Europan water pressure, how does the ice contribute to the pressure?

[JacopoPeterman]

Disclaimer: all of the following is mostly theoretical* So on Europa the pressure on the surface of the ice crust is 0.1 microPa
* Gravity on the surface is 1.314 m/s^2
* The ice crust is estimated to be ~10-30 km thick
* Beneath the crust is about 100 km of liquid water
* According to my professor's notes the pressure at the surface is 85 MPa - 200 MPa (dependent on the ice crust thickness)

So now my question may or may not be simple.

1) What is the pressure on the bottom side of the ice crust?

With that calculation I can use the following formula:

P(chosen depth) = P(bottom of ice sheet) + rho*g*depthNow a couple other questions:

2) I am assuming rho is constant because water is an incompressible fluid, is this a reasonable assumption?

3) the total depth is 100 km (approximately), is it reasonable to assume g, 1.314 m/s^2, is also constant?

Thanks, for your help guys (I'm off to see Fury with my buddy, I can answer any questions when I get back, feel free to make reasonable assumptions though)

 

[Orodruin]

2 is a reasonable assumption as long as the pressure stays significantly below 10^10 Pa (water compressibility is around 10^-10 Pa^-1). Based on the figures in your notes, this might be violated. The check you can do is to compute it and see what you get. If you get something much smaller than 10^10 Pa, you are fine, if not you may need to rethink depending on intended precision.

1 and 3 are both relying on the depth being much smaller than the radius of Europa. Europa's radius is ca 1560 km so it may be a borderline case depending on the kind of precision you are looking for.

 

[oz93666]

regarding reduction of gravity at 100km depth... radius Europa=1560km

Without doing the calculation I would gesstimate 1.314 surface g would be reduced to about 1.15 at 100km depth.

 

[Orodruin]

A gravitational field linear in radius (corresponding to a homogeneous Europa) would have a g of 1.22 at the bottom. However, the Europa mean density is about 3 g/cm^3 so it (like most celestial bodies) is not homogeneous. Gravity might even be increasing as is (initially) the case when going down through the Earth's surface.

 

[JacopoPeterman]

Alright, thanks guys, any ideas how to figure out the pressure at the very top of the liquid layer (immediately after the ice crust)? I've got mean thickness of the crust and a pressure on the surface of he crust, which is essentially 0. I feel like this might be a hoop stress problem or something, but I'm not quite sure.

And according to the data my prof collected, the maximum pressure is expected to be 200 MPa, or 2*10^8 Pa so less than 10^10... which I have just realized is incredibly high, it's only about 100 MPa at the bottom of the Marianas Trench, granted it is also only 11 km deep ("only" haha).

I plan on building something very similar to the device created in this video .

It's a salinity meter, and is one of the suggested instruments we have been asked to design.

 

[jbriggs444]

Treat the ice as if it were a fluid. It would not be able to support its own weight as a rigid hoop and will flow to relieve the resulting stress.