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Engineering
Mechanical Engineering
Leak from a container w/ a bellow and air bubble
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[QUOTE="snyper10x, post: 4854174, member: 521052"] Hey guys! I'm doing a project and having a tough time deriving the equations to model it (Matlab (ODE/PDE) or Excel (cell/dv/dt)). I would love some insight/help etc! To start off there's a sealed rigid container which has a bellow attached internally and a valve. The inside of the bellow has its own constant air pressure source. The bellow has a spring rate and can only extend in the x direction (diameter is constant). The container is full of water at an initial pressure and also contains an air bubble. The air bubble will always be a bubble (i.e. will never go into solution). The bellow starts with some deflection (in -x, compressed) from the initial water pressure. At t=0 the valve is opened so there is a leak out of the container. (m_dot_e) The leak causes a pressure drop in the fluid and the bubble and bellow expand to equalize pressure. I started this off as cell based modeling with just the container and a bubble, plotting pressure as a function of volume of water removed. That gave a characteristic isothermal p-v chart. Then I did the container with just the bellows, again plotting pressure as a function of volume of water removed. That gave a linear decrease in pressure (as the spring rate is linear) (I ensured the bellows never got to free state). Next I assumed it was differential between the volume of the bubble and volume of the bellows but wasn't able to derive them to where I could model it. I then tried to use 1st Law to get an analytical solution but appear to be stuck. Did start in the wrong place?! Thanks in advance for the help guys! Jason [/QUOTE]
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Leak from a container w/ a bellow and air bubble
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