Calling all math gurus

[blaisetd]

I’m trying to figure out how much pressure the water in my pool is going to put on the walls. It’s a basic rectangle 304”x192”x54”. I spent a few hours this morning searching google for formulas and came up with some numbers. Just wanted to see what someone else comes up with for comparison. I figured the capacity was ~ 13644 gallons, 113,245 lbs of water or 56 tons of water. I came up with a pressure 280 lbs per sq ft or 1.94 PSI for the bottom. When computing the pressure on the upright side wall I came up with 6.89 PSI or 1002 lbs per sq ft on the long wall and 10.9 PSI or 1572 lbs per sq ft on short. I used a basic P=F/A for this part. Doesn’t seem correct with the wall pressure being so much higher than the bottom pressure. The reason for all this is I’m trying to determine what material to use for backfill for the walls. TIA blaise

 

[5-90]

My thoughts would be to take the total weight of the water for the bottom, and do the walls in "bands" - say, 6" to 1' wide.

Take the portion of water at that band and above, and use that to figure force.

Since I haven't taken too many engineering classes yet, I'd say to add 20-30% for "overage" and "fudge factor" once you've got the numbers crunched - also, to allow for shifts in force due to kids jumping in (cannonball!) &c.

HTH

5-90

 

[Skullver]

the formula for hydrostatic pressure is a function of depth(p=roeXgXh) where roe is the density of the fluid, g is gravitational constant and h is the depth of water(your pressure will be a triangular profile with 0 pressure at the surface and a max pressure at the bottom). from this pressure formula you can calculate a force and then apply that force to the center/middle of the wall and you can then estimate the avg pressure. hope this makes sense as it has been 5 or so years since I have thought about this.

 

[blaisetd]

More searchs and more grey hair. Figured i had the wall pressure wrong. It would seem logical that the water pressure at the bottom of the wall would be close to or equal to the pressure on the bottom surface (280 lbs per sq ft) and then gradually decrease moving toward the top of the wall. blaise

 

[rallyemore]

Lateral pressure is going to remain the same at varying depths. Vertical pressure will increase with depth.

 

[bj-666]

Lateral pressure is going to remain the same at varying depths. Vertical pressure will increase with depth.

please explain i find this very hard to beleive.

 

[8Mud]

I've been so long out of school I can't even recollect the formulas. I use rule of thumb. 10 meters of fluid doubles the pressure ( I usually figure 20 feet, which is 2/3 or so of 10 meters), in pretty much all directions. Any retaining wall over three feet, needs a double thickness. And any empty container, sunk in the ground needs to be full of something (or anchored), especially if the water table is high (ask me how I know this? :laugh3: ).
If the soil has a lot of organic material in it, forget it. If the back fill has some clay in it, compact it. If it's sand, mix some cement with it to fix it. If the retaining wall is over 3 feet (and single row), you can compact the fixed sand for extra strength. Which makes it kind of bullet proof. I've never worked much with fine or large gravel. You can also use lime to fix sand, it's often cheaper.
I usually fix sand at one to five, but have seen other guys use one to ten or even more. A little research would probably be in order, to save some work and materials. I usually over engineer everything.

 

[Dirk Pitt]

You are all complicating this way too much.

The pressure at any point in the pool (assuming plain water) is 62.4 lb/ft^3 * the depth at that point.

So if the pool is 4 ft deep the pressure (which will be exerted in all directions) is 62.4 * 4 = 249.6 lb/ft^2 or 1.73 lb/in^ (psig). To know the actual pressure you have to add atmospheric pressure which is 14.7 psi.

To get the pressure at any point in a column of water you multiply 62.4 by the depth in feet and divide by 144 to convert to psi. Add 14.7 for atmospheric pressure (14.7 psi) and you have it.

Pressure at 4 ft = 16.4 psia.

Pressure at 5 ft = 16.8 psia.

Pressure at 6 ft = 17.3 psia.

Pressure at 7 ft = 17.7 psia.

HTH

Also note that the diameter does not play a part in the calculation. If the pool is 4 ft in diameter, it's the same pressure at the bottom as a pool 100 ft in diameter (at the same depth).

In other words, throw away all measurements except depth, and multiply...

depth*62.4/144+14.7 = absolute pressure at that depth.

 

[8Mud]

0.1 atmoshere of pressure for every meter of rise (depth). Some ways the metric system is just so much easier. :laugh3:

 

[Dirk Pitt]

0.1 atmoshere of pressure for every meter of rise (depth). In almost every way the metric system is just so much easier. :laugh3:

FIXED.

Also can consider 0.4 psi for every ft. depth increase just to estimate.