The discussion focuses on the behavior of gas passing through a porous plug, specifically addressing the changes in pressure and temperature. It is established that the gas experiences a viscous pressure drop due to the tiny passages in the porous medium, as described by Darcy's law: $$\frac{dp}{dx}=-\frac{\mu}{k}v$$. The exit temperature of an ideal gas remains the same as its inlet temperature, but the pressure decreases due to the resistance encountered while flowing through the porous structure. Understanding viscous flow and the Hagen-Poiseuille equation is crucial for comprehending these phenomena.
PREREQUISITESEngineers, physicists, and students studying fluid dynamics, particularly those interested in gas flow through porous materials and the principles of pressure and temperature changes in such systems.
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 said: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?'
Can you explain that viscous drop much more clear?Chestermiller said: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.
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 said:Can you explain that viscous drop much more clear?
Then what is it about what I said that you do not understand?Vivek98phyboy said:Yeah I have a little knowledge about that
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.Vivek98phyboy said: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