Sea level

[Goldilocks]

Need some help with this hypothetical. If you added 139,989,929,200,000,000 gallons of water to the ocean how high would the sea level become? If you could explain the math that would be more helpful too. There’s no use in knowing the answer if I can’t do it myself.

Edited April 12, 2020 by Goldilocks
Grammar

[studiot]

US gallons or Imperial gallons?

[Strange]

About 1.5 metres or 5 feet (assuming US gallons; 1.9m for Ye Olde Imperial Gallon)

https://www.wolframalpha.com/input/?i=139%2C989%2C929%2C200%2C000%2C000+gallons+%2F+surface+area+of+oceans

[Goldilocks]

20 minutes ago, studiot said:

US gallons or Imperial gallons?

US

13 minutes ago, Strange said:

About 1.5 metres or 5 feet (assuming US gallons; 1.9m for Ye Olde Imperial Gallon)

https://www.wolframalpha.com/input/?i=139%2C989%2C929%2C200%2C000%2C000+gallons+%2F+surface+area+of+oceans

This helped a lot.

[J.C.MacSwell]

2 hours ago, studiot said:

US gallons or Imperial gallons?

 African or European?  

[Sensei]

2 hours ago, Strange said:

About 1.5 metres or 5 feet (assuming US gallons; 1.9m for Ye Olde Imperial Gallon)

https://www.wolframalpha.com/input/?i=139%2C989%2C929%2C200%2C000%2C000+gallons+%2F+surface+area+of+oceans

It is approximation which works for cans, glasses, aquariums etc.

Attempt to calculate the real value for Earth case would be much harder. You would have to check how much of land lies below 1.5m or 1.9m altitude and include them in calculations..

When ocean water level rises lands are flooded.

[Strange]

47 minutes ago, Sensei said:

Attempt to calculate the real value for Earth case would be much harder. You would have to check how much of land lies below 1.5m or 1.9m altitude and include them in calculations..

Good point. That will reduce the increase in level. My guess is not by much.

For example, we could estimate/guess that the amount of land below 1.5m averages about 10m from the coast (a lot of coastlines are steep or cliffs; a lot are very flat). Given the total length of coast is about 356,000 km [1] then this adds another 3.5 million square kilometres to the area to be covered, or about 1%. Much less than the rounding in my reporting of the figure as 1.5m!

That is slightly complicated by whether we are only concerned with land that could be reached by rising ocean water, or if we were more interested in distributing the water evenly over the surface of the Earth.

Anyway, looks like my estimate for the extra area that would be covered is not unreasonable (too large, if anything). About 1% of land is below 5m [3]. The total area of land is about 500 million km² [1]. So less than 5 million km² extra to be covered. You could assume a linear relationship between height and area, so the area under 1.5m would be about 5 million * 1.5 / 5 = 1.5 million km². About half my initial estimate.

[1] https://www.cia.gov/library/publications/the-world-factbook/geos/xx.html [2]

[2] I have a print copy of this from the days before the internet. We used love browsing it and amazing each other with things like: "Hey, do you know which country has the most TVs per capita?" [4]

[3] https://data.worldbank.org/indicator/AG.LND.EL5M.ZS

[4] Bermuda, surprisingly.

4 hours ago, Goldilocks said:

If you added 139,989,929,200,000,000 gallons of water to the ocean

That is a bizarrely precise number. What is it based on?

3 hours ago, Goldilocks said:

This helped a lot.

I hope that was enough explanation of the math? Let us know if not.