Wow impressive!!

Back of the envelope on the amount of energy being pumped in to Earth via the portal: If we're talking 30*10^8 m³/s of water being raised from 11,000 m below sea level to 800 m above sea level, that's 3*10^12 kg/s of water being raised 11,800 m, or 3.5*10^17 Joules of power being introduced per second (by E=mgh). This compares to about 1.74*10^17 Joules per second for solar energy for the entire earth. "in the long run, the Earth might just heat up" indeed - you just added the equivalent of an additional two suns worth of energy input.

@rm Nice one, I'll do some of the math in a bit and see how much it heats up then.

geographically, this much water would turn the Mediterranean into another ocean, by connecting it to the red sea and most likely expand the straight of Gibraltar, correct?

@Reed The straight of Gibraltar is actually quite mountainous, so it might just flow around through Southern France, I'm not sure.

Add another sun equivalent of energy because the water is at a few hundred meters per second when it comes out of the portal.

You forgot to mention the effects of this temperature change on marine life, which would be to end it pretty quickly, which would be tragic, given how tasty much of that marine life is when paired with a butter sauce and a nice white wine.

@Swier: It won't be mountainous very long.

Water will surely heat up with it's kinetic and potential energy! (It reminds of old man Joule's experiment) so no time for ice age 😉😅

Will the river flow like Whataroughbeasts answer?

@R.M. and Swier, does the simple Torricelli's law hold when we're talking of velocities comparable to the thermal motion of water molecules and an appreciable fraction of the speed of sound in water?

@user7386 No it won't. It isn't a river, it's more like the entire African continent flooding.

@LLlAMnYP I'm guessing it won't, which is why I cut the throughput by a factor of 10 for the energy calculation. However, the temperature increase per water volume will remain constant as the overal height change remains the same.

@Swier right, I missed that. But, I suppose, a static flow should eventually be established and the exit velocity of the water will climb up to 400m/s, just not immediately.

"To add to this, warmer water evaporates more readily, and water vapor is also a very strong greenhouse gas." False water vapor would actually decrease earth's temperature although deserts make a pretty important job at reflecting the radiation from the sun so that would warm up earth.

@wannabeLearner Water vapor does not decrease or increase temperature in and of itself, it is just another gas in the atmosphere. It absorbs very considerably in the infrared, making it an excellent greenhouse gas. The albedo of deserts lies within the range of most terrestrial surfaces, albeit towards the upper limit; influencing that would be the least of concerns.

@LLlAMnYP never claimed it decreased by itself but in the long run would decrease the temperature. (Dry) Sand is at the 40% so it does reflect a bit more than good old mud.

wouldn't teleporting 100,000 cubic kilometers of water per hour for a long time also impact the planet's orbit? I imagine that the planet's mass and orbital speed dwarves that amount of momentum, but how long would it take for it to be noticeable?

Seems very strange to assume all the potential energy goes into heat. It would only be a fraction of it; a lot of it would be kinetic energy.

@wannabeLearner but in the long run would decrease the temperature. by what mechanism? Also not all deserts are the well-known hot sandy ones; the Sahara is only third by area after the two larger polar deserts, which also have even higher albedo. JMac, what will happen to all this kinetic energy when water hits the ground and comes to more or less a halt, compared to falling at 400m/s?

How about the marine animals that rely on that warm water? Do they all die off? (Do they get carried away with that water and shoved through the portal at such a fast rate that they're dead before they even hit the ground?)

@FlorianCastellane Assuming the portals are steady above a specific (rotating) point on the Earth's rotating surface: yes, something is going to happen to the Earth's rotation. The Sahara is at 23 degrees N, the Mariana Trench at 17 degrees N. The Sahara portal is about 200 km closer to the rotational axis, so a lot of mass will flow from the Sahara portal, away from the rotational axis towards the Mariana portal. This costs rotational energy so the Earth's rotation will slow down. I don't know if it has slowed down by much before all the water's gone.

@JMac in the long term, everything (including kinetic force) turns into heat. What this answer ignores however is that the flow steadily dimishes, because the water column immediately above the portal lowers as water is drained away. At first this is offset by water streaming in from the sides, but after a while there will be less than 11 Km water pressure (and a greatly reduced stream of water going through the portal). Other than that, great answer.

