Hello. This isnt a homework question. Where i work there is a gas leak in a nitrogen filled cable. I wanted to figure out how much gas was leaking. (Vaguely remember the gas laws from high school). Every 5 days it takes 9 bottles of G size (7200L volume at 16.3 mPa). Initial pressure is 2400 psi (about 16.3mpa) before the regulator but the bottles are changed when they read 500psi before the regulator. The regulator for the actual gas output is set at 1500psi. Am i correct in my understanding that the flow rate if averaged (and used from full to empty) is 9 liters per minute? 64800L (7200L x 9 bottles) divided by 5 days (12960L per day) divided by 24 hours (540L per hour) divided by 60 minutes. Is there a formula for determining volume left in the 9 bottles when they are swapped over when they reach 500psi to see how much gas has leaked, as well as the average rate per minute? I was thinking boyles law but the mass here is not constant as the mass decreases due to the gas leak so wasnt sure. Thanks

I doubt the volume of the cylinder is 7,200L at 16.5 mPa. More likely 7,200L at STP. Boyle's law is useful here, it indirectly says unlike solids and liquids you need to know two things about a gas to know how much of it there is. The exception is knowing the mass. The same applies to flow, you need to know the velocity and pressure to know how much gas is moving. Once you know that it's common to then normalise everything to Standard Temperature and Pressure (STP). So if you know the mass of nitrogen in the bottle when its full and empty you know how much was lost and you know the time it took for it to be lost. You can use the density to convert the mass back to volume at STP. With your problem as you only know the difference in pressure in the cylinder you probably have to assume the temperature was constant and you could assume 20degC. That's a pretty reasonable assumption as at human friendly temperature ranges there's not a significant impact on the figures.

Ok thanks ill try find a scale to see the mass of nitrogen lost. If 5 of the bottles are at one end and 4 are at the other end of the cable (the cable is kms long), would they lose pressure at the same rate per bottle or could you kind of figure out which side of the cable the leak is? (I.e. if One side has significantly lower pressure relative to the other side, assuming the 1 remaining bottle is considered). Its quite interesting thinking about actual physics and how it relates to an actual situation!

Kind of been there trying to find out how to calculate gas flow in a long thin tube. If the gas is moving slowly then it's relatively simple but if not good luck because you cannot ignore what happens with the gas at the boundary with the walls of the tube i.e. turbulence. There are a number of ways to find leaks in pipes or at least narrow down the area to be physically inspected. There's ultrasonic leak detection and adding a tracer gas. If this cable is buried then the former probably isn't going to work. Assuming the cable is in some form of conduit and there's pits every so often along the length then adding a tracer gas would enable the place where the leak is occurring could be narrowed down to between two pits. I'd go for mercaptan as the tracer. It's what's added to flammable gases so a leak is easily detected, it has an odour threshold of around 1 ppb. You only need your nose to detect it.