# Air flow from atmosphere into a tank

• I
• JCB123
In summary, the conversation discusses the determination of flow rate into a tank of air using equations and principles of vacuum technology. It is suggested to use the equations for viscous flow and assume laminar flow. The flow rate can be related to the time derivative of pressure using the ideal gas law, resulting in a first order differential equation that can be easily solved. The concept of conductance is also discussed, which applies regardless of whether the vacuum pump is switched on or not. The difference between pump on and pump off is that without pumping, the low pressure side will change over time according to the flow rate. At the given pressures, only viscous flow is used.
JCB123
Hi,
I have a tank of air which has been depressurized to 0.2bar (absolute) via a vacuum pump, where air can be let in from atmosphere through pipework controlled by a valve. What would be the equation I can use to determine the flow rate into the tank with time? As the flow rate is determined by the pressure inside the tank, and the pressure inside the tank is determined by the flow rate.
Thanks

At any moment you will have a flow rate determined by the conductance of the pipe. You can read about that here:

https://www.pfeiffer-vacuum.com/en/...o-vacuum-technology/fundamentals/conductance/

At your pressures the mean free path is always smaller than the dimensions of the vessels, so you will use the equations for viscous flow and you will probably also want to assume the flow is laminar.

So that will give you flow rate as a function of pressure. However the flow rate can be related to the time derivative of pressure by the ideal gas law, so this will give you a first order differential equation in pressure which you can easily solve (you'll get a simple exponential)

JCB123
JCB123 said:
Hi,
I have a tank of air which has been depressurized to 0.2bar (absolute) via a vacuum pump, where air can be let in from atmosphere through pipework controlled by a valve. What would be the equation I can use to determine the flow rate into the tank with time? As the flow rate is determined by the pressure inside the tank, and the pressure inside the tank is determined by the flow rate.
Thanks

Another good reference is "Building Scientific Apparatus" by John Moore which in addition to pumping also discusses just about everything of practical interest to the experimental physicist. I highly recommend it.

Thanks!
Does conductance only apply when the vacuum pump is switched on? If I switch off the pump and just open the valve to let the flow in, is it the equations for viscous flow I need to use?

JCB123 said:
Thanks!
Does conductance only apply when the vacuum pump is switched on? If I switch off the pump and just open the valve to let the flow in, is it the equations for viscous flow I need to use?

The conductance applies for a difference in pressure regardless of how that is achieved. The difference between pump on and pump off is that without pumping the low pressure side will change pressure over time according to the flow rate dictated by the conductance. You therefore have to integrate over time. This integrates easily to a simple exponential.

Molecular flow vs viscous flow does not depend on pump on or pump off. It only depends on the pressure. At your pressures you will only ever use viscous flow.

JCB123

## 1. How does air flow from the atmosphere into a tank?

Air flows into a tank through a process called diffusion. As the tank is filled with air, the concentration of air molecules inside the tank becomes higher than the concentration of air molecules in the surrounding atmosphere. This difference in concentration causes air molecules to move from the higher concentration area (the atmosphere) to the lower concentration area (the tank) until equilibrium is reached.

## 2. What factors affect the rate of air flow into a tank?

The rate of air flow into a tank is affected by several factors, including the size and shape of the tank, the temperature and pressure of the air, and the presence of any barriers or obstacles that may impede the flow.

## 3. Can the rate of air flow into a tank be controlled?

Yes, the rate of air flow into a tank can be controlled by adjusting the pressure and temperature of the air, as well as the size and shape of the tank. Additionally, the use of valves or other mechanisms can be used to regulate the flow of air into the tank.

## 4. What happens to the air in the tank once it has reached equilibrium with the atmosphere?

Once the air in the tank has reached equilibrium with the surrounding atmosphere, there will be no net flow of air into or out of the tank. The air molecules will continue to move around within the tank, but the overall concentration of air will remain constant.

## 5. How does air flow into a tank impact the pressure inside the tank?

The pressure inside a tank can increase as air flows into it, since the air molecules take up space and exert pressure on the walls of the tank. However, once equilibrium is reached, the pressure inside the tank will stabilize and will be equal to the pressure of the surrounding atmosphere.

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