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A Question On Pressure

03/27/2018 10:16 PM

In a gedanken experiment in which all water has been stored on mars so we can examine the ocean beds I stipulated that we should pretend that this does not cause any discomfort to marine life, that the release of pressure does not cause a change in normal submarine geologic activity and that we had free access to the sea bed. Now, while there are plenty of sites on the net to find the atmospheric pressure as we ascend from sea level I could not find any reference to how to calculate the pressure as we descend. I want to know how the atmospheric pressure increases as we climb down the continental shelves and descend down a trench. With water the pressure at the bottom of the Puerto Rica trench, at 8648 meters, is about 860 atmospheres. How would I calculate what it would be with out water above us. I am not sure if this is a mech. engineering question or a general question. Thanks.

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#1

Re: A question on pressure

03/27/2018 10:27 PM

Maybe try to search for: "how to calculate atmospheric pressure with depth"

The short answer is Density of Air versus depth.

Check these out:

https://appmeas.co.uk/resources/pressure-measurement-notes/how-is-pressure-related-to-altitude-and-depth/

http://theory.uwinnipeg.ca/physics/fluids/node8.html

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#2

Re: A question on pressure

03/27/2018 11:42 PM

Let's just pretend that "atmospheric pressure" adds 1 bar of pressure.

At the deepest point on Earth, the pressure would be 3.66 bar.

Could you survive at the deepest point of the ocean, if there was no ...

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#3

Re: A question on pressure

03/27/2018 11:50 PM

A lot will depend on the temperature of the air column....

http://nopr.niscair.res.in/bitstream/123456789/2506/1/IJRSP%2037%281%29%2064-67.pdf

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#4

Re: A question on pressure

03/28/2018 2:46 AM
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#5

Re: A question on pressure

03/28/2018 5:53 AM
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#6

Re: A Question On Pressure

03/28/2018 10:18 AM

Deep mine barometric concerns have been studied. That paper concluded that nitrogen narcosis and oxygen toxicity would only become a concern at about twice the depth of Challenger Deep.

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#7

Re: A Question On Pressure

03/28/2018 10:45 AM

Here is a rough analysis.

The pressure under the ocean at any depth is equal to the weight of the water above it. For example, a column of water 1 square inch 34 feet tall would weigh 14.7 pounds, and the pressure would be 2 atmospheres or 2 x 14.7 psi.

The weight of an air column 1 square inch the height of the atmosphere weighs 14.7 pounds. The pressure at any altitude is the weight of the atmosphere above that point. (Not exactly true, but extremely close because the height of the atmosphere is minuscule compared with the radius of the earth.) Because the density of a gas is proportional to the pressure, the rate that the pressure increases is proportional to the pressure.

The function that has the property that the rate of change is proportional to itself is the exponential function (e-ax, where a is a constant and x is altitude). Air pressure on earth halves about every 17000 feet in altitude.

The deepest ocean trench is about 35000 feet, so if the oceans were empty, the pressure would be about 4 times the air pressure on the continents.

Oceans occupy about 3/4 of the earth's surface and the average depth is about 10000 feet. So a good estimate is the air pressure on the edge of the continents would be the current pressure at 7500 feet, about 11.5 psi. Multiply that by 4 for the ocean trench would be about 45 psi, 3 times the current air pressure at sea level.

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#11
In reply to #7

Re: A Question On Pressure

03/30/2018 12:41 AM

If the water were removed from the oceans and replaced with the air currently available ( with water in the oceans ) . Would your hypothesis still hold true ?

It seems now that we have more air and less space, if you remove the water, then you would have less air and more space.

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#12
In reply to #11

Re: A Question On Pressure

03/30/2018 9:43 AM

Actually, I was taking into consideration the volume of the oceans. If the average depth of the oceans is 10000 ft and the oceans cover 3/4 of the globe, then I estimated the atmospheric pressure at the current shoreline (sea level) would be what the current pressure is at 7500 ft (3/4 x 10000), based on a volume measurement.

Actually, 10000 ft pressure would be a more accurate estimate for the shoreline pressure, but even this is not exact. The ocean basin is a container with an irregular bottom contour, whereas the current ocean surface is very flat.

Gas concentrates at the bottom of a container, so to get a good estimate would require getting a contour map of the world (oceans and land), say with resolution 100 ft. With a contour map, you can compute the mass distribution of the atmosphere by multiplying the area at each elevation by 100 (layer thickness) by the density at that elevation. Doing this integration (with oceans filled) to a very high altitude where the density is negligible would give a value of the total mass of the atmosphere.

If you do this contour integration again, this time with the oceans empty using the ocean bottom contour and assuming a density value, you could come up with a new atmosphere total mass. Adjust the density value until the new total atmosphere value is the same as the current value.

You still have the problem that the density is inversely proportional to temperature, so you have to assume a temperature profile. It really is very difficult to come up with an accurate estimate.

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#14
In reply to #12

Re: A Question On Pressure

03/30/2018 4:09 PM

Good explanations.

In Death valley, it is cooler at the top of the valley, as you descend( below sea level ) the temperature increases. Would it be possible to use the differential as a base in approximating the temperature at lowest and highest elevation ?

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#15
In reply to #14

Re: A Question On Pressure

03/30/2018 10:16 PM

That's a very good point. Death Valley might be a good small-scale model of how dry ocean beds might behave.

