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

• philip porhammer
In summary, when an iceberg melts, the water level in the pool goes up by the amount of the ice that melted. If all the ice in an iceberg melted, the water level in the pool would go up by 20 feet.
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?

philip porhammer said:
if I have a pool that is 20x20 surface area

Units?

philip porhammer said:
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?)

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

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?

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.

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):

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

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

philip porhammer said:
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

At the rate they're going we won't have to wait long before calculation is obsolete - superceded by observation...

Klystron
philip porhammer said:
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.

Janus said:
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.

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.

Kevin the Crackpot said:
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
Nugatory said:
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.

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.

## 1. How will the melting ice affect the water level in a pool?

As the ice melts, the water level in the pool will increase. This is because the ice takes up more space in its solid form than it does in its liquid form. So as it melts, it will take up less space and cause the water level to rise.

## 2. Will the water level continue to rise as more ice melts?

Yes, the water level will continue to rise as long as there is still ice melting in the pool. Once all the ice has melted, the water level will stabilize.

## 3. Is there a certain amount of ice that will cause a noticeable change in the water level?

The amount of ice needed to cause a noticeable change in the water level will depend on the size of the pool. Generally, the larger the pool, the more ice will be needed to see a significant change in the water level.

## 4. Will the water level decrease once the ice has melted completely?

No, the water level will not decrease once the ice has melted completely. The water level may decrease slightly due to evaporation, but it will not decrease significantly.

## 5. How long will it take for the ice to melt and the water level to stabilize?

The time it takes for the ice to melt and the water level to stabilize will depend on several factors such as the temperature of the pool, the amount of ice, and the size of the pool. Generally, it can take a few hours to a day for the ice to melt completely and for the water level to stabilize.

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