How fast would a methane cloud rise in air?

[Mock]

Homework Statement

Hi everyone,

This is a conceptual question, so there are no variables, per se. I'm trying to figure out how to calculate the velocity at which methane would rise into the atmosphere when released on the ground.

Density of air: 1.225kg/m^3

Density of methane: 0.717kg/m^3

Homework Equations

Unknown, intuitively I feel it should be based on buoyancy.

The Attempt at a Solution

I've tried using the buoyancy approach, but since I would imagine the cloud could be any size, there is no way to use volume as a variable. The only method I can think of is to use the ratio of the densities of the atmosphere and methane, both of which are known constants, but I'm not quite sure how to go about doing this. This is my first post, so I apologize if I've made any template errors. Thanks!

 

[Student100]

Homework Statement

Hi everyone,

This is a conceptual question, so there are no variables, per se. I'm trying to figure out how to calculate the rate at which methane would rise into the atmosphere.

Density of air: 1.225kg/m^3

Density of methane: 0.717kg/m^3

Homework Equations

Unknown, intuitively I feel it should be based on buoyancy.

The Attempt at a Solution

I've tried using the buoyancy approach, but since I would imagine the cloud could be any size, there is no way to use volume as a variable. The only method I can think of is to use the ratio of the densities of the atmosphere and methane, both of which are known constants, but I'm not quite sure how to go about doing this. This is my first post, so I apologize if I've made any template errors. Thanks!

I'm not sure how you came to the conclusion that either density is constant.

 

[Mock]

I'm not sure how you came to the conclusion that either density is constant.

I know how to calculate density, these are just good, relatively "normal" numbers to use.

 

[Student100]

I know how to calculate density, these are just good, relatively "normal" numbers to use.

Your question:

I'm trying to figure out how to calculate the rate at which methane would rise into the atmosphere.

Maybe you need to rework the question.

 

[Mock]

Maybe you need to rework the question.

Edited, thanks.

 

[Orodruin]

The density difference would give you the net force on the methane volume due to Archimedes' principle. However, the cloud would also diffuse and induce air currents, leading to dispersion and drag on the cloud, which would therefore also mix with the air. Without knowing these things in more detail, I feel this would make life significantly more complicated than simple force analysis.

 

[Student100]

Edited, thanks.

It's still impossible to attempt to solve what you want to solve in this manner. If you're still curious about this subject read up on industry risk management gas dispersion models. Otherwise try to design an experiment.

If you want to just do an equation in which everything is ideal, calculating buoyance should be good enough.