Rotating Cylinder - Understanding Gas Pressure and Density

In summary, the conversation discusses the effects of rotation on the atmosphere inside a cylindrical container filled with gas. The container is accelerating and reaching a constant speed, causing the gas to become more compressed against the inside surface and less dense at the axis. The speaker is interested in calculating the pressure and density of the gas at various points, taking into account the changing artificial gravity and centripetal force. Two scenarios are considered: a sealed cylinder with a fixed volume of gas and a cylinder with a hole at the axis allowing gas to flow in. Parameters such as cylinder volume, radius, and rotational speed are provided. The conversation also mentions the possibility of using the formula P=dgh, where F=mw^2r is substituted for g, to
  • #1
Johnsson
2
0
Hi,

I have a cylindrical container of gas that is rotating about the axis (of symmetry).
I'm trying to understand and calculate what is happening to the atmosphere inside.

Obviously, as the cylinder accelerates up to speed, the gas will also accelerate and eventually get to the same speed as the container (I have baffles to help this) and the gas will be more compressed/dense against the inside surface and less dense at the axis.

I'm wanting to get some idea of the pressure and density of the air at various points (inside surface and axis).
I can't use standard formulas that relate to a constant gravity/density (Pres.=Density x g x height) due to the fact that the artificial gravity/centripetal force created by the rotation is not constant across the radius of the cylinder and therefore the density also changes.The two scenarios I am looking at are -

1) a sealed cylinder i.e. fixed volume of gas - Is there any effect on the calculation if the rotational speed is such that the axis is under vacuum?

2) a cylinder with a hole at the axis i.e. gas can flow into cylinder as it accelerates up to speed. - I guess we can assume that gas pressure at the axis is constant at 1 atmosphere (ambient)

rough parameters I'm working with are
Cylinder volume - 1 litre
Cylinder radius - 0.05m
Rot speed - 2000 rpm
Air is at standard room temp and pressure
 
Last edited:
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  • #2
how about if I substitute F=mw^2r into the P=dgh formula.

P=dmw^2r^2

Can I use this for gas pressure calculation in this case.

Please not this is not a hypothetical question or an academic problem but rather a scenario in our work environment.
 

Related to Rotating Cylinder - Understanding Gas Pressure and Density

1. What is the Rotating Cylinder experiment?

The Rotating Cylinder experiment is a classic experiment in physics that demonstrates the relationship between gas pressure and density. It involves a closed cylinder filled with a gas that is rotated at a constant speed. As the cylinder rotates, the gas inside experiences centrifugal force, causing it to move towards the outer walls of the cylinder and increase in density.

2. How does the rotation of the cylinder affect gas pressure?

The rotation of the cylinder causes the gas molecules to move towards the outer walls of the cylinder, increasing their density. This increase in density leads to an increase in gas pressure, as the molecules are now colliding with the walls of the cylinder more frequently and with more force.

3. What is the relationship between gas pressure and density in the Rotating Cylinder experiment?

The relationship between gas pressure and density in the Rotating Cylinder experiment is directly proportional. As the density of the gas increases due to centrifugal force, the gas pressure also increases. This relationship follows the ideal gas law, which states that at a constant temperature, pressure and density are directly proportional.

4. How does the rotation speed of the cylinder affect the results of the experiment?

The rotation speed of the cylinder directly affects the magnitude of the results in the experiment. A higher rotation speed will result in a greater increase in gas pressure and density, as the centrifugal force will be stronger and the gas molecules will be pushed towards the outer walls with more force. A lower rotation speed will lead to a smaller increase in gas pressure and density.

5. What other factors can affect the results of the Rotating Cylinder experiment?

Other factors that can affect the results of the experiment include the type of gas used, the temperature of the gas, and the size and shape of the cylinder. Different gases have different molecular weights and properties, which can affect their response to centrifugal force. Higher temperatures can also lead to increased molecular motion and therefore, higher gas pressure. Lastly, the size and shape of the cylinder can impact the distribution of gas molecules and the resulting pressure and density changes.

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