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Let's pretend the lithosphere of Earth were smoothed somehow to fit a perfect geoid and maintained in this shape; all the water would turn into a uniform layer flowing over the ground.

According to wikipedia, sea water volume is 1.332$\times$109 km3, and this is 97.5% of all the hydrosphere waters, which gives us 1.366$\times$109 km3 of water total. Total Earth volume is estimated as 1.08321$\times$1012 km3.

If my calculations (hopefully) are correct, thickness of the water layer should be ~3 km.

I'm just curious about two things:

  • Will any piece of ground ever be exposed over the water surface even for a short periods of time due to internal or external forces, such as moon gravity, centrifugal force or for any other reason?

  • Will the mean temperature on a surface of this weird world be the same as a current mean surface temperature (288 K)?

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  • $\begingroup$ the centrifugal bit would depend on whether you make the actual planet a perfect sphere (in which case I guess the rotation would mean more water around the equator than at the poles, though I don't want to do the math to see how much more^^) or flatten the whole thing so much that it evens out... which would likely be the more natural shape, if you want the shape to have come about through natural-ish means $\endgroup$ – Syndic Jun 14 '16 at 11:33
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Will any piece of ground ever be exposed over the water surface even for a short periods of time due to internal or external forces, such as moon gravity, centrifugal force or for any other reason?

Currently, the greatest tidal ranges, of about 16 meters, occur in the Bay of Fundy. Why is this the case? Resonance is apparently created by an alignment of the shape of the bay and the Moon, which happens in very few places (see also this paper). Without the coastline to interact with the water, the tides wouldn't be nearly so drastic.

In your world, you would need tidal ranges roughly 187.5 times greater - actually, double that, since the depth of three kilometers is presumably from the mean water level. With no land above water, you won't see any tides nearly as significant.

Will the mean temperature on a surface of this weird world be the same as a current mean surface temperature (288 K)?

No. The effective temperature - without accounting for greenhouse gases - will be different, because the albedo would be different. That Wikipedia page says (citing this paper) that temperatures would rise 27 °C if the world was covered with water, as in your case. That's likely too hot for life.

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  • $\begingroup$ that's for you What Physics Teachers Get Wrong About Tides! | Space Time | PBS Digital Studios use with care $\endgroup$ – MolbOrg Jun 14 '16 at 18:37
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    $\begingroup$ @MolbOrg interesting watch. I did not know that, or at least never heard that approach. But whether the tides are a consequence of a "stretch" along the Moon-Earth axis or essentially a side-way compression starting from a perpendicular line is not really relevant here, is it? $\endgroup$ – bilbo_pingouin Jun 14 '16 at 20:18
  • $\begingroup$ Relevant here, hm. Hard question. What cough my eye, reference to 16m tides. May it be bigger in dynamic system where earth covered with water and no obstacle. Big big wave maybe (too fast but) 100 meter tall. One point of video is that, it is a way for amplification, like Hydraulic ram. Stretching is sorta static representation, of system which is't static, and tide itselfs is result of dynamics of that system. As Q is't reality-check, I do not mess, but I think that system is't stable. But if it is as given, do I believe effects are more the 3km, No. Would I like to know, yes definitely. $\endgroup$ – MolbOrg Jun 14 '16 at 23:37
  • $\begingroup$ The change in temparature would probably impact climate a bit[citation needed]. Evaporation would rise. Do you think the impact of that would be significant? $\endgroup$ – PatJ Jun 15 '16 at 1:48
  • $\begingroup$ @PatJ You know, I'm not really sure. Given that water's a greenhouse gas, it should contribute to radiative forcing and raise temperatures a bit. Reading the paper's abstract, it seems that the 27 degree change already takes that into account. You could have some sort of runaway greenhouse cycle, but I'm doubtful that the effects would be that drastic. $\endgroup$ – HDE 226868 Jun 15 '16 at 1:54
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  • Will any piece of ground ever be exposed over the water surface even for a short periods of time due to internal or external forces, such as moon gravity, centrifugal force or for any other reason?

tldr
Add more water if you wish water covered planet. Poles although, may be like it is now, icy and solid surface where live some creatures.

Yes.

Yes, it will(may and will over geological time), for that other reason.

I'll recommend to watch 2 videos:

They are not strongly related to answer and question, but it builds overview on topic, and maybe some moments are related.

Why and Which reason?

There is a picture for you to guess: Sahara Desert, rippled sand dunes with Blue sky Sahara Desert, rippled sand dunes with Blue sky

System with is described by OP Q is not stable. At begin, Earth may be perfect geoid, mass of crust is even distributed, magma is consistent, evenly heated(no density changes from temperature), equal salty(or not), etc etc. That everything will not change the fact, it will get those ripples over time, but it may affect time needed for that.

