Calculating pressure drop from a pressure vessel leak

[fluxfire71]

THIS PROBLEM WAS MOVED FROM GENERAL PHYSICS TO THIS FORUM BECAUSE OF ITS HOMEWORK-LIKE NATURE. SO THERE IS NO TEMPLATE.

Pressure vessel has a electrical (coiled) furnace inside.

A pressure vessel @ 550 bar @ 500 C containing argon has its gas inlet pipe (1 inch ext Diameter) that has come loose and become exposed.

Temperature is not constant as the heat shield contains heat and heat loss by gas convection/conduction becomes inadequate as pressure is lost.

Calculate the maximum flow of argon through the hole.

What assumptions will i need to make? and what equations do i use?

Much apprecieated

Fluxfire :)

Edit:

Volume of argon is fixed
system is a closed prior to rupture

 

[Chestermiller]

Pressure vessel has a electrical (coiled) furnace inside.

A pressure vessel @ 550 bar @ 500 C containing argon has its gas inlet pipe (1 inch ext Diameter) that has come loose and become exposed.

Temperature is not constant as the heat shield contains heat and heat loss by gas convection/conduction becomes inadequate as pressure is lost.

Calculate the maximum flow of argon through the hole.

What assumptions will i need to make? and what equations do i use?

Much apprecieated

Fluxfire :)

Is this a homework problem?

Chet

 

[fluxfire71]

Is this a homework problem?

Chet

No problem at work, i have been out of university for a while and am unfamilliar with the theory now.

 

[berkeman]

No problem at work, i have been out of university for a while and am unfamilliar with the theory now.

You've been asked to do these calculations for a safety problem at work, but have no background in it? Sounds strange (and dangerous)...

 

[fluxfire71]

You've been asked to do these calculations for a safety problem at work, but have no background in it? Sounds strange (and dangerous)...

I'm a chemical engineer by trade its just a problem i have to have a look at since I am a newbie, everything is checked by senior engineers so fret not.

I think i will focus on using the choked flow formula (https://www.grc.nasa.gov/www/k-12/airplane/mflchk.html) i think this will give me an approximation as it doesn't seem to consider laminar/turbulent flow..your thoughts?

 

[Chestermiller]

When you say you want to "Calculate the maximum flow of argon through the hole.", do you mean you want to determine the total amount of argon that exits through the hole from start to finish, or do you mean that you want to determine the rate of argon loss through the hole as a function of time?

Chet

 

[fluxfire71]

When you say you want to "Calculate the maximum flow of argon through the hole.", do you mean you want to determine the total amount of argon that exits through the hole from start to finish, or do you mean that you want to determine the rate of argon loss through the hole as a function of time?

Chet

Hi Chet, that's right.. the rate of argon loss as a function of time. The purpose is to find out how long it would take for argon to leave the vessel and the drop in pressure. When the pressure in the vessel will equalise external surroundings i expect oxygen to diffuse into the vessel leading to oxidation.

- rate of argon loss as a function of time
- drop in pressure over time.

Much appreciated

Fluxfire

 

[Chestermiller]

Do you know the geometry and area of the exit hole?

Chet

 

[fluxfire71]

Assume the circle is smooth and perfect annulus
Radius = 30 mm
Diameter = 2 x r = 60 mm
Circumference = pi D = 189 mm
Are = 2 *pi* r = 2827 mm 2

I know in reality it won't be perfect in shape.

Cheers,

Hassan