How to calculate the leak rate based on pressure drop

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Discussion Overview

The discussion revolves around calculating the leak rate and fluid loss from pressurized vessels filled with water over a specified time period. Participants explore various methods and considerations related to pressure drop, fluid dynamics, and the physical properties of water in the context of potential leaks through cracks in the vessel.

Discussion Character

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

Main Points Raised

  • One participant describes using Boyle's Law to relate pressure and volume changes, but questions whether this approach is appropriate for their specific scenario.
  • Another participant asks for clarification on whether the vessel contains liquid water, water vapor, or both, emphasizing the need to establish a relationship between pressure drop and flow rate.
  • A participant outlines their method of calculating volume loss based on hydrostatic pressure and the change in water height, expressing concerns about the complications encountered with Boyle's Law.
  • Further inquiries are made regarding the presence of headspace above the liquid, the nature of the cracks, and the dimensions of the vessel and cracks, indicating the complexity of the problem.
  • One participant provides links to external resources related to pressure vessel inspection and hydrostatic testing, suggesting they may contain relevant information.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method for calculating leak rate, with multiple competing views and approaches presented. The discussion remains unresolved regarding the most effective technique to apply in this context.

Contextual Notes

Participants express uncertainty about the applicability of Boyle's Law in this scenario and highlight various assumptions, such as the completeness of the vessel's filling with water and the characteristics of potential cracks.

Who May Find This Useful

This discussion may be useful for individuals involved in engineering, fluid dynamics, or pressure vessel design and inspection, particularly those interested in leak detection methodologies.

blinkz303
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TL;DR
I am currently working on a project trying to calculate leak rates from pressurised vessels filled with water.
I am currently working on a project trying to calculate leak rate and fluid loss from pressurised vessels filled with water over a time period of 30 minutes. So far I have used the Boyles Law which assumes that PV/T = constant which gets us P1 * V1 = P2 * V2 and PdV+VdP = 0 I formed this over to PdV=VdP. and divided by the change in time to get dV/dt = - VdP/Pdt

Could anyone help me and tell me if I am on the right track here or have I overlooked something.
 
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Is it liquid water or water vapor or are both present in the vessel. You need to establish the pressure drop vs flow rate relationship for the valve.
 
To clarify further: I am an intern at a company and I have been tasked with finding a method to calculate the leak rate and amount of fluid lost through possible cracks in a vessel. It can be assumed that the vessel is completely filled with water. I know the volume of the vessel and can figure out the hydrostatic pressure at the bottom of the vessel based on the volume. I have tried calculating the volume loss by calculating the change in the height of the water WH=P/rho*g
P being Pressure, rho being the density of water, g being the acceleration due to gravity.
I know the volume of water per meter of height and can therefore calculate the amount of water lost.
Would this be a viable method? I realized I am running into way to many problems using Boyle's law.
 
blinkz303 said:
To clarify further: I am an intern at a company and I have been tasked with finding a method to calculate the leak rate and amount of fluid lost through possible cracks in a vessel. It can be assumed that the vessel is completely filled with water. I know the volume of the vessel and can figure out the hydrostatic pressure at the bottom of the vessel based on the volume. I have tried calculating the volume loss by calculating the change in the height of the water WH=P/rho*g
P being Pressure, rho being the density of water, g being the acceleration due to gravity.
I know the volume of water per meter of height and can therefore calculate the amount of water lost.
Would this be a viable method? I realized I am running into way to many problems using Boyle's law.
Is there head space above the liquid water in the vessel? If so, what is in the head space, pure water vapor? Are the cracks exclusively on the bottom of the vessel, or are there cracks along the sides as well? how thick is the wall, and what are the approximate lengths of the cracks. Do you have any idea what the size of the crack openings are?
 
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