Hydrostatic Pressure Calculation (Pressure on tank walls)

Fuzzy Duck

Feeder Fish
MFK Member
Mar 7, 2009
62
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England
Here is a question for you all,
If you have a tank that internaly messures 1' Deep 2' Wide and 1' Front to back
What is the weight of water it will hold and what is the pressure on each side and the total pressure on the combined 4 sides?
Answers on a post card children
 

Jgray152

Feeder Fish
MFK Member
Dec 23, 2006
1,659
2
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NH
To get the total forward pressure, multiply the length * height * above result:

12 * 5 * 310 = 18600 lbs total pressure on front wall (and back since same dimensions.
Pressure is different the deeper you go. So I don't think you can find out an actual number to pounds of force that is exerted on the side glass. Let me know if I am wrong about that. I do believe below is accurate, let me know if I have made a mistake.

You are right about the pounds of water contained in a cubic foot.

Self Check

12" of water equals = .4329 PSI
Since we want the weight of water in 1 cubic foot, we want the weight at the bottom of the cube right? The area would be. 12 x 12
12*12 = 144sq/in

144*.4329 = 62.33 pounds of force.

Measurements

2.31 feet = 1PSI

Feet of water / 2.31 = PSI

If your tank is 39" deep. 39 / 12 = 3.25ft

3.25 / 2.31 = 1.41 PSI

Now at 39 inches is where you want to get the AREA of glass to calculate. In this case, the bottom glass. If you tank is 48" L x 18" W.

48 x 18 = 864 sq/in

864sqin * 1.41psi = 1218.24 pounds of force on the bottom glass. (This is how much all the water weighs in your tank, minus the tank its self.)

If you want to know the total pounds of pressure on the front/bottom glass seam, you can get an estimate by doing below.

48"L*1"H = 48 sq/in

1.41psi * 48sqin = 67.68 pounds of force..

There is an estimated .038 psi difference for every inch of depth of water.

You 5 foot tank.

5' / 2.31 = 2.16 PSI at the bottom of the tank.
So. L * W *2.16 = Total Pounds of Force at the bottom glass.

I don't know your total dimensions so...
72" * 24" = 1728 sq/in

1728 * 2.16 = 3732 pounds of force.
 

Jgray152

Feeder Fish
MFK Member
Dec 23, 2006
1,659
2
0
NH
Found your dimentions
12' x 8' x 5'


144"x98"= 14112 sq/in

2.16 * 14112 = 30481 Lbs at the bottom.

2000 lbs = 1 ton (roughly)
30481 / 2000 = 15.24 tons
 

islander671

Feeder Fish
MFK Member
Fuzzy Duck;2946047; said:
NolaPete answer the girl, She has 839 Lb of water in her tank so the pressure on one side is 839 Lb Yes or No??????
Islander the man says it dont matter about how deep your tank is front to back its just top to Btm and left to right so that would make your pressure on your front glass only 559.8 Lbs !!
Nola Pete yor answer please:)
LOL..Fuzzy duck im not a girl, but thank you?

The main reason i was looking for outward pressure is because im using a clamp rated at 1500lbs to keep my 72X18X16.5 tank from bowing (center brace is gone), and i was wondering if their was any formula to figure out if 1500lbs is enough to combat the outward pressure of water. So far, so good.
 

Jgray152

Feeder Fish
MFK Member
Dec 23, 2006
1,659
2
0
NH
She has 839 Lb of water in her tank so the pressure on one side is 839 Lb Yes or No??????
Nope. If the pound figure is correct, Islander would have 839 lbs at the bottom of her tank. Not the side glass.

Islander, the man says it dont matter about how deep your tank is FRONT to BACK, its just top to Btm and left to right so that would make your pressure on your front glass only 559.8 Lbs !!
Nola Pete yor answer please
The pressure comes from the DEPTH of water. Length and Width, Left, Right, none of that matters.

Left to right, is length or width, depends how your looking at it.

I made bold where you were right and underlined where you should start erasing. :)

The pressure exerted on the side glass panels vary with depth only. You need to figure out the pressure (PSI) to find out the total pounds (Force).

Length and Width matters when wanting to find the FORCE since you need to find out the surface's sqaure inch area AT the specific depth.
 

nolapete

Jack Dempsey
MFK Member
Jun 1, 2007
2,726
9
38
New Orleans, LA
Nolapete- You are correct about the hydrostatic paradox & basic hydraulics (uniform pressure on surfaces of a fluid-filled container).
My formula is from an engineer. You can calculate the weight of 1 cubic foot of water yourself.

