969: Delta-P

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Delta-P

Title text: If you fire a Portal gun through the door of the wardrobe, space and time knot together, which leads to a frustrated Aslan trying to impart Christian morality to the Space sphere.

Explanation

The Lion, the Witch and the Wardrobe is a book in which four children accidentally wander into a world known as Narnia through a wardrobe that only allows passage through to Narnia when you aren't looking for it. In the comic, someone connects an anchor to the wardrobe and throws it into the ocean. The formula describes the flow of water through the open doors when the wardrobe sits at the bottom of the ocean in 2 km depth, which means that a steady stream of water at an approximate velocity of 200 meters per second will flow into Narnia.

The evil White Witch, who has made it "always winter, and never Christmas," could not have anticipated that a wardrobe portal would suddenly begin spewing approximately 400,000 liters of water per second into Narnia.^{[citation needed]}

Sea water freezes at low temperatures and flowing water freezes at even lower temperatures, depending how fast it is going. Water jetting out from this portal would be flowing very quickly indeed, approximately 200 meters per second (450 mph or 720 km/h) as the comic says; this is over half the speed of sound. And the water flow is approximately 400,000 liters per second, again, provided in the image above. The force of this water jet would be incredible.

This water would not freeze. First it would devastate any forest trees or iron lamp posts in front of it until it eventually slowed down and fell to the ground. There it would create a rapidly expanding river of sea water. Narnia would not stay frozen for long. Snow would melt, ice would break apart and the valley would quickly flood.

Delta-P is a mathematical term for the difference in pressure. The Hagen–Poiseuille equation which can be applied to a flowing liquid in a long cylindrical pipe results in an unphysically high flow rate because the opening is rectangular and too short for a laminar flow. However' one can use Bernoull's principle to bound the flow velocity, even in the case of turbulent flow. The maximum flow rate is given by:

$Q_\max{} = \pi R^2 \sqrt\frac{2 \Delta P}{\rho}$

$\pi R^2$ is the pipe cross-sectional area (m²) and $\rho$ is the fluid density (kg/m³).

From the hydrostatics of water the pressure difference depends on gravity and the height:

$\Delta P = \rho g h,$

$g$ is the gravitational acceleration (m/s²) and $h$ is the height (m).

Putting this together and changing the cross-sectional area to a rectangular area $A$ we get the formula used by Randall:

$Q_\max{} = A \sqrt{2 g h}$

Assuming the wardrobe is two meter high and one in width (A = 2 m²) and using the gravitational constant g = 9.81 m/s² the flow rate is 396 m³ per second, or roughly 400,000 liters per second. The water jet velocity v is based on Torricelli's law:

$v=\sqrt{{2 g}{h}}$

It gives 198 ^m/_s in this scenario.

The title text references the video game Portal in which you solve puzzles using a gun which projects portals onto certain surfaces. In the game you cannot shoot a portal through a portal, but Randall says that if you try to create a portal with the portal gun through the wardrobe, space and time knot together. C. S. Lewis's The Chronicles of Narnia series (like most of his writing) is influenced by his views on Christianity and morality (he did not set out to write a "Christian story", but later accepted that there are many parallels between the Chronicles and his faith), with Aslan the lion representing Jesus Christ. As such, Aslan often provides lessons and advice on morality and faith to the main characters; however, the Space Sphere (a minor character in the game Portal 2) is a barely-sentient AI whose only preoccupation is going to space, and it would not be receptive to Aslan's teachings. The Space Sphere might be more interested in Lewis's The Space Trilogy, a trilogy of science-fiction books in which the main character travels through space and learns that the divine struggles between good and evil on Earth are also reflected elsewhere in the solar system.

Trivia

• In the dark fantasy light novel series Goblin Slayer (and its anime adaptation), the titular main character uses a portal scroll keyed to the bottom of the ocean to slay a powerful ogre with a water jet as described here.

Transcript

[An open wardrobe, with a boat anchor attached to one corner, falling towards water.]

[Below the water line a formula with its variables explained is shown:]

Q = A * sqrt(2 * g * d)

Q = flow rate

A = area of opening

d = ocean depth (2 km)

g = Earth gravity

[And below the formula:]

Flow: ~400,000 ^liters/_s

Water jet velocity: ~200 ^m/_s

[Caption below the frame:]

The White Witch didn't know what hit her.

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Discussion

First, it is worth noting that water jet velocity = (Q/A) = sqrt(2 * g * d). As such, it is not dependent on the opening size of the wardrobe. The figures given appear to assume the wardrobe is 2 square meters, which is probably fairly large.

