# Vessel Depressurization

#### mdvalhe

Hi,

I want to know how I calculate the mass flow rate, volumetric flow rate and time required to depressurize a vessel, knowing the pressure inside the vessel, the output pressure, the orifice and the gas characteristics.

For example, imagine a vessel full of compressed air (let’s say 10 bar, 10 m3), for any reason the vessel fail, a known orifice is formed (model for a crack, 10 mm diameter), how long will take for the pressure inside to equalize the atmospheric pressure.

Thank you

#### Mech_Engineer

Science Advisor
Gold Member
This problem is more dificult than you might think, due to several coupled properties. The gas is cooling, the pressure is changing, and it's likely the flow will transition from choked flow to free flow. If you describe the differential equations of the fluid flow accurately, you can probably solve it with a robust solver package. Otherwise, you'll have to go with some reasonable estimate based on empirically derived equations.

Here is a thread here on this exact subject which gives a few suggestions: https://www.physicsforums.com/showthread.php?t=341015

#### mugaliens

Hi,

I want to know how I calculate the mass flow rate, volumetric flow rate and time required to depressurize a vessel, knowing the pressure inside the vessel, the output pressure, the orifice and the gas characteristics.

For example, imagine a vessel full of compressed air (let’s say 10 bar, 10 m3), for any reason the vessel fail, a known orifice is formed (model for a crack, 10 mm diameter), how long will take for the pressure inside to equalize the atmospheric pressure.

Thank you
After the crack propogates and the vessel explosively decompresses...

...about half a second.

Seriously, "a crack" involves many orders of magnitude of variance, with answers ranging from between a few seconds to a few days. You're going to have to be more specific, and I'd recommend focussing on known geometries, such as a simple hole, or a tube of length L and diameter D protruding through the vessel wall.

#### Brian_C

As stated above, getting results for a crack isn't easy to do. You would have to calculate the crack opening displacements, then calculate the conductance based on the geometry and fluid dynamics.

I looked at the abstract of the paper titled "Circulation in Blowdown Flows," and they point out some interesting facts. Heat transfer between the gas and container walls creates a radial temperature gradient in the vessel, and buoyancy driven flow recirculates the gas. You're talking about stress analysis, fracture mechanics, thermodynamics, and CFD in one problem. I think you would need to do some heavy duty modelling with ANSYS or NASTRAN to get realistic results.

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