calculating the pressure generated in vessel walls by displaced substa

[paulpatrick]

Hi
I have a problem... My boss wants me to determine the pressure developed by lets say "fluid" leaving a vessel and being equalised by Atmosphere.
The vessel is like 4 metres tall with curved walls towards the bottom, the walls are curved outwards, and slope back in at the bottom. see image.approx 11 long. the area where atmosphere comes in is about a metre in cross section but may get smaller.
The liquid leaves through the bottom.
The atmosphere comes in through the top.
I know the time taken to empty the vessel.
The volume of fluid when the vessel is at capacity.

My boss wants to use fluid dynamics to solve it.
However the fluid is not fluid its made up of grain.
I can understand what he is trying to achieve, i.e pressure exerted on the wall of the vessel so he can determine if the deflection due to the dumping makes the wall deflect inwards...
The trouble is neither of us know how to do it. He is smart ... me I have not touched college maths like this in Donkey's years so I have to remind myself all about fluid theory etc.
I was thinking of either using bulk solids theory or just using Buckingham pie stuff to come up with an equation.
help or examples would be handy will be going through my fluids book looking for equivalent examples!

 

[MortenA]

Suggestion:

Assuming that you know the volume flow out of the vessel then assume that in order for the pressure in the vessel NOT to drop any further the inflow rate of air must be the same at the given dP.

The assume that the opening is an orifice and use std. formula for calculating flow trough an orifice. Be conservative at first (sharp edged etc) and then see what the result is. If this result does not pose a problem stop. If it is a problem try get a consultant?

Best regards

Morten