1) Planning to build my own in-ground pool and I was trying to calculate the pressure against each sidewall and the bottom of the pool.

-pool is 1.2m deep x 9.15m long x 6.1m wide

after doing some rough calculations I decided I'm going to need to be more accurate and also...

How the hell do those lawn pools hold so much water without those thin little plastic sidewalls just bursting open?

Ground helps.

The pressure is a function of depth only. Most above ground pools are only about 4 feet deep. Without doing the calculation, I can't imagine that this would be *THAT* much pressure. You would have quite a bit of force, but it's spread out over quite a bit of area.

How do you plan to build it? What will you use?

P=d*g*x (d density ie 1000kgr/m^3, g=9.81m/s^2, x= 1.2m ) (so say 0.11 Atm extra at the lowest point)

The force on each side will be like 1/2*d*g*x^2*L (L=9.15m side x the depth or height)

Will you use concrete and then tiles or what?

Maybe if you build around you need to use geometry like /| to support the increased pressure with depth.
The ground needs to be able to support 67 tons of weight over 56 m^2 area which is also a nontrivial stress so you must make sure the ground is very solid and cant start moving under the pressure. A human being standing on ground is half an atmosphere basically and the ground is not giving in at the location of the shoes but the forces are spread around eventually as you go inside the ground. But what happens if you collect 1000 people in that area all standing up (the equivalent of your pool in water over 56m^2 which is half a small medium apartment)? My point is the ground can potentially cave eventually and destroy the tiles etc. So you need to use proper construction not just trivial material with no care.

Yes the inside will be a layer of concrete and tiles... the outside will be cinder block backfilled. My plan was to dig a hole, fill it with 10cm of cement to make a solid foundation, build the walls of the pool, let the cement cure for about a week and then backfill it with dirt. Every 30cm or so I will compact the dirt behind the wall with a "jumping jack." Once the cinderblock wall is completely in-ground I will either tile the inside and use a plastic pool liner or use a type of stucco or plaster for the inside, seal it, and paint, tile, or whatever the inside for looks. Oh and I forgot to mention I will be putting some steel rebar rods about every 1 meter inside the cinder block holes to add strength. Apparently that is something standard with cinder block walls from what I understand by my initial research.

Here is a video that shows step by step of something very similar to what I want to do. I am fairly certain my methods will be strong enough but I thought I would try to calculate it out anyway.

SKIP TO ~2 min to see the pool.

I didn't know that. I figured depth would be by far the most important factor which is why I planned to make it only about 4 feet deep but I thought the rest of the geometry of the pool would matter as well. E.g. 4 foot deep hot tub would have less force against the sidewalls than a 4 foot deep pool. Thinking about it a little more it makes sense that it would't matter and I feel a bit sheepish now.

Does pressure increase arithmetically as you increase depth? For some reason I thought it would make a massive difference to add another foot or 2 of depth but maybe I am wrong on that also?

It looks like you're mixing two concepts. Pressure is the same, force is dependent upon the area. (F = P * A.) So a 4 foot deep hot tub will create less total force on the walls than a full pool.

Here's a thought experiment that might help to intuitively grasp the pressure idea. Suppose you fill your sink with water and you have a cookie sheet that fits vertically (upright) in the sink and is just the right size to essentially cut the sink into two parts (left side/right side). You should be able to imagine that no matter where you put the cookie sheet in the sink, that it's not being pushed to the side. If the total volume of water on one side or the other really increased the force on the pan, it should want to go to the side where there's less water.

So the only thing that matters is the depth when it comes to pressure and not the volume of water. But the force is dependent upon the area. Another thought experiment.

Imagine a rectangular box that's 1 foot wide by 5 feet wide that's full of water (and let's say one foot deep, but it doesn't matter). Now imagine the small side starts to come loose and you have to push against it to keep it in place. While you're holding it in place, someone else comes by and screws it in place. Now the 5 foot side starts to come loose. You should expect that you would have to push harder to keep the 5 foot side in place than you did the 1 foot side.

The pressure is linear with respect to depth. There will be more pressure at the bottom of the the pool, but it is simply proportional to the depth. The total force will be "much more" because force = pressure * area and since total area increases linearly with depth, the total force will ultimately end up being quadratic with respect to depth.

Indeed. I said, "pressure" but what I am really interested in is force because I want to make sure the walls are strong enough.

Yes this makes a lot of sense now.

Yes I was intuitively thinking this which was leaning me toward going for a 4 or 4.5 foot deep pool instead of 5 or 6 feet deep.

Sorry for being a time waster if you guys gave me all the info about pressure when I was looking for force. Hopefully my walls will hold up but if not maybe in a few months I can post pictures of a pool that can't hold water.