How long will it take for compressed air to reach 29 psi?

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Discussion Overview

The discussion revolves around calculating the time it takes for compressed air in a tank to reach a pressure of 29 PSI from an initial pressure of 49 PSI. The problem involves considerations of fluid dynamics, specifically the changing flow rate as the pressure decreases, and assumes constant temperature throughout the process.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about how to approach the problem, noting that the flow rate will change as the pressure decreases and mentions using Bernoulli's Equation for velocity calculations.
  • Another participant questions whether the problem is homework, which is clarified as not being the case.
  • A participant emphasizes the necessity of knowing the volume of the tank to calculate the time required for the pressure drop.
  • It is noted that the tank volume is 1050 gallons or 140.365 cubic feet, which is provided by another participant.
  • One participant proposes an approach to the problem, suggesting that the transition from sonic to subsonic flow at 29 PSI is significant and that the average flow rates can be used to estimate the time required for the pressure drop.
  • This participant also mentions calculating the volume of air in the tank at both pressures and determining the air volume loss to find the time needed for the pressure to decrease.

Areas of Agreement / Disagreement

Participants generally agree on the importance of knowing the tank volume and the implications of flow transitioning from sonic to subsonic. However, there is no consensus on the specific method to calculate the time required, as different approaches are suggested.

Contextual Notes

The discussion does not resolve the mathematical steps needed to calculate the time, and assumptions regarding temperature and flow characteristics are not fully detailed.

Matt13
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A large tank filled with air is compressed to 49 PSI. A valve is open and air escapes through the hole (d = 0.04 ft) to the atmosphere. How long will it take for the compressed air to reach 29 PSI.
Assume constant temperature.

Not exactly sure how to approach this problem since the flow rate will change as the pressure changes.
I've been trying to use Bernoulli's Equation to get velocity and therefore flowrate, but that is instantaneous velocity so it doesn't help much. If anyone could point me in the right direction that would be much appreciated.
 
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Is this homework?
 
No it isn't homework, just something I am working on
 
The volume of the tank is required to calculate the time. What is the volume of the tank?
 
JBA said:
The volume of the tank is required to calculate the time. What is the volume of the tank?
Volume of tank is 1050 gal or 140.365 cubic ft
 
Based upon the information given plus the tank volume and an assumed or known air temperature this is the way I would approach solving the problem.

It appears that the 29 psi minimum has been carefully selected because it is just above the point that the orifice flow would transition from sonic flow to subsonic flow for an orifice discharging to atmosphere (14.7 psi) . As a result, the orifice sonic flow rate equation can be used to calculate the discharge rate at both pressures; and, since flow rate vs pressure is linear for sonic orifices and constant temperature is to be assumed, then average of the flow rates at 49 to 29 psi can be used for the entire discharge period.
Once that rate is determined, then what remains is to calculate the volume of air in the tank at the two pressures, again assuming constant temperature, to determine the vessel's air volume loss.
With the air volume loss and the average loss rate (average orifice flow) determined, it is simple to calculate the time required.
 

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