Does an Air Bubble Impact the Accuracy of a Water Leveling Tool?

[recon]

"It is the practice of carpenters herabouts, when laying out and leveling up the foundations of relatively long buildings, to use a garden hose filled with water, with glass tubes 10 to 12 inches long thrust into the ends of the hose. The theory is that water, seeking a common level, will be the same height in both the tubes and thus effect a level. Now the question rises as to what happens if a bubble of air is left in the hose?"

Would important inaccuracies be caused?

http://img100.imageshack.us/img100/9878/airbubble9bg.jpg

There should be a relatively simple approach to it, but I just can't seem to figure it out. Any help would be much appreciated.

 

[DaveC426913]

What exactly is the problem you're having in solving this? The problem can be seen right in the diagram. Look at the close-up picture.

 

[recon]

Well, I think that the water level in the two opposite tubes will be different, because the volume of water in the two separate parts of the tube (separated by the air bubble) may be different.

 

[recon]

Someone please help. This is a Challenge Problem from a textbook, so it's not supposed to be too trivial. Or can someone point out something obvious that I've been missing? :(

 

[recon]

Since no one in the Introductory Physics forum can help me, can/should this be moved somewhere else?

 

[quark]

Which law we are using to compare the levels at both ends? Which other law we are using to nullify the redundant components of the first law?

 

[recon]

Which law we are using to compare the levels at both ends?

$$P = P_0 + h \rho g$$

Which other law we are using to nullify the redundant components of the first law?

I don't know...

 

[DaveC426913]

Simply put, the bubble will fight to reach the top of the gap whilet he water will fight to equalize. (Note that the water in the diagram cannot flow from one side to the other.) This will put unequal pressure on the opposite sides of the water column, and thus create inaccuracies in measurement.

 

[quark]

Yes, that is Bernoulli's principle.

The second one is Pascal's law. Does the compressible nature of air has anything to oppose it? Will the pressure be uniform in the horizontal section of the pipe?

 

[recon]

Simply put, the bubble will fight to reach the top of the gap whilet he water will fight to equalize. (Note that the water in the diagram cannot flow from one side to the other.) This will put unequal pressure on the opposite sides of the water column, and thus create inaccuracies in measurement.

I thought that the pressure that the air bubble exerts on both water columns was the same. Perhaps I misunderstand what you mean by unequal pressure.

Yes, that is Bernoulli's principle.

The second one is Pascal's law. Does the compressible nature of air has anything to oppose it? Will the pressure be uniform in the horizontal section of the pipe?

There is a height difference in the ends of each of the two water columns, so this provides the pressure to oppose the pressure in the air bubble. Which horizontal section of the hose do you mean? I think that the pressure in the air bubble is the same throughout.

 

[DaveC426913]

The air bubble fights to rise. To do so, it wants to slide one way or the other (in the diagram, that's to the right), pushing on the water column. This creates an artificial back pressure on the natural attempt of the water column to reach equilibrium.