How Does a Pressurized Tank Empty Over Time Through a Hole?

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Discussion Overview

The discussion revolves around the dynamics of a pressurized tank emptying through a hole, specifically focusing on developing a pressure vs. time curve as the tank's pressure decreases from 100 psi to atmospheric pressure. The scope includes fluid dynamics principles and the application of relevant engineering formulas.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in applying fluid dynamics to model the emptying of a 10L tank of compressed air at 100 psi through a hole, seeking a general curve for pressure vs. time.
  • Another participant suggests consulting engineering formulas from valve manufacturers and pneumatic handbooks, indicating the need for different equations based on pressure regimes (sonic vs. subsonic).
  • A participant points out that 100 psi relative translates to 114 psi absolute, which is significantly above atmospheric pressure, and inquires about methods for estimating the flow rate during the tank's emptying process.
  • Further advice is given to explore the LOHMS concept for calculating flow rates based on orifice size and pressure differences.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a specific method or formula for modeling the pressure drop over time, and multiple approaches and considerations are presented without resolution.

Contextual Notes

Participants mention the need to consider different flow regimes based on pressure levels, indicating that assumptions about flow characteristics may affect the modeling approach.

ab042896
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I having difficulty wrapping my head around a concept that I wish to solve. I have a 10L tank of compressed air at 100psi. When an outlet hole of cross-sectional area of 0.115 in^2 is opened, I wish to develop a curve of pressure vs. time from t=0 until pressure drops to atmospheric. Many things can be neglected in this situation, such as friction etc., since I would like a general curve to compare with experimental data. I am unsure of how to apply fluid dynamics to a vessel that empties simply due to its own pressure difference through an area.

Temperature can be assumed to be constant at 25C as well.
 
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You can find engineering formula in places such as valve manufacturers, pneumatic handbooks, etc. Here is an example http://www.theleeco.com/engineering/engineering.cfm#lohm-laws-working-with-gases

You have to be aware that you will need two regimes for your problem: initially the inside pressure is greater than 1.9 x atmospheric and you need a sonic formula. At lower pressures subsonic equations will do.
 
Doesn't
Henryk said:
You can find engineering formula in places such as valve manufacturers, pneumatic handbooks, etc. Here is an example http://www.theleeco.com/engineering/engineering.cfm#lohm-laws-working-with-gases

You have to be aware that you will need two regimes for your problem: initially the inside pressure is greater than 1.9 x atmospheric and you need a sonic formula. At lower pressures subsonic equations will do.
100psi relative is 114psi absolute, which is nearly eight times greater than atmospheric. Are you aware of any ways that this could be done to give a rugh estimate? After all I will be testing this and ultimately have the real data to compare this to.
 
Follow the link. You will find a number of pages with relevant information. Lee valve company uses LOHMS concept. Find how to calculate LOHM for a give size orifice and then the flow rate as a function of pressure.
 

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