Calculating pressure drop from a pressure vessel leak

In summary, a pressure vessel containing argon at high pressure and temperature has a gas inlet pipe that has become exposed, causing heat loss and a decrease in pressure. The task is to calculate the maximum flow of argon through the hole and determine the rate of argon loss as a function of time. Assumptions need to be made and the choked flow formula may be used. The goal is to find out how long it will take for the pressure to equalize with the external surroundings and the potential for oxygen diffusion and oxidation. The exit hole has a radius of 30 mm and area of 2827 mm2, although it may not be perfect in shape. This is a safety problem at work for which the calculations will be checked
  • #1
fluxfire71
7
0
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
 
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  • #2
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
 
  • #3
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.
 
  • #4
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)...
 
  • #5
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?
 
  • #6
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
 
  • #7
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
 
  • #8
Do you know the geometry and area of the exit hole?

Chet
 
  • #9
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
 

1. How do you calculate the pressure drop from a pressure vessel leak?

The pressure drop from a pressure vessel leak can be calculated using the following formula: Pressure Drop = (Leak Rate x Time) / Vessel Volume. This formula takes into account the rate at which the pressure is leaking, the length of time it has been leaking, and the total volume of the vessel.

2. What is the leak rate and how do you determine it?

The leak rate is the amount of pressure that is escaping from the vessel per unit of time. It can be determined by measuring the change in pressure over a given period of time. The difference in pressure between the starting and ending point, divided by the time elapsed, will give you the leak rate.

3. Can pressure drop calculations be used for any type of pressure vessel leak?

Yes, pressure drop calculations can be used for any type of pressure vessel leak, whether it is a small or large leak. The calculations will give you an estimate of the pressure drop, but it is important to note that the actual pressure drop may vary depending on the specific conditions of the leak.

4. What factors can affect the accuracy of pressure drop calculations?

There are several factors that can affect the accuracy of pressure drop calculations, including the type of gas or fluid in the vessel, the size and location of the leak, and the temperature and pressure of the vessel. Additionally, the assumptions made in the calculation may also impact the accuracy.

5. Are there any safety precautions that should be taken when calculating pressure drop from a pressure vessel leak?

Yes, it is important to take proper safety precautions when calculating pressure drop from a pressure vessel leak. This may include wearing protective gear, working in a well-ventilated area, and following safety protocols for handling potentially hazardous materials. It is also important to consult with a qualified professional before attempting to calculate pressure drop from a pressure vessel leak.

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