Calculating pressure drop from a pressure vessel leak

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Discussion Overview

The discussion revolves around calculating the maximum flow of argon from a pressure vessel that has experienced a leak due to a loose gas inlet pipe. Participants explore the implications of the leak on pressure and temperature, and the calculations required to determine the rate of argon loss over time.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant describes the scenario of a pressure vessel at 550 bar and 500 C containing argon, with a loose gas inlet pipe, and seeks to calculate the maximum flow of argon through the hole.
  • Another participant questions whether the problem is a homework assignment, indicating a concern about the context of the calculations.
  • A participant expresses uncertainty about their background in the theory and mentions being a chemical engineer tasked with the calculations for a safety problem.
  • One participant suggests focusing on the choked flow formula as a potential method for approximating the flow, noting it does not consider laminar or turbulent flow.
  • A participant seeks clarification on whether the goal is to determine the total amount of argon exiting the vessel or the rate of loss over time.
  • Another participant confirms the interest in determining the rate of argon loss as a function of time, emphasizing the need to understand how long it will take for the argon to leave the vessel and the resulting pressure drop.
  • One participant inquires about the geometry and area of the exit hole to aid in calculations.
  • A participant provides details about the geometry of the exit hole, including its radius and area, while acknowledging that the actual shape may not be perfect.

Areas of Agreement / Disagreement

Participants express varying levels of familiarity with the theoretical background required for the calculations. There is no consensus on the specific methods to be used, and multiple approaches are suggested, indicating an unresolved discussion regarding the best way to calculate the flow of argon.

Contextual Notes

Participants mention the need for assumptions regarding the flow characteristics and the geometry of the exit hole, which may affect the calculations. There is also an acknowledgment of the complexities involved in real-world applications versus idealized models.

fluxfire71
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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
 
Last edited by a moderator:
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fluxfire71 said:
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
 
Chestermiller said:
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.
 
fluxfire71 said:
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)...
 
berkeman said:
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?
 
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
 
Chestermiller said:
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
 
Do you know the geometry and area of the exit hole?

Chet
 
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
 

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