12" x 12" x 12" = 1728 /
231 (1 US gallon) =
7.48 gallons in a cubic foot *
8.33 lbs. per gallon =
62.31

Show me my error if that's wrong.

I compared my results with the results on the hydrostatic paradox page by using 62 and 600 ft. and came up with 18.6 tons. They showed 18 tons, so evidently rounded, but close enough. I said 62 was approximate.

However, I have doubts about the number you used regarding the weight of a cubic foot (ft^3) of water. I'm not trying to call you out or anything, but I've seen this a few times on various fish forums, converting units of volume (ft^3) to weight and/or converting flow rates to water velocity, etc. Using straight volume, my software says 1 ft^3 of water is equal to 7.481 Gallons. If we use 8 lbs/Gallon of water weight,
According to my roommate who works for PSI, a construction testing firm, water weighs 8.33 lbs. per gallon. I used that number.

That said, we all know that total dissolved solids can increase or decrease the weight. It doesn't matter what weight you use, the formula still works. I could put 59 in and it would still come out very close to what I have.

I get 59.848 lbs. per ft^3. Seems like a small difference, but you have a really BIG tank, so it adds up quick. Where did you get your 62 lb/ft^3 number?
See above.

Obviously I cant take into account any chemicals/treatments, so if this is a measurement you took from your own water, disregard the lower weight. All that said, your order of operations is incorrect (parentheses first)
Isn't order of operations multiply/divide then add/subtract? I shouldn't need parentheses then.

& your final answer (18,600) is essentially the square footage of 310 of your tank sides,
No, 12 ft. long * 5 ft. high = 60
60 * 310 = 18600

Until you can grasp that front to back DOES NOT matter, you won't be able to understand this. That's why I posted the link to the hydrostatic paradox page (which isn't mine btw) to show you examples. The best on that page that explains it is the Lake Mead/Lake Mudd one.


or volume (in ft^3) of your tank if it were 310 ft. deep front to back.
See above.


In addition, shouldn't exerted pressure be in PSI?
You're right, but I wanted to keep it simpler, so I left it as a total. In reality, the forward thrust PSI at the bottom of the tank is higher than the forward thrust at the bottom of the tank. That gets way too complicated to explain.

You evidently know there's a lot of scientific measurements out there that us common people have a hard time grasping. I know I do. I won't begin to try to explain it to others.


I could be wrong, but I believe your equation should have been:
(62 lbs * 5 ft) * 12 ft = 3,720 lbs total forward pressure
Using my (slightly rounded) numbers, I get:
59.85 lbs * 5 ft = 299.25 lbs per vertical foot of glass (not sq.ft.)
299.25 lbs * 12 ft = 3,591 lbs total forward pressure
I'm not sure about this part, but with 10,368 sq.in. of glass per wall, that is only about .35 lbs/sq.in (psi) by my calcs & 1.79 psi by your calcs.
2.1527 psi @ 62 lbs

I won't try to figure out why and where your equation is wrong other than the fact that when foot is used as the measurement on

http://www.ajdesigner.com/phppipehydrostatic/external_hydrostatic_pressure_equation.php

with 62 lbs the result is

external hydrostatic pressure (PG) = 310 pound/foot^2
I'm no scientist, and I'm not 100% sure, so...Let the games begin!!!!!!
I'm not trying to be right, but I did ask my friend to ask his wife who is an engineer and that site is what she gave him to give me.
 

nolapete

Jack Dempsey
MFK Member
Jun 1, 2007
2,726
9
38
New Orleans, LA
In regard to side pressure, just substitute the measurements for the side in place of the one for the front. It doesn't matter which side you use, the calculation is the same.

If you used 6 * 1.5 for your front and your side is 1.5 * 1.5 use that in place of the 6 * 1.5. Understand?
 

nolapete

Jack Dempsey
MFK Member
Jun 1, 2007
2,726
9
38
New Orleans, LA
Also, whatever you call the pressure of the water against the front glass doesn't really change what it is. Whether it's in PSI or pounds of forward thrust, it's the same thing.

The two most important things about hydrostatic pressure is that it increases by the height of the container and it does NOT matter what the front to back or side to side dimensions are.
 
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