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

In summary, the problem involves a large tank filled with air at 49 PSI that is compressed to 29 PSI through an open valve with an orifice diameter of 0.04 ft. The volume of the tank is 1050 gallons or 140.365 cubic feet. The orifice flow rate equation can be used to determine the discharge rate at both pressures, and the average of these rates can be used to calculate the time required for the compressed air to reach 29 PSI. The volume of air in the tank at both pressures must also be considered, along with the average loss rate, to accurately calculate the time.
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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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No it isn't homework, just something I am working on
 
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The volume of the tank is required to calculate the time. What is the volume of the tank?
 
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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
 
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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.
 

1. How is the rate of air compression determined?

The rate of air compression is determined by the volume of the container, the initial pressure, and the rate at which air is being pumped into the container.

2. What is the unit of measurement for compressed air pressure?

The unit of measurement for compressed air pressure is pounds per square inch (psi).

3. How does temperature affect the time it takes for air to reach 29 psi?

Temperature can affect the time it takes for air to reach 29 psi as it can impact the volume and pressure of the air. Warmer temperatures can cause the air to expand, resulting in a lower pressure and longer compression time.

4. Can the material of the container affect the compression time?

Yes, the material of the container can affect the compression time. Materials with a lower thermal conductivity, such as steel, can retain heat and slow down the compression process.

5. Is there a formula to calculate the time it will take for compressed air to reach 29 psi?

Yes, the formula to calculate the time it will take for compressed air to reach 29 psi is: t = (V * (P2-P1)) / (Q * P2), where t is the time (in seconds), V is the volume of the container (in cubic feet), P1 is the initial pressure (in psi), P2 is the final pressure (in psi), and Q is the flow rate of air into the container (in cubic feet per minute).

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