Thread: What is the Formula for pressure as a function of depth, gravity, temperature...

1. What is the Formula for pressure as a function of depth, gravity, temperature...

What is the Formula for pressure as a function of depth, gravity, temperature and density?

Would it work for solids?

At what depth under Martian ice can we expect a high enough pressure to result in liquid water (assume 0 degrees Celsius)?

2. For fluids (which includes gases, but not solids):

p=Rgh

where:

p is static pressure
R (should be the greek letter rho) is density
h is the distance below the surface of the fluid

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Originally Posted by Saluki
For fluids (which includes gases, but not solids):

p=Rgh

where:

p is static pressure
R (should be the greek letter rho) is density
h is the distance below the surface of the fluid
I think due to the increasing depth and pressure the R (rho) will also be a function of h . So the formula may become : p(h)=r(h)*g*h. r(h) must be increasing with depth in some way .

4. The average water temperature is around −3 °C; it remains liquid below the normal freezing point because of high pressure from the weight of the ice above it. Geothermal heat from the Earth's interior warms the bottom of the lake. The ice sheet itself insulates the lake from cold temperatures on the surface.
Source

The ice pocket may be as deep as 200 meters thick.
Source

Any estimates as to the possibility of existence of pockets of liquid water under the linked crater ice or the Martian southern ice cap?
Last edited by a1call; 2007-Dec-09 at 05:39 AM.

5. What is the Formula for pressure as a function of depth, gravity, temperature and density?
there is a fermula for pressure on earth like planets at various height below 86 km .
find it here :
http://en.wikipedia.org/wiki/Atmospheric_pressure

this formula is the result of combination of hydrostatic equilibrium equation
and ideal gas equation .
using hydrostatic equilibrium you have a general way of calculating pressure .

6. Originally Posted by a1call
At what depth under Martian ice can we expect a high enough pressure to result in liquid water (assume 0 degrees Celsius)?
(Why assume 0 degrees? That's the melting point at one atmosphere. Aren't you interested in higher pressure?)

It could be deeper than the ice, but it's still under study.

NASA: Mars Express Mission News: Mars' South Pole Ice Deep and Wide (2007 March)

The polar layered deposits extend beyond and beneath a polar cap of bright-white frozen carbon dioxide and water at Mars' south pole. Dust darkens many of the layers. However, the strength of the echo that the radar receives from the rocky surface underneath the layered deposits suggests the composition of the layered deposits is at least 90 percent frozen water. One area with an especially bright reflection from the base of the deposits puzzles researchers. It resembles what a thin layer of liquid water might look like to the radar instrument, but the conditions are so cold that the presence of melted water is deemed highly unlikely.

7. Thank you all for the posts.

01101001,
I assume I chose 0 degrees because that is the temperature of water ice. In other words that is the temperature where slight variation in pressure would shift the ice/water equilibrium (as you mentioned at about 1 atm).

Very interesting article. Thank you.