A small open container (blue) has water in it. I put this small container in a bigger, closed, no diffusion, no deformable container. I add an effervescence tablet in the big container. Small container is fixed in the bigger. I measure weight of all. I would like to understand how speed of pressure can do for equilibrate in real time the weight if I put effervescence tablet in water. The speed of pressure move like speed of sound: around 340 m/s in gas and around 1435 m/s in water. When bubbles move up, their volume increase (lower pressure at top than at bottom), so water move up, and add bubbles increase pressure at top of water, the speed of pressure must impact the result of Archimedes law because it's like a wave (very fast). Even weight is equilibrate with speed of sound in water (need to be verified), pressure in gas is not the same outside small container, the Archimedes law are around small container faster than everywhere in the big container (it's bigger). And the top surface of the big container is reached faster than bottom surface.
An example: the pressure due to the tablet change in 2 minutes of 100000 Pa. The speed of sound in gas is 340 m/s (if air). So for me the differential pressure is 100000/(2*60*340) = 2.45 Pa/m. The weight in gram is 2.45*1000/9.81 = 249 g per height per surface. If I want the difference of pressure of 0.1 m for a surface of 0.01 m², the weight change of 0.249 g. Gas inside big container can be the same of bubble (easier to resolve). Pressure increase speed of sound.
With height of gas = H = 0.1 m
Surface at contact = S = 0.01 m²
Speed of sound = V = 340 m/s
Gravity = g = 9.81 m/s²
Difference of pressure = P = 100000 Pa
Duration of bubbles = T = 120 s
This need to take a lot of parameters, but the position of the small container can be more at bottom than at top, this change the delay in one or other direction. How speed of pressure can give a zero force ?
