# How will melted ice in a pool change the water level

philip porhammer
if I have a pool that is 20x20 surface area and I put a 200 gallon block of ice it, the water level will go up by X amount. when it melts how much will the water level change?

DrStupid
if I have a pool that is 20x20 surface area

Units?

and I put a 200 gallon block of ice it, the water level will go up by X amount. when it melts how much will the water level change?

Does the ice block swim in the water or is it laying on the ground? (Is X kown or unknown?)

Gold Member
At the risk of violating the rule of 'Ask, don't tell' I attach this diagram which addressed the same question posted here a long time ago.

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• pic_icefloats.gif
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Gold Member
Which, by the way, is why floating Arctic ice won't change the sea level when it melts.

Gold Member
Good old Archimedes got it when he said the weight of water displaced is equal to the upthrust. When an object floats, what does that tell you?

Staff Emeritus
Units units units. If you add one kg of water or one kg of ice to a pool of water, the level rise is the same. But one kg of ice needs more gallons (volume) than a kg of water. That is why ice floats instead of sinking.

DrStupid
As it seems we lost the OP it doesn't hurt if I post my solution for the case that X is known (and neglecting the change of water density due to cooling):

$\Delta h = \frac{{V_{ice} \cdot \rho _{ice} }}{{A_{pool} \cdot \rho _{water} }} - X$

philip porhammer
NICE! that's what I thought! only Ice that is grounded will effect the sea level. thanks
Philip

Mentor
NICE! that's what I thought! only Ice that is grounded will effect the sea level. thanks
Philip
That is correct, although it is an interesting exercise to calculate how much the sea level would rise if
A) all the Greenland ice cap were to completely melt
B) all the Antarctic ice cap were to completely melt

Gold Member
At the rate they're going we won't have to wait long before calculation is obsolete - superceded by observation...

Klystron
Staff Emeritus
Gold Member
NICE! that's what I thought! only Ice that is grounded will effect the sea level. thanks
Philip
Well, not quite. Much of the floating sea ice is fresh water ice. Sea water is denser than fresh water. Ergo, the volume of fresh water produced by the melting ice will be a slight bit larger than the volume of sea water that it displaced. It's a small effect, but an effect none the less.

Gold Member
Well, not quite. Much of the floating sea ice is fresh water ice. Sea water is denser than fresh water. Ergo, the volume of fresh water produced by the melting ice will be a slight bit larger than the volume of sea water that it displaced. It's a small effect, but an effect none the less.
True. I was thinking of mentioning that, but decided it would just confound the central question.

Kevin the Crackpot
I would have thought that the water level won't change at all.

Ice is less dense than water (very few substances are less dense as a solid rather than a liquid). That's why an iceberg only shows ten percent or so above water, and the other 90% is under water.

When the ice melts, the water perfectly occupies the 90% under water that was originally occupied by the iceberg, so no change in water level.

Staff Emeritus
Gold Member
I would have thought that the water level won't change at all.

Ice is less dense than water (very few substances are less dense as a solid rather than a liquid). That's why an iceberg only shows ten percent or so above water, and the other 90% is under water.

When the ice melts, the water perfectly occupies the 90% under water that was originally occupied by the iceberg, so no change in water level.
That's true if it is fresh water ice floating in fresh water. But fresh water ice floating in salt water is a different case because salt water is denser than fresh water. ( one way to look at it is that the fresh water iceberg floats a bit higher in salt water than it does in fresh water, so a little less than 90% of it will be underwater, but it still produces the same volume of water when it melts.

Kevin the Crackpot
Michaela SJ
That is correct, although it is an interesting exercise to calculate how much the sea level would rise if
A) all the Greenland ice cap were to completely melt
B) all the Antarctic ice cap were to completely melt
This is from the page referenced below:
If the Greenland Ice Sheet melted, scientists estimate that sea level would rise about 6 meters (20 feet). If the Antarctic Ice Sheet melted, sea level would rise by about 60 meters (200 feet).
https://nsidc.org/cryosphere/quickfacts/icesheets.html
A lot. It is interesting to note that in the region of Central American, there are caves under water greater than 60 meters where bones, including human bones have been found. This is the effect of the various ice ages reducing the sea level. It should hold that if all of the current ice were to vanish, the sea levels would rise, and dramatically.
As real estate developer I had to take into account sea level rise and the impact that would have on a proposed community. It is a reality that must not be ignored.

Homework Helper
How much difference in sea level would occur due to a temperature change in the water? I assume a small change for say a change of 1 degree Celsius.