Second, there is also the matter of momentum. The water mass is ~400,000 kg/sec, at ~200 m/sec, for a net of 80,000,000 kg meter/sec. If the receiving portal is subject to conservation momentum and is another wardrobe, it will be traveling at over 99% of the water jet speed. (The reduction would actually be less than the adjustment for the correct gravitational force.) So part of what the white queen would have to worry about is this wardrobe darting all over the place at ~700 km/hour or ~440 miles/hour. Of course, the sending wardrobe will be zipping around the ocean as well, which might make "Glass Half Empty" relevant. Divad27182 (talk) 15:39, 5 October 2012 (UTC)

Two wardrobes? 108.162.237.158 05:14, 20 June 2015 (UTC)

Well, the suction of the vacuum might increase the momentum of the wardrobe AND the jet.--Jimmy C (talk) 15:01, 12 November 2012 (UTC)

I have a feeling that the inconstant passage of time, between the two realms, should factor into this somehow. At the start, Lucy is in Narnia for a whole evening, and returns moments later. By the end the whole group stay for many years and are hardly away for much longer (while the 'tour' is still passing). So the amount of water that leaves Earth's oceans in a short time can probably afford to trickle out into the Lantern Wastes at a much lower volume/time. In reverse, would the passive thermal energy of Narnia (even during its snowbound period) over a long Narnian period now be exiting Earthside in a compressed form (if not in frequency, certainly in rate) making the open wardrobe door furnace, like? Or, given the above, and that nobody seems to notice any strange dilation effects during transition, and the fact that Edmund enters shortly after Lucy yet is not several days later in arriving (though possibly up to an hour or two) there may be a "time lock" facility, which means that one or more transitional areas betwixt Earth and Narnia are sealed shut behind one traveller while they start travelling further into (or out of) the furs/firs hybrid areas. We already know that the 'normal' wardrobe back can present itself at times when transit isn't required, so who knows whether it's an active compartmentalising, or just passively not wormholing betwixt the relevent domains.

And for my next essay, I shall be discussing how to automate the use of the rings made by the original Magician (the Professor's Uncle) in order to transfer spent nuclear waste to Charn, or some other, similar dead world. (And the security measures needed to ensure that Jadis does not obtain the necessary material to make radiologically-active weaponry in her conquests of other worlds brought into being by Aslan.) 178.105.230.21 16:24, 23 April 2013 (UTC)

Why do you suppose that so called Nuclear Waste needs drastic measures to deal with it? You should know by now that vested interests are making silly money out of merely collecting it. They don't need to even ensure it is kept safely if silly minions are so easily controlled by stupid initiatives.

If they had a pressing need to dispose of it carefully and immediately I am pretty sure that competent engineers could readily be found to ensure that they do so. Stop frightening yourself into believing you need to give rich people money. You don't. I used Google News BEFORE it was clickbait (talk) 20:04, 22 January 2015 (UTC)

After the loooong trip mentioned above, the owner of the wardrobe (the Magicians Nephew) explains that they should not expect to ever get back into Narnia again through the Wardrobe. It will of course only open for children, and not for anyone throwing it into the ocean or for anyone shooting a portal gun through the door. So nothing would be hitting the witch! ;-) Who by the way is dead at that time. Time passes in Narnia so it fits with what is needed for the children to be the right place at the right time. But nice spotted though that it would be a problem if the portal was indeed always open. However, if the door could be kept open and the witch was still alive... There is not a connecting wardrobe in Narnia, but just a forest - the fur skins in the wardrobe suddenly turns into threes. So there would be no wardrobe shooting around. Finally - if the earth oceans would be transferred to Narnia - the whole Narnia world would be flooded, and the heat capacity of the earths water would surely melt all snow and ice without freezing over, since new water would continue to flow through for a very long time. (See the What if - Drain the Oceans: http://what-if.xkcd.com/53/ )Kynde (talk) 19:26, 16 January 2014 (UTC)

The doors look ready to be surprised or in the process of so being. The anchor on the other hand is too smug for its own good. Suppose that the anchor is ripped off at impact and the doors slam shut. The flow rate is now dramatically altered. Isn't this what comics and magic is all about? I used Google News BEFORE it was clickbait (talk) 20:04, 22 January 2015 (UTC)

I did some minor reworking of the truck comparison. I think we should keep it to give people a sense of scale but can someone run a quick calculation to figure out how many tractor trailer trucks (with their trailers) going at a hundred miles per hour would approximately equal the force of the jet? Lackadaisical (talk) 20:18, 9 May 2016 (UTC)

Im surprised nobody mentioned that when the wardrobe gets deep enough it will be crushed into dust by the water pressure. 108.162.238.83 16:29, 14 September 2019 (UTC)

As long as the (open) wardrobe is facing upwards, there wouldn't be any significant water pressure.

Here is something interesting: GLaDOS states that the portals are "intradimensional holes", which means that you wouldn't be able to pair a blue portal in Narnia and an orange portal on the real world (or vice versa). All you would be able to do is get the water flowing into Narnia to somewhere else also inside Narnia. And if portal funneling is cannonical, you could capture almost all of the pressure and place it anywhere else in Narnia. 172.70.51.172 13:53, 5 July 2021 (UTC)

drain the oceans 162.158.42.63 18:59, 30 October 2024 (UTC)

hmmm. okay! Caliban (talk) 11:38, 18 November 2024 (UTC)