deformation is what allows the gauge to accurately measure pressure.

In order to create perpetual motion, as you mentioned, the tube would need to be perfectly curved and the pressure applied would need to be constant. In reality, this is not the case. The tube is not perfectly curved, and the pressure being measured is constantly changing, thus preventing perpetual motion.

I hope this helps clarify the design and function of the Bourdon Gauge for you. Let me know if you have any further questions.