Leak in vacuum vessel question

[Zrq]

Question:
How can I estimate the amount of air that leakes into a vacuum vessel. I know the pressure outside the vessel (1020 mBar), the pressure achieved in the vessel (10 mBar), the pumping speed of the vacuum pump (400 cubic metres per hour) and the duration of the leaking (6 hours). Volume of the vessel = 4800 litres.

 

[etudiant]

The amount of leakage is measured by the pressure rise during the 6hr leak interval.
If you had a 10mBar rise during that period, you had about 1/100th of the volume leak in, so about 48 liters in 6 hrs, or about 8 liters/hr.

 

[Zrq]

The amount of leakage is measured by the pressure rise during the 6hr leak interval.
If you had a 10mBar rise during that period, you had about 1/100th of the volume leak in, so about 48 liters in 6 hrs, or about 8 liters/hr.

Thank you for answer. I should have made clear that there was a stable pressure of 10 mBar during the 6 hours. During this time several pumps were operating. Turns out I overestimated the pumping speed of the system. It is in fact 130 m³/hour. I now believe the estimate to be: ((pumping speed)*(duration))/100 so (130*6)/100≈1*10¹ m³.

 

[etudiant]

Thank you for answer. I should have made clear that there was a stable pressure of 10 mBar during the 6 hours. During this time several pumps were operating. Turns out I overestimated the pumping speed of the system. It is in fact 130 m³/hour. I now believe the estimate to be: ((pumping speed)*(duration))/100 so (130*6)/100≈1*10¹ m³.

In practice, you want to be pretty cautious about pump efficiencies.
Rough pumps that are used initially to pump down the installation can't produce a good vacuum, although they should get to maybe 10**-2 mB.
A 4800 liter vessel is good size and may have elements that outgas in a vacuum, which might become a factor.

 

[alphy]

There are a few different ways to estimate the amount of air that leaks into a vacuum vessel, depending on the specific conditions and assumptions. One approach is to use the ideal gas law, which states that the pressure, volume, and temperature of a gas are all related. In this case, we can assume that the temperature remains constant, and therefore the ratio of the pressure and volume will remain constant as well.

Using the given information, we can calculate the initial volume of air in the vessel before leaking occurs:

P1V1 = P2V2
(1020 mBar)(4800 L) = (10 mBar)(V2)
V2 = 489.6 L

This means that initially, there is 489.6 L of air in the vessel. As the air leaks out, the pressure and volume will change, but the ratio will remain constant. Therefore, after 6 hours of leaking, the new volume of air in the vessel can be calculated:

P1V1 = P2V2
(1020 mBar)(4800 L) = (10 mBar)(V2)
V2 = 48.96 L

The difference between the initial and final volume represents the amount of air that has leaked into the vessel. In this case, it is approximately 440.64 L.

Another approach to estimating the amount of air that leaks into the vessel is to use the pumping speed of the vacuum pump. The pumping speed is a measure of how much gas the pump can remove from the vessel per unit time. In this case, the pumping speed is 400 cubic meters per hour. This means that in one hour, the pump can remove 400 cubic meters of gas from the vessel.

Therefore, in 6 hours, the pump can remove 2400 cubic meters of gas. However, this does not necessarily mean that 2400 cubic meters of air has leaked into the vessel. Some of the air may have been pumped out of the vessel, and the remaining amount may have been due to leaks. To get a more accurate estimate, we would need to know the pumping speed in relation to the amount of air in the vessel before and after the leaking occurred.

In summary, there are a few different approaches to estimating the amount of air that leaks into a vacuum vessel, and the most appropriate method will depend on the specific conditions and assumptions. The ideal gas law and the pumping speed of the vacuum pump are