passive pressure compensation: time to equalise
Posted: Thu May 07, 2015 2:53 am
Bit of a tricky one.....
I have a pressure sensitive underwater vessel (+/- 50kPa operating pressure), say 10L fixed air volume, connected to a pressure compensating bladder via a 2m long, 8mm dia hose (same depth as vessel). The bladder balances the internal pressure of the vessel to avoid it being crushed as it dives. Lets say the bladder has infinite volume & can adjust to a change in pressure instantaneously (take the bladder out of the equation, the vessel needs to equalise with the water depth via the hose). Standard smooth hose, no other obstructions. The depth of the vessel can be controlled, from 2m down to 100m.
I need to be able to perform two calculations;
a) if there was a sudden change of depth (eg 10m down to 15m), how long would it take to equalise
b) what is the constant rate of descent (or ascent) I can maintain without exceeding the limit of the vessel. I realise this could also change with depth, ie 10m to 15m would be a different velocity than 95m to 100m.
I see the application is similar to the 'discharge' calculator (fantastic web site by the way, please keep it up). The mass flow of air would degrade as the pressure gets closer to equalising (flow approaches zero as P1/P2 approaches 1). As its a differential relationship, I've tried iterating the results in excel, but without success. Please help!
I have a pressure sensitive underwater vessel (+/- 50kPa operating pressure), say 10L fixed air volume, connected to a pressure compensating bladder via a 2m long, 8mm dia hose (same depth as vessel). The bladder balances the internal pressure of the vessel to avoid it being crushed as it dives. Lets say the bladder has infinite volume & can adjust to a change in pressure instantaneously (take the bladder out of the equation, the vessel needs to equalise with the water depth via the hose). Standard smooth hose, no other obstructions. The depth of the vessel can be controlled, from 2m down to 100m.
I need to be able to perform two calculations;
a) if there was a sudden change of depth (eg 10m down to 15m), how long would it take to equalise
b) what is the constant rate of descent (or ascent) I can maintain without exceeding the limit of the vessel. I realise this could also change with depth, ie 10m to 15m would be a different velocity than 95m to 100m.
I see the application is similar to the 'discharge' calculator (fantastic web site by the way, please keep it up). The mass flow of air would degrade as the pressure gets closer to equalising (flow approaches zero as P1/P2 approaches 1). As its a differential relationship, I've tried iterating the results in excel, but without success. Please help!