Momentum transport in gases in 2d

[Mohankpvk]

I was trying to understand the momentum transport between gas molecules in 2d.In the image below, it is stated that half of the molecules move up(positive velocity in y direction) and half negative.But the author didnt explain why he assumed it.

 

[anorlunda]

Because the whole gas mass is assumed to be static, not moving up, down, left, right.

You could do a different analysis for an upward accelerating gas mass, such as on a rocket, but the answers would change.

 

[Mohankpvk]

Because the whole gas mass is assumed to be static, not moving up, down, left, right.

You could do a different analysis for an upward accelerating gas mass, such as on a rocket, but the answers would change.

But why half if the gas is static?Please explain.I referred a few books for momentum transport but all of them used tensors.Is there any book(or other source) in which transport is explained only in 2d?

 

[anorlunda]

But why half if the gas is static?

No, all the particles are moving, some + some -, the average speed of all is zero.