Gas Through Porous Plug: Pressure & Temp Change Explained

[Vivek98phyboy]

I can't understand why a gas passing through a porous plug experiences change in its pressure and why does the cooling or heating process depends upon the initial temperature

 

[CWatters]

Please cite an example. Hint.. Why would a gas pass through a restriction like porous plug? I have a ball of cotton wool sitting on my desk. I don't think there is any significant air flowing through it.

 

[Vivek98phyboy]

Consider a high pressure gas is passing through a tube of small diameter. Now, you are trying to block its passage by placing a cotton wool at the half of its way but it'll pass through the cotton wool as it is having high pressure. The gas that emerges on the other side of the cotton wool will be of low pressure and low temperature. My question is ' why is it so?'

 

[Chestermiller]

Consider a high pressure gas is passing through a tube of small diameter. Now, you are trying to block its passage by placing a cotton wool at the half of its way but it'll pass through the cotton wool as it is having high pressure. The gas that emerges on the other side of the cotton wool will be of low pressure and low temperature. My question is ' why is it so?'

If it is an ideal gas, its exit temperature will be the same as its inlet temperature. Regarding the pressure change, the porous plug has tiny passages through which the gas flows. So there will be a viscous pressure drop between the inlet side and the outlet side of the plug. Flow through a porous medium is typically described using Darcy's law: $$\frac{dp}{dx}=-\frac{\mu}{k}v$$ where p is the pressure, x is the axial distance along the plug, v is the volume flow rate divided by the cross sectional area of the plug, k is the "permeability" of the plug (a physical property related to the microscopic geometry of the pore channels), and $\mu$ is the viscosity of the gas.

 

[Vivek98phyboy]

If it is an ideal gas, its exit temperature will be the same as its inlet temperature. Regarding the pressure change, the porous plug has tiny passages through which the gas flows. So there will be a viscous pressure drop between the inlet side and the outlet side of the plug. Flow through a porous medium is typically described using Darcy's law: $$\frac{dp}{dx}=-\frac{\mu}{k}v$$ where p is the pressure, x is the axial distance along the plug, v is the volume flow rate divided by the cross sectional area of the plug, k is the "permeability" of the plug (a physical property related to the microscopic geometry of the pore channels), and $\mu$ is the viscosity of the gas.

Can you explain that viscous drop much more clear?

 

[Chestermiller]

Can you explain that viscous drop much more clear?

Are you familiar with the term viscosity and the concept of viscous fluid flow? Do you know that the inlet pressure of a fluid flowing through a pipe has to be higher than the outlet pressure?

 

[Vivek98phyboy]

Yeah I have a little knowledge about that

 

[Chestermiller]

Yeah I have a little knowledge about that

Then what is it about what I said that you do not understand?

 

[Vivek98phyboy]

My problem is how does the pressure of the gas changes on the other side of the porous plug? What is the state of molecules before and after passing through the porous plug? What actually causes this differences? All these doubts of mine arised from the topic of throttling

 

[Chestermiller]

My problem is how does the pressure of the gas changes on the other side of the porous plug? What is the state of molecules before and after passing through the porous plug? What actually causes this differences? All these doubts of mine arised from the topic of throttling

The porous plug can be envisioned as an array of tiny pipes in parallel. The flow rate of gas through each pipe is proportional to the pressure drop across the porous plug. The sum of the flows through the pipes is equal to the total flow of gas through the plug. Have you learned about viscous flow through a pipe, and are you aware of the Hagen Poiseuille equation? If not Google it. You need to understand viscous flow in pipes before you can understand throttling through a porous plug.

 

[CWatters]

Another way to think about it is that air will only flow from A to B when there is a pressure difference between those two points. If you make the pressure the same both sides of the porus plug then no gas flows.