# I Minimum gas pressure to measure its volume with an eudiometer

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1. May 1, 2018

### Irl495

Hello,

As you can see in the attached hand drawing+calculation, my question concerns the typical method of evolved gas volume measurement by water displacement in an inverted graduated cylinder or "eudiometer". Once a bubble (cavity to be precise) of gas leaves the end of the tube through which it enters the inverted water column, a net buoyancy force easily carries it to the closed space at the top of the column, thereby displacing (pushing down) the water column by an amount Δh and increasing the pressure there by the amount ρwgΔh, where ρw is the water density. The open bath into which the bottom open end of the cylinder is submerged is exposed to atmospheric pressure patm.

Now, suppose the gas input tube terminates at a location in the water column exactly level with the free bath surface so that the water pressure there is pw,A=patm (see attachment if unclear).

My question: I'm looking for confirmation or correction in my thinking about the minimum gas input pressure required for bubbles to actually detach from the input tube so that they may rise to fill the space at the top of the column. According to "Laplace's law", the equilibrium pressure pi inside a single-walled "bubble" such as the gas cavities in this example, must be larger than the equilibrium pressure in the surrounding fluid, po, by the amount 2γ/R, where γ is the interfacial tension and R is the bubble radius. In the present system, I can therefore estimate a minimum required pressure of gas flow into the base of the water column (call it pg,A), below which gas bubbles will not detach from the end of the tube into the water, but will rather form a concave interface from the perspective of the water and remain in the tube: So for successful bubble detachment in this system, we require pg,A ≥ patm + 2γ/R. Is this correct, at least in the ideal case? In practice would mean that the tubing and vessels upstream of the inverted collection cylinder will be left with residual gas at non-zero pressure even after bubbling has ceased.

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2. May 7, 2018

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.