If i have a body of water say 1 m2 with no air and in a container with no absorbsion sat at 1 bar, what quantity of water is required to raise the pressure by one bar ? and is this linear ie 1 litre for 1 bar, 2 litres for 2 bar etc
or is there a "simple" formula for this ??
I believe quark answer covers what you are asking. Just look up density vs pressure data for water. Say at 2 bar the density is 1.001 vs 1.000 at 1 bar, it means you would need to add 0.001 cubic meter to raise the pressure from 1 to 2 bars. This assumes you are using a chamber that doesn't deform under pressure.
You do not mention exactly what use you intend to make of this information; however, I believe the following are from the “Pipe Line Rules of Thumb Handbook”:
In other words, in theory e.g. if you wanted to estimate how much a volume of 50 degF water would be reduced by pressure in e.g. say a sort of 64” diameter (see volumes contained at Table 17-4 page 17-12 of the web page at
, or metric pipe volumes from the “International” area of this site) unyielding “tank” 5,000 feet long already completely full of water, in bringing up the pressure from zero to 250 psi, that amount water would be roughly as follows (incidentally if you did a Google search e.g. with the key words ‘modulus of compressibility or bulk modulus of compressibility water’, I believe you would find in detail where these relationships come from); :
0.00000314x168.7 gal/ft x 5,000 ft x 250 psi = 662 gal (or the equivalent to the volume of about a four feet length of 64” pipe!)
However, in actuality I suspect at least some more water will most likely need to be pumped in to an actual pipeline, due to the fact that the water pumped in will also undergo a volume change through the pump, as previously mentioned there could be some water absorbed into linings, slight expansion of pipe walls due to Young’s modulus etc. effects, even slight movements of individual pipes in the ground, temperature changes during filling and testing processes, and as previously hinted the fact that some inevitable air will be in the pipeline (along with the water being pressurized), and that air might also be going into and/or out of solution, and will be even more affected volume-wise by temperature changes in particularly long duration tests etc. and according to gas laws etc.
I think it is e.g. for such reasons and others that well-known and long-standing pipeline testing standards (such as ANSI/AWWA C600) require that air be expelled from pipelines in filling and before testing, and they also provide for reasonable, small “make-up water allowances” etc. for such real world conditions (that may not have anything to do with water leakage). In summary, air in pipelines may or may not cause substantial negative (or for that matter positive, if it heats up!) fluctuations in test gauge needle positions, but I’ve heard many contractors over the years say that it sure can cause problems!! In cases where instability is encountered, I think locating/removing large air pockets and/or at least multiple pressurizations to diagnose what's going on, have been found to help on many occasions.