Also about the notion that earth could getting warmer: Most of the sunlight is absorbed into oceans. Land is much better at reflecting light. Therefore less ocean means less heat (ignoring the energy introduced by the portal).

What about the instantaneous drop in pressure? The water at the bottom of the trench is at or near 4C under tons of pressure and you're essentially letting it free expand. So, I'd at least expect it there to be a chance that some of it is no longer liquid when it hits the desert. Of course, this heats up the atmosphere faster, too, as the energy from the pressure loss has to go somewhere. Not to mention the salt content, too.

@rcollyer 80kJ per m3 due to low compressibility, compared to 160MJ kinetic energy per m3.

@antipattern the energy gain per volume of water flowing through the portal is constant, it is teleported up the same distance. Though later on most of this energy is converted to heat on the way from the Sahara to the Mariana Trench, rather than right after exiting the portal. As for the Earths average surface albedo, there will likely be more rather than less water surface on Earth as a considerable amount of landmass will be (and remain) flooded.

Something's way off. When you pull the bathplug, the water doesn't dump directly out, it finds its path and gurgles quite a lot. Plus, the backpressure from the ground and the already-transferred water at the output portal is going to limit the flow, almost exactly like a drain blocked with sand. I suspect you're ignoring the entirety of fluid dynamics, which would severely limit all the figures you're plugging in.

The noise will be absurd as well, the zanclear flood was only 2×108 m3/s of water and it would have been deafening. I should mention that you will not have much flooding after long, that much water will just carve a new seaway for all the water to travel down.

@Rich: Yeah, I don't agree with the flow rate calculation in the answer. Early on there's going to be backpressure, but since energy just keeps getting added, the speed just keeps increasing. And because the power is proportional to the flow rate, this is a differential equation with an exponential solution (it's not directly a first-order system because the flow is not proportional to kinetic energy but to its square root).

@Rich @ BenVoigt Yes, I don't think the 400m/s flow will be sustainable, that's why I just divided it by 10 for the energy calculation. I intend to figure out how to calculate this and then do the calculations as soon as I have the time.

@LLlAMnYP "The long run" i meant was if the only thing happening was the water evaporation not talking about the whole situation.

@Rich It does in fact "dump directly out". A back-of-the-envelope calculation using the very same formulas as in this answer gives an initial discharge rate of 2 liters per second. This is perfectly in line with observed draining times of a bath tub (roughly two-three minutes). The more I think about this, the more I convince myself that after some time a flow of 400m/s will be established.

Can we assume the expansive cooling of water coming from that depth is negligible? The pressure of that water is going to change by a factor of ~1000.

And after the earth turns into Venus will it attain some equilibrium with heat being absorbed and radiated out to be green again?

Once all liquid water has evaporated, this process of adding (heat) energy to the earth will presumably still continue, only now with compressed hot air moving through the portal.

This answer is small potatoes compared to the real cataclysm at hand. I doubt greenhouse gasses will have much of an effect on Earth's temperature after these portals open.

@16807 Yes, we can. Water doesn't compress very well. You can't apply ideal gas laws to liquids :) The massive difference in pressure only makes about 5% difference in density. The heat in a liquid doesn't depend much on the linear kinetic energy of individual molecules, unlike in a gas, so there's barely any expansive cooling even if you could drop density low enough (which you can't without turning the liquid into a gas, and while evaporation has a cooling effect on the ambient environment, the "now-gaseous molecules" have more energy than before - it adds up to zero).

@Swier. Thanks for the response. Second point: "The shortest path from the Saharan portal back to the Mariana Trench is through the Himalaya's, so my guess is the water will mainly flow through ..." Not so fast! The volume of water being shifted is starting to be on a planetary scale (the diameter of the portals is 0.7% that of Earth) so that would have a planetary-scale effect. Would the Poles shift? Even if not, would the flow be different? Wouldn't the flow actually go mainly westward?

@Rich the Trench is 10km deep, and the diameter is also 10km. If your bathtub has a 1-meter opening, there is not much gurgling :)

@antipattern @Swier as antipattern said the bath tub case, in which air tries to come out of same hole water hole is going in and this slowing down the draining, portal's diameter is 10km but area above it , is very vast. Does something like the bath tub case will happen in our case?