"Death Valley has a subtropical, hot desert climate (Köppen: BWh), with long, extremely hot summers and short, mild winters, as well as little rainfall. As a general rule, lower altitudes tend to have higher temperatures. When the sun heats the ground, that heat is then radiated upward, but the dense below-sea-level air absorbs some of this radiation and radiates some of it back towards the ground. In addition, the high valley walls trap rising hot air and recycle it back down to the valley floor, where it is heated by compression.[14]"

https://en.wikipedia.org/wiki/Death_Valley#Climate

The temperature gradient in the lower atmosphere is primarily caused by solar radiation heating the ground, which in turn heats the air.

As air rises it expands and cools due to the decreased pressure and when it descends it is heated by the compression, a phenomenon known as the adiabatic lapse rate.

As long as the temperature gradient caused by the sunshine is less than the adiabatic lapse rate the air will be stable. When the temperature gradient exceeds the adiabatic lapse rate, the air begins to circulate, limiting the temperature gradient.

In an oceanless earth, the air pressure would be greater in the ocean basins, the rate of change with of pressure with elevation (the slope) would be greater and therefore the adiabatic lapse rate and maximum temperature gradient would be greater.

(An extreme example of this effect is Venus, where the surface pressure of 90 bar can support a very large temperature gradient.)

The oceanless earth would have hot dense air in the ocean basins that would make Death Valley seem like a nice place.

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#8

Re: A Question On Pressure

03/28/2018 9:06 PM

There seems to be general agreement in the previous answers about the approximate pressure at the deepest parts of the ocean if all the water were removed to Mars.

However, in the original hypothetical, no mention is made of increasing the amount of atmosphere surrounding the Earth. Where is this large increase in atmospheric mass supposed to be coming from?

Since there is no mention of additional gasses being shipped Earth to compensate for the removed volume of water, my view differs from the majority so far. The pressure increase would be slight at the deepest part of the ocean since the height of tye column would be slightly greater due to decreased volume required to cover to the same height the reduced surface area for the smaller (without ocean) sphere of Earth. Additionally since the oceans only cover ~ 2/3 of the globe, this would also slightly increase pressure. Additionally the very depest parts of the ocean are far deeper than average depth, and a correction will be neexdd as well.

The pressure at current sea level would be much reduced below current pressure as much of the atmosphere previously above would have descended to fill the voids left by the oceans.

So as a rough estimate, water covers 2/3 of the planet, most with oceans. Oceans are about 12000 feet deep on averag. This suggests that after all the watetr is shipped to Mars, approximately 8000 feet below curent sea level will have a similar pressure as current sea level, i.e. before all water is shipped to Mars.

Some spots are far deeper than average. Marianas trench gets to somewhere around 36,000 ft, so it would be about 24,000 ft below the the place the old sea level moved to.

Oops, I just noticed Rixter's excellent answer. I am in agreement.

I do think a significant correction might be needed that would further reduce expected pressure in most places on the waterless globe due to the greater amount of atmosphere stored at the deepest points due to the depth dependent density.

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#16
In reply to #8

Re: A Question On Pressure

03/30/2018 10:22 PM

"I do think a significant correction might be needed that would further reduce expected pressure in most places on the waterless globe due to the greater amount of atmosphere stored at the deepest points due to the depth dependent density."

Good point, I agree. My initial estimate was a bit of a fudge.

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#9

Re: A Question On Pressure

03/29/2018 5:51 AM

There's another calculator here

https://www.mide.com/pages/air-pressure-at-altitude-calculator

Which works if you're boring a dry hole, but as Rixter and TINAC have pointed out removing the water reduces the total "height" of the air. Here's a picture which shows how much water and air (at STP Standard Temperature and Pressure) there is on earth:

_____________________________________________________________________

The water sphere (blue) in this computer visualization measures 1390 kilometres across and has a volume of 1.4 billion cubic kilometres. This includes all the water in the oceans, seas, ice caps, lakes and rivers as well as ground water, and that in the atmosphere. The air sphere (pink) measures 1999 kilometres across and weighs 5140 trillion tonnes. As the atmosphere extends from Earth it becomes less dense. Half of the air lies within the first 5 kilometres of the atmosphere. The spheres show how finite water and air supplies are.

___________________________________________________________________________

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#13
In reply to #9

Re: A Question On Pressure

03/30/2018 10:15 AM

its interesting on the size comparison when you group the water like that.... going off topic here...

when comparing the earth to size... if the earth was proportionally (Highest mountain deepest trench kept in tacked proportionally) shrunk down to the size of a pool cue ball, the earth would be smoother then an actual cue ball.

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#17
In reply to #13

Re: A Question On Pressure

04/01/2018 12:21 PM

They have misinterpreted the tollerance in the link you provided. The tollerance is for diameter. It is unlikely to be a tollerance for smoothness/roughness as typical pool balls are far far more smooth.

The link claims the +0.005" is for smoothness, but that is pretty coarse. Far more course than a pool ball. 120 grit sandpaper is more smooth with a grit size around 0.0045".

Pretty funny it's called 'bad astronomy'.

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#10

Re: A Question On Pressure

03/29/2018 8:16 PM

Thank you all for your answers. They were all helpful. There was a vital flaw in the original experiment which was that no allowance was made for the air having replaced the removed water. This was well explained by truth is not a compromise in reply 8. I think I will have to accept that it would be very difficult to calculate the pressure in the trenches due to too many variable factors. My main concern was the well being of any explorers that descended to these dry depths. I will go with the assumption that the air pressure, density and temperature will still be adequate for survival. Again, thanks every one. Time to welcome the dolphins back and give them some fish.

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