Origin of water on Earth

  • Comets, trans-Neptunian objects or water-rich meteoroids (protoplanets) from the outer reaches of the asteroid belt colliding with Earth may have brought water to the world's oceans.
  • Gradual leakage of water stored in hydrate minerals of Earth's rocks could have formed a portion of its water.

Important moment for any earth-like planet, both of that sources internal and external adding imperfections to planet mass distribution, crust strength, craters, etc.

Tides means water movement, not imaginable movements like waves in ocean or sound waves, but real flow of water, which drags materials. That water flows will be different in different parts of earth just because geometry of earth and forces involved. Let say virtual poles in plain of moon orbit - there are slower water flows, on equator (earth cut of moon orbit plane) it will be faster.

That difference may be important, but also it may have some strange effects too, take look at Saturn's hexagon which may affect material movements on bottom.
I'm not capable to say how fast will be such flows, I'm curios by my self.

Reason

Bald earth, I mean with flat surface and water on it - is not stable system.
Water, like wind in desert, will form same ripples on bottom, and more ripples there are, more and faster will they grow and form new ones. That will lead to imperfection on earth crust, because of mass of sedimentation layer, because of they do actually have viscosity - it will compress solidify, as any sedimentary rocks do(all that stuff). It will affect crust it will be thinner ticker, crust weight will affect's magma etc. Step by step there will be more and more imperfections - it will move as dynamic system to some sort of dynamically-chaotically equilibrium.

Water is more dense then air, so it will have more effects on earth upper layer.

Sahara

Many of its sand dunes reach over 180 meters (590 ft) in height.

So 3km tall plateau, why not. All that process will take place long before earth-like planet gets all that water, because magma also is a fluid actually(not solid at least).

Water will evaporate differently, more salty in some places, more cold, more dense etc. That affects forming Concretion with may affect differently erosion etc etc.

It so much things and complex stuff involved, so no one may say what it will be, except it will not be a bald earth geoid, just cant't happen. If you see that you may know it's artificial and fresh made, geologically speaking.

If there is already sand available, any material with small particles, some dunes may be formed pretty fast, depends on how much and which quality is surface material. 100-1000-10000 years will be enough I guess, if material is easy movable by water flows. There will be the limit, how tall they can be, as it is for the mountains.

(google) "deserts sand ripples" for science bro

Temperature

Very important factor will be established water movements flows and air flows. Air movements will affect water and will be affected by water (tides). If it will happens to be cloudy, and it may because of lack of big chunk of land, mountains specially, it may so happen to be more cloudy. So even water is't so reflective, but clouds have potentially high albedo and may regulate temperature.

As land not drain clouds I guess average temperature may be even less then now, it depends. One is sure, frozen water as result practically no clouds. Hmm but snow ice have also high albedo. So first is't sure, depends. But clouds forming, which is water evaporation, will have buffer effect, and may regulate temperature. What I wish to say, temperature is't just matter of albedo, but properties of water too - not so simple, simple assumption shall not pass here. Second is sure, temperature distribution will not be even, some places will be warmer some colder.

Just add more water for water world, 20km-30km layer of water for earth-mass planet, 100km for mars mass planet.

Example

Recall one example which I definitely wish to add here.

The Moving Island of Schiermonnikoog

  • Schiermonnikoog is a small island off the coast of the Netherlands that has been continuously moving to the south and the east, due to the combining effect of tidal current, prevailing wind and the sea. Just 762 years ago the island lay roughly 2 km to the north of its present position, and it had a significantly different shape. If you work out the math, that is 2.62 meters per year, on average.
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  • $\begingroup$ Do you think water flows probably can drag enough ground material to sculpt dry land from 3km depths even without tectonic shifts? $\endgroup$ – Diligent Key Presser Jun 15 '16 at 4:16
  • $\begingroup$ If it's enough material for that, then yes. Sand will weight 1/3 lesser then in air, water is 800 times denser so forces applied will be 10-100 times stronger, at todays big river speeds. I expect for established water currents to be faster then that. Entry ocean moving 2 times per day, without obstacles, all around the planet - it plenty of forces. Limits for mountains are 8-9km by height, so it easy may be 12km limits in water. So it depends on picture of currents and their movements, changes. Chemistry will also be a factor, live if it is also. But yes, current alone capable to form land. $\endgroup$ – MolbOrg Jun 15 '16 at 11:46
  • $\begingroup$ Thank you for bringing it up! I would never come to this concepts. $\endgroup$ – Diligent Key Presser Jun 15 '16 at 23:26
  • $\begingroup$ May the Force community be with you. $\endgroup$ – MolbOrg Jun 16 '16 at 1:43

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