How does the pressure vary as we go deep into the mines

[Amith2006]

Sir,
How does the pressure vary as we go deep into the mines and as move up into the atmosphere? I think as we move up into the atmosphere the pressure decreases. I am not sure.

 

[maverick280857]

You can derive this yourself by considering the forces on a column of air in equilibrium.

For a liquid, the relationship is too familiar, $P(h) = P_{atm} + \rho g h$ where h is the depth below the free surface at which the pressure is atmospheric. Note that this equation holds only if the density $\rho$ is constant. This too can be derived as above.

Show your work here if you need more help.

 

[Hootenanny]

One can estimate the pressure at a certain height above the ground using the exponential relationship;

$$P_{h} \approx P_{0}e^{-\frac{mg}{kT}}$$

This is not entirely accurate as it does not take into account the changes in temperature which will occur. Therefore, this equation will give an overestimate of the pressure.

Also, I would like to inquire as why you title all your post Heat?

~H

 

[maverick280857]

You are right about the atmosphere. In general how pressure varies with height (or depth) in a fluid depends on how density varies. I can't say much about a mine. Are you asking how pressure changes as you below the Earth's surface?

EDIT: Sorry this post was written before I saw Hootenanny's reply.

 

[Amith2006]

Sir,
This expression given by you i.e. P(h) = P(o)e^(-mg/kT) doesn't have a direct dependence on h. Is the pressure indirectly related to h through g(acceleration due to gravity)?

 

[Hootenanny]

Sir,
This expression given by you i.e. P(h) = P(o)e^(-mg/kT) doesn't have a direct dependence on h. Is the pressure indirectly related to h through g(acceleration due to gravity)?

My apologies Sir, it was a typo mistake on my part, the formula should read;

$$P_{h} \approx P_{0}e^{-\frac{mgh}{kT}}$$

Apologies for any inconvience. I am still interested however as to why this thread is entiled 'Heat'

~H

 

[Amith2006]

Sir,
I feel that Pressure, Volume and temperature are terms closely related to Heat. So whenever my doubts involve these terms I give them the title heat. I think its troubling you a lot. Next time I will try to give a different title.

 

[Amith2006]

Is the above mentioned expression applicable to pressure variation below the Earth's surface also?

 

[Hootenanny]

Sir,
I feel that Pressure, Volume and temperature are terms closely related to Heat. So whenever my doubts involve these terms I give them the title heat. I think its troubling you a lot. Next time I will try to give a different title.

You are right, they are inseparable. The title doesn't bother me it was just I noticed that you were posting a lot of Heat titled threads. I would just like to point out that you may get faster and more applicable responses if you had a more informative title. For example, one could entitle this thread 'Pressure dependence and height'. It is not a critisism and please do not take it as such, it is only a suggestion.

~H

 

[Hootenanny]

Is the above mentioned expression applicable to pressure variation below the Earth's surface also?

I'm afraid not, the difference between predicted values and actual values become significant below the Earth's surface.

~H

 

[Amith2006]

Sir,
Actually I never thought about it. I will surely take your suggestions in the right spirit. Next time I will try to be more specific in giving titles.