How dangerous would a vertical water surface be?

Question

In my setting, there is an area that is usually filled with water at high tide and a land bridge at low tide. One day, a magical wall appeared that does not let water through, but does let through anything else. The shape of the wall is a vertical cylinder (with radius high enough that locally, it as well may be a vertical plane). The wall appeared during hight tide, so at low tide, there is now a vertical water surface.

1. What is the safest way to cross this wall for a human during low tide in each direction? I can imagine that if a human is partially submerged in the water, then the water pressure would only create force on one of his sides and thus might try to eject him rather forcefully.
2. How dangerous is it to cross in an "improper" way by a person who has no experience with this wall but is otherwise fit?

I figured when you would swim on the surface, you wouldn't be ejected sideways with a large force, but you will then fall form a really awkward position. On the other hand, trying to swim deep in the water will create a lot of sideways force but probably much more manageable fall. Still, you would be shot across the rough sea bed.

Things you can assume:

• The water at the border is about 10 feet deep.
• The floor is your average rocky beach, relatively lifeless, there aren't any large rocks but some of the smaller ones can be pointy.
• The people crossing it are a (relatively) weak high fantasy heroes in vaguely medieval setting (in fact, it's a low level DnD 5e party, but I am interested more in an real-world physics answer than a 5e mechanics answer, thats why I ask here. Assume Earth gravity, Earth-like salt water, regular physically fit human with no modern gear, also no other magic than whatever created the wall.)
• The wall behaves the way you'd expect it to without thinking too hard about it, eg. it lets through any liquid that is part of body of a living creature, and also the scenario where the hero gets hurt by a last drop of water that doesn't have anywhere to escape when it's pressed between the hero and the wall just doesn't happen. It also doesn't let through anything that is too small to be visible with a human eye (no pile of microbes/originally dissolved stuff right at the border) and the stuff that's dissolved in water doesn't sediment on it. At any time there aren't any major currents at either side of the wall, even if it would make sense for them to be present.

Answer 1

You can get past it using something very buoyant.

Have a hatch in the object that can be opened and closed from a ways away. Tie a rope to the object, preferably with knots in it to climb.

Take the object and throw it over the edge. Very quickly open the hatch and then close it after letting a small amount of water in.

The water will then prevent the buoyant object from being able to cross over, allowing you to climb the rope up to the other side. In order to hold your weight, the object would need to be large, meaning more than one person could sometimes be needed to get it over and then execute the process.

This diagram I made in ms paint should explain how it works. The reason a jug wouldn't work is that your weight would push it down and then you couldn't get up. The shown design is simplified.

The danger would not be excessive, it would push you away before you could get far enough in. That said, it would push you away (based on my rough assumptions and calculations) so you probably couldn’t just swim through it.

Answer 2

BUILD A RAMP OR SCAFFOLD AND LAUNCH A BOAT

10 feet isn't very deep. It would be a work of an hour or less to build a makeshift construction up the side of the wall. Then lift a boat to the top and put it in the water, where the side of the construction prevents it from slipping over the edge. Then board the boat and row or sail where you want. When you reach your destination (assuming it is still low tide), have two rowers keep the boat from the edge while the others climb down a rope. Then the last two can swim to the edge and jump down to be caught by the people on the ground, possibly in a big blanket.

The construction can be quite simple. You can use the buoyancy of the water to your advantage by building a wooden ladder or A-shaped structure and lean it on the edge of the water, perhaps propped up by inflated bladders. You may even be able to pull this up once you are in the boat and drag it with you to your destination for easy descent.

Lacking access to wood, you pile rocks to get you to the top. Lacking a boat, you could swim, possibly aided by swimming bladders or similar.

If this is a regular occurence, somebody could even have pulled a rope through the wall all the way to the destination. Then it is just a matter of pulling yourself through the wall by the rope. Away from the ends of the wall, this rope would float, propped up by air bladders or air-filled jugs or flasks.

Answer 3

So I ended up actually figuring out how to do the math and since it seems that people still sometimes stumble into this question, I will post it.

Lets assume the human body has the same density as water (mostly so we can disregard vertical forces and focus on the horizontal force). When a body of the same density as a liquid is submerged in said liquid, it doesn't move, meaning all the forces acting on it sum to zero.

Lets apply that to the part of the human that already passed through the wall. If it was in water, it wouldn't move, but there is a part of the water forces missing, which is exactly equal to the presure of water at given depth times the area of the cross section of the human that is just passing through the wall.

Now lets say our human has about $180\ cm$ and $80\ kg$ (and so about $0.08\ m^3$), working out to an average vertical cross section of about $0.044\ m^2$. Now pressure of water is about $10^4\ N/m^2$ per meter of depth, meaning the force acting on the human is about $440\ N$ per meter of depth. At the depth of 10 feet, that works out to about $1341\ N$, meaning a strong human might be able to push himself head first into the wall given good enough grips. On the other side, just walking into the wall is not possible since horizontal cross section area is clearly much larger.

Can you run through it though? Assuming there are no energy losses anywhere, you would need to have kinetic energy equal to the potential energy gained by the water you will displace. Again at a density of $1000\ kg/m^3$, that means: $$ \frac 12mv ^ 2 = m g h$$ Technically, the mass on right side is the mass of water and on the left side of the human, but with same density assumption, those cancel out. Plug in $g = 10$ and get $$ v = \sqrt{20h},$$

meaning at the depth of 10 feet, we get $7.8\ m/s \approx 28\ km/h$, which is about the top speed of a fit human runner, so this is an option as well.

Answer 4

Pull yourself towards an anchor

Tie a rope to something that will stay put, like a grappling hook or a literal nautical anchor, and throw the object directly through the wall as hard as you can. Then pull yourself through the water barrier, hand over hand.

A dense metal object should have no problem displacing enough water. And it doesn't have to penetrate more than a few feet, because the rope's help is only needed by a person as they pull themselves through the barrier; once they are completely across the barrier, they will have displaced their own volume of water, and the forces around them will be equalized.

Children are strong enough to swim down 10 feet, so pulling oneself in should be pretty easy, and swimming upward is even easier because people are generally buoyant.

If the group needs to traverse the magically-retained body of water, they will want some kind of vessel. It should be easy to push a canoe or kayak through the barrier, but getting it to the surface will be trickier, because boats are not buoyant when submerged. But in ~10' of water, a couple decent swimmers should be able to swim down from the surface, raise the boat, and drain it.

Ropes, grappling hooks, and nautical anchors are generally not hard to come by in a quasi-medieval setting; an adventuring party is extremely likely to have the rope & hook, and any settlement near the shore is likely to have some kind of water-based industry (e.g. fishermen), or even a marina with real ships (and their anchors).

If hooks and anchors are unavailable, you could use one or two saw horses that are weighted down with rocks, straddling the